Ruud A De Mooij

Bas Jacobs
email: b.jacobs@few.eur.nl

Kees Folmer
email: c.folmer@cpb.nl

Ruud Mooij

Cpb Jacobs

Flat Income Taxation, Redistribution and Labour Market Performance

Keywords: Flat tax, Labour market, General equilibrium, Equity, Optimal taxation Flat tax, Labour market, General equilibrium, Equity, Optimal taxation. JEL classification: D3, D5, H2

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Introduction

The flat tax has considerable appeal to many. In the Moreover, they are generally perceived to be efficient in creating better incentives than the progressive tax structures that currently prevail in Western economies.

Flat tax reforms have gained further ground since a number of Central and Eastern European countries have introduced them over the past decade. In particular, Estonia and Lithuania introduced a flat tax in 1994 with rates of 26% and 33%, respectively. In 1995, Latvia followed with a flat rate of 25%. Nowadays, Georgia (12%), Russia and Ukraine (13%), Serbia (14%), Romania (16%) and Slovakia (19%) have all introduced flat income taxes. In some of these countries, the introduction of the flat tax has come along with a rise in tax revenues and a boost in economic growth. It feeds perceptions about the favourable economic implications of flat-tax reforms.

Yet, the economic effects of flat tax reforms have hardly been studied rigorously [START_REF] Keen | The 'flat tax(es)': Principles and experience[END_REF]). An exception is perhaps the Russian flat tax, which was analysed in more detail by [START_REF] Ivanova | The Russian Flat Tax Reform[END_REF]. They conclude that there is no evidence for strong positive revenue or economic effects of the Russian flat tax reform. It appears that the simultaneous improvements in administration and compliance have been responsible for the surge in tax revenues. The Russian experience thus teaches us little about the economic effects of the flat tax reform itself.

It teaches even less about the economic effects of a flat tax in Western Europe, where countries have very different economic and social structures. How would flat tax reforms affect economies in these grown-up welfare states?

Since there is no Western European country that has a flat tax, its likely consequences need to be assessed on the basis of either economic theory and/or model simulations. This is the purpose of this paper. In particular, we first discuss the lessons from the literature on optimal income taxation regarding the optimality of a linear income tax. The optimal tax models, however, are very stylized and usually do not apply actual data. We therefore supplement the theoretical insights with simulations using an applied general equilibrium model. The model is empirically grounded in Dutch data and encompasses decisions on hours worked, labour force participation, skill formation, wage bargaining between unions and firms, and a wide variety of institutional details. Moreover, the model distinguishes a large number of household types and employs micro data to calibrate the income distribution for each of these types. With the model, we explore the consequences of three flat tax reforms for the income distribution and the labour market: (i) a proportional flat income tax of 29% where the general tax credit is abolished; (ii) a flat tax of 38% where the general tax credit is unchanged as compared to the current situation; (iii) a flat tax of 43% that allows for an increase in the general tax credit so as to keep our aggregate inequality index (the Theil coefficient) at the same level as before the reform. The latter choice follows the methodology adopted by [START_REF] Davies | Flat rate taxes and inequality measurement[END_REF].

Our simulations reveal that a flat tax reform can improve labour market performance in the Netherlands, but only if larger income inequality is tolerated. If income inequality is contained through a higher general tax credit, a flat income tax harms labour market performance. This result is reminiscent of the optimal tax literature, showing that linear tax systems with a general tax credit are less efficient than non-linear tax systems to achieve a certain degree of income equality.

Note that the flat analyzed in this paper differs from the one proposed by [START_REF] Hall | Low Tax, Simple Tax, Flat Tax[END_REF]. Similar to our case, their proposal contains a single tax rate on all labour income, combined with a fixed tax credit to render the system progressive. In addition to that, their flat tax applies also to income from interest, the return to equity and profits. In particular, investment is fully tax deductible for corporations so that the system effectively boils down to a cash-flow tax. Interest and dividends are not tax deductible at the firm level so it also resembles a comprehensive business income tax. In this paper, we pay no attention to this second component of the Hall-Rabushka flat tax, i.e. the taxation of capital income.

The rest of this paper is organized as follows. In section 2, we discuss the flat tax in the context of the theory of optimal income taxation. Section 3 explains the model that is used to explore the labour market implications of our tax reforms. Section 4 presents the analysis of two flat tax reforms in the Netherlands. Section 5 elaborates on other arguments for a flat tax, which cannot be assessed with the model. Finally, section 6 concludes.

Optimal income taxation

The Dutch government aims at reducing inequality. To that end, it uses progressive taxation, social benefits and tax credits that either or not depend on earned income. This redistribution of income does not come free. Indeed, income taxes reduce the price of leisure and household production relative to consumption, thereby inducing substitution away from labour supply towards untaxed activities. This reduces welfare in the presence of an income tax since the value of extra production from additional labour exceeds the social costs from foregone leisure.

The government thus faces a trade-off between equity and efficiency.

In light of this trade-off between equity and efficiency, the question is how the government can obtain the best combinations between them. Following the seminal contribution by [START_REF] Mirrlees | An Exploration in the Theory of Optimum Income Taxation[END_REF], the literature on optimal taxation has derived the optimal structure of the income tax in the presence of equity concerns and labour-supply distortions. It reveals that the optimal marginal tax schedule depends on four factors. First, there are two factors that determine the benefits from redistribution, namely (i) pre-tax income inequality and (ii) social preference for redistribution. If pre-tax inequality is large and society features much aversion against incomes. The elasticity of labour supply determines the classical distortionary impact of marginal tax rates on the consumption/leisure choice. The larger is the elasticity, the bigger is the distortionary impact of redistributive taxation and the less redistribution is optimal.

Moreover, the optimal tax depends on the population density at various margins. If density is higher at some point in the income distribution, a marginal tax creates larger aggregate distortions so that the optimal tax rate is lower.

The optimal-tax literature reports a variety of results with respect to the optimal marginal tax schedule. In general, these findings can be understood by the variation in assumptions on the above factors. [START_REF] Mirrlees | An Exploration in the Theory of Optimum Income Taxation[END_REF] simulates the optimal marginal tax schedule for a utilitarian social welfare function, Cobb-Douglas preferences in consumption and leisure, and a lognormal distribution of abilities. He concludes that "… the most striking feature of the results is the closeness to linearity of the optimal tax schedules" (p.206). Subsequent contributions have raised doubts on this optimality of the linear income tax schedule. Tuomala (1990) finds that the optimal marginal tax schedule is sensitive to the underlying assumptions. In fact, the optimal structure is non-linear if social welfare functions feature relatively high inequality aversion and if labour supply responses are different between agents. The non-linear structure is more efficient because it employs more information on individual earnings so that it can achieve the same redistribution with less dead weight loss.

The older simulations in the literature typically found hump-shaped optimal tax schedules where marginal tax rates are generally declining with income over a wide range (cf. Tuomala, 1990). These simulations used bounded, synthetic log-normal distributions for skills and CESutility functions with elasticities of substitution smaller than one, such that labour supply curves are backward bending at zero non-labour income. These features are less attractive from an empirical point of view. Actual income distributions are not bounded and appear to look more like the Pareto distribution especially near the top. The Pareto distribution eliminates the result of a zero marginal tax at the top as well, see [START_REF] Diamond | Optimal Income Taxation: an Example with a U-shaped Pattern of Optimal Marginal Tax rates[END_REF]. And, labour supply generally features a non-negative uncompensated wage elasticity of labour supply, which rules out the backward bending labour supply curve.

More recently, [START_REF] Diamond | Optimal Income Taxation: an Example with a U-shaped Pattern of Optimal Marginal Tax rates[END_REF] and [START_REF] Saez | Using Elasticities to Derive Optimal Income Tax Rates[END_REF] have used empirical pre-tax income distributions for the United States and a uniform positive labour supply elasticity to show that the optimal marginal tax structure typically features a U-shaped pattern: high at the bottom and top of the distribution and low for middle incomes. This result is driven by population densities.

Intuitively, a negative average tax for the poor is necessary to redistribute income. It should be phased out with income in a range where the population density is not so high. In the United States, this is just above the minimum income. Beyond this level, the optimal marginal tax falls Most contributions to the literature thus suggest that a non-linear tax structure is more efficient than a linear structure, i.e. a flat tax. The reason is that the flat tax is informationally inferior to the non-linear tax because the government does not employ information on individual or household earnings under a linear income tax. With the same amount of dead weight loss, the non-linear tax structure redistributes more income than the linear income tax and vice versa [START_REF] Saez | Using Elasticities to Derive Optimal Income Tax Rates[END_REF].

Redistributive policies may also distort decision margins other than the marginal consumption/leisure choice. Examples are the extensive margin of labour supply, the search and acceptance behaviour of the unemployed, the schooling or training decision of workers, and wage demands in a unionized labour market. This may change the optimal tax results. For instance, [START_REF] Saez | Optimal Income Transfer Programs: Intensive versus Extensive Labor Supply Responses[END_REF] shows how participation distortions reduce the optimal marginal tax rates at the bottom of the income distribution to limit the distortions on job-search. Moreover, elasticities may vary with income, which further modifies the equity-efficiency trade-off.

Optimal tax models would become analytically intractable if they would include a large number of decision margins or a larger degree of heterogeneity in elasticities and empirical income distributions. A way to explore flat tax reforms in a more complex but also more realistic setting is, therefore, to adopt an applied simulation model that includes these aspects. This will be done in the next sections.

An applied framework for the Netherlands

This section presents our applied general equilibrium model -MIMIC -that is used to explore flat tax reforms in the Netherlands. 1 The model encompasses various decision margins, such as effects on labour supply, human capital formation and equilibrium unemployment. A distinctive feature of MIMIC is a disaggregated household model. The large number of household types, together with microdata for the income distribution, make that MIMIC is best described as a mix of a microsimulation model and a general equilibrium framework. The model pays due attention to the institutional details of the Dutch tax and social insurance systems, which makes it especially relevant for policy analysis.

Labour supply

MIMIC contains a disaggregated household model aimed at describing the impact of the taxbenefit system on labour supply and the income distribution. First, the model accounts for heterogeneity in various dimensions, including skill, cohabitation, the presence of children, Within each type, we make a further distinction with respect to discrete options for labour supply. For instance, primary earners can choose their optimal working time between the options 80%, 100% and 120% of a full-time equivalent. Secondary earners and singles face more options. Thereby, secondary earners in couples can opt for voluntary non-participation.

Empirical studies suggest that participation distortions are indeed relatively important for aggregate labour supply [START_REF] Blundell | Welfare-to-Work: Which Policies Work and Why?[END_REF]. The particular option an individual chooses is derived from utility maximisation, with consumption and leisure as arguments, subject to a household budget constraint. The preference for leisure is heterogeneous across agents. We use a uniform distribution of this preference parameter to calibrate the high share of part-time work of secondary earners and single persons in the Netherlands. Hence, part-timers feature a relatively high marginal utility of leisure. In determining labour supply of couples, we assume that each partner makes an individual decision, given an average income from his or her spouse.

In interpreting the labour supply responses to changes in prices and incomes, the traditional income and substitution effects are at work. Hence, if the marginal tax rate declines, labour supply increases on account of the substitution effect. A lower average tax exerts a positive income effect, which reduces labour supply. Based on a meta analysis of labour-supply elasticities by [START_REF] Evers | What Explains the Variation in Estimates of Labour Supply Elasticities?[END_REF], we set utility parameters such that the uncompensated laboursupply elasticity equals 0.5 for secondary earners, 0.1 for primary earners and 0.25 for singles.

Within each combination of household-hours type, we employ a wage distribution based on Dutch microdata. We distinguish 10 income classes for each group and base the density of each class on the data for 1992. The average wage levels in the model are updated on the basis of realised wage growth in the Netherlands until 2006. For each income class, we derive disposable income by applying the Dutch tax-benefit system to the gross incomes. The after-tax disposable incomes and the marginal tax burdens determine labour supply behaviour.

Labour demand

Labour demand for high-skilled and low-skilled workers is derived from firms that maximise profits subject to a CES production technology. The first-order conditions reveal that labour demand depends on the relative wage costs for the respective types of labour. Based on time series estimates for the Netherlands, the substitution elasticity between high-skilled and lowskilled workers is set at 1.15. The substitution elasticity between capital and labour is set at 0.25. Economic profits originate from monopolistic competition without free entry. Hence, firms set prices as a mark-up over marginal production costs. This setting allows for endogenous terms-of-trade effects. As the export elasticity is set at a high value of -5 for this small open economy, these effects are of minor importance for our simulations. In our model, it depends on unemployment benefits and an untaxed informal wage. The latter is modelled as a function of labour productivity and the price of consumption. Labour productivity is a proxy for the wage rate in the black market, while the price of consumption reflects the value of household production. This specification yields a non-linear wage equation in which several institutional variables enter. The non-linear equation has been estimated using Dutch time-series data (see [START_REF] Graafland | Taxes and Benefits in a Non-Linear Wage Equation[END_REF]. In linearised form and evaluated in the initial equilibrium of MIMIC, it reads as:

log W = log h+ 0.3 log RR -0.6 log(1-Ta) + 0.1 log(1-Tm) -0.1 log U
where W is the real producer wage and h stands for labour productivity. The positive coefficient for the replacement rate (RR) reflects larger bargaining power of the union if social benefits increase. Higher benefits thus raise wage demands. The elasticity of 0.1 for the unemployment rate (U) is consistent with a consensus estimate from empirical studies reported by [START_REF] Blanchflower | The Wage Curve Reloaded[END_REF]. The average tax rate enters the wage equation via (1-Ta).

This is because the untaxed informal wage is part of the outside option of the union. Higher average labour taxes therefore strengthen the relative bargaining position of the union and increase wage demands. The marginal tax rate enters the wage equation via (1-Tm). This term exerts a positive effect on wages. Hence, progressive income taxes mitigate labour-market imperfections. Intuitively, tax progression makes it less attractive for unions to bid for high wages because a larger share of wage claims is transferred to the government instead of the workers. Therefore, trade unions will reduce wage claims, thereby reducing involuntary unemployment (see e.g. [START_REF] Bovenberg | Effects of tax and benefit systems on wage formation and unemployment[END_REF]. Empirical evidence supports this effect of tax progression on wages for a number of countries and in particular for the Netherlands (Tyrvainen, 1995;Sørensen, 1997;[START_REF] Graafland | Taxes and Benefits in a Non-Linear Wage Equation[END_REF][START_REF] Ewijk | Efficient Progressive Taxes and Education Subsidies[END_REF]. Hence, while progressive taxes hurt welfare by reducing labour supply, participation and human capital, they can improve welfare by reducing equilibrium unemployment. Some degree of tax progression can therefore be efficient in an imperfect labour market. 2

2 MIMIC also contains a search-matching framework that further affects the labour-market and the impact of institutional changes. This part of the model is especially important for reforms that are very much targeted to specific groups in the labour market. As it is of minor importance for the flat tax reforms, we do not discuss this part of the model in great detail.

For a more detailed description, see [START_REF] Graafland | MIMICing Tax Policies and the Labour Market[END_REF].

Human capital

When human capital formation is endogenous, marginal income taxes not only affect the quantity of labour supply but also on its quality. 3 In MIMIC, the skill composition of the labour force is endogenous as people choose the amount of on-the-job training. In particular, after-tax wage differentials determine the incentive for agents to improve their skill. Larger wage dispersion encourages education and training and raises the share of skilled workers in the labour force. Based on empirical studies, the elasticity of skill premium is calibrated at 0.5, see e.g. [START_REF] Kuhry | Trends in Onderwijsdeelname[END_REF]. The costs of training are modelled as an effort cost.

Government

Government behaviour is exogenous in MIMIC. The model describes the most important details of the Dutch income tax system, including the rate structure and a number of tax credits and allowances. The structure in the personal income tax is summarized in Table 3.1. In 2006, it contains a general tax credit of almost 2 000 euro, an in-work tax credit with a maximum of 1 350 euro and a number of specific tax credits targeted to certain groups. While the tax system is in principle individualized, this does not apply to the general tax credit. In particular, nonparticipating partners in couples can transfer their credit to their working spouse. The various tax credits imply that employed people do not pay tax for at least the first 10 000 euro of their income. Beyond this level, a piecewise linear tax structure applies, with rates moving from 34.15% to 52%. The highest rate is paid on incomes above 52 000 euro. In analyzing (flat-tax) reforms with MIMIC, we consider equal-revenue changes (see also e.g. [START_REF] Bhattarai | Welfare impacts of equal-yield tax reforms in the UK economy[END_REF]. In particular, our flat-tax reforms are balanced-budget on an ex-ante basis, i.e.

3 [START_REF] Jacobs | Optimal Income Taxation with Endogenous Human Capital[END_REF] and [START_REF] Bovenberg | Redistribution and Education Subsidies are Siamese Twins[END_REF] show that optimal marginal income taxes are lowered when learning is taken into account. before the endogenous behavioural consequences are taken into account. Hence, tax revenue changes in response to adjustments in labour supply or unemployment do not feed back into additional changes in the income tax rate in our simulations. Instead, we assume that the government budget is closed ex-post by changes in public consumption. The ex-post impact on public consumption thus provides a measure for the tax revenue implications induced by behavioural responses to the reform. We prefer this approach to closing the government budget with the income tax rate ex-post because it allows us to distinguish between the effects of the reforms and the effects associated with endogenous feedback effects.

Note that MIMIC essentially is a comparative static analysis. Therefore, the effects of flattax reforms should be interpreted as the structural, long-term implications of the flat tax reforms.

Simulating a flat income tax

The analysis focuses on three flat-tax reforms in the Netherlands. They differ with respect to the tax rate and the general tax credit. In the first version, the general tax credit remains unchanged.

A flat tax rate of 38% is found to keep the government budget balanced in this case. In the second flat-tax reform, we increase the general tax credit by 1 400 euro and raise the flat tax rate to 43% to keep the government budget balanced. 4 The choice for this second reform is governed by its impact on our aggregate inequality index, the Theil coefficient. It is an indicator that equals 0 if all N persons have the same income and reaches a maximum of ln(N) if all income accrues to one person. The Theil coefficient remains unaffected by this reform. In a third flat-tax reform, a 29% flat tax goes along with an abolishment of the general tax credit.

This transforms the Dutch income tax into a proportional system -although the in-work tax credit is unchanged and means-tested benefits remain in place. 5 In presenting the results of our analysis, we concentrate on the income distribution and the labour market (compare e.g. [START_REF] Castañer | Evaluating social welfare and redistributive effects of Spanish personal income tax reform[END_REF]. We present the ex-ante effects on the income distribution, showing scatter plots based on micro simulations for 40,000 Dutch households. The labour-market effects of the flat tax reforms are obtained from simulations with the MIMIC model. 4 We increase the tax credit only for people with a positive income, not for non-participating partners. This avoids overcompensation of single earner couples. In the simulations, we assume that there is no problem associated with take up of the credit, e.g. because the tax bill becomes negative. Hence, the credit can be interpreted as a payable transfer, i.e. a negative income tax. In both reforms, we maintain the reduced rate in the first two brackets for the elderly above 65. Hence, the tax structure for the elderly is not flat. 5 If the public budget would be closed ex-post by changes in tax rates, endogenous revenues effects associated with behavioural responses would feed back into changes in the tax rate. In that case, we would arrive at flat tax rates of, respectively, 37%, 43.5% and 26%. The economic effects will then be reinforced by this extra change in tax rates. each point in the scatter represents one household. We see that the reform is especially harmful to people with low incomes, which is due to the rise of the tax rate in the first bracket from 34% to 38%. The reduction in income is about 3.5% for couples with an income of around 25 000 euro and for singles below this level of income. Singles and one-earner couples with a median income of 29 500 euro also lose, but to a lesser degree than the lowest incomes. For incomes of around 31 000 euro, the reduction in the marginal rate in the second tax bracket more or less outweighs the impact of the higher rate in the first bracket, i.e. this is the break even point.

People relying on government assistance generally lose as they typically collect lower incomes than employees. People with high incomes gain, up to 10 to 12% for the highest income groups among working singles and couples. The figures suggest that these benefits accelerate at around 55 000 euro, which is where the top marginal income tax rate of 52% in the current system starts to apply. Overall, the flat tax reform is found to redistribute income from low to high incomes. The aggregate Theil measure rises by 6.4 percent.

With the 43% flat-tax reform, the higher general tax credit of 1 400 euro favours especially low income groups; the higher tax rate of 43% hurts especially people collecting high incomes.

Therefore, the 43% flat-tax reform yields smaller distributional effects than the first. This is shown in Figure 4.2. We see that people earning low incomes generally lose only little from the reform (one-earner couples) or even gain (singles and two-earner couples). For these people the higher credit more than compensates for the increase in the flat tax rate. For very high income levels, the reduction in the marginal tax from 52 to 43% still reduces the tax burden on a major share of their income. Hence, these people gain, although less than under the 38% flat-tax reform. Again, we observe that the income gains start to accelerate at around 55 000 euro, i.e.

where the 52% top marginal tax rate starts. The middle income groups typically lose as the rise in the tax rate to 43% applies to the lion share of their income. The higher tax credit only partially compensates for this. Therefore, the 43% flat-tax reform redistributes the tax burden from very low and very high incomes towards the middle groups. We thus observe a U-shape pattern for the income effects in Figure 4.2. By construction of the reform, the aggregate Theil coefficient does not change compared to the current system. Hence, overall inequality is broadly unchanged. as the income effects are considerably larger. Indeed, the effects range between plus and minus 25%. The pattern is very similar to the 38% flat tax though: the lower income groups lose considerably while the higher income groups gain considerably. The break-even point is somewhere around 25 000 for singles and between 40 000 and 55 000 euro for couples. 4.1 shows the labour market effects of three flat tax reforms. With the 38% flat-tax reform, the first column of Table 4.1 shows that the marginal tax rate falls by 2.9% on average across individuals. 6 This lower marginal tax increases labour supply incentives due to substitution from leisure to consumption. Overall, labour supply expands by 0.9%. The increase in hours worked does not apply to all individuals, however. On the one hand, most primary earners and single persons face lower marginal tax rates as they are taxed at the margin in the higher tax brackets. Hence, these groups raise hours worked. On the other hand, many secondary earners in couples hold part-time jobs where they are taxed at the margin in the first bracket. The increase in the tax rate from 34% to 38% in the first bracket discourages non- participating partners to occupy small part-time jobs. Accordingly, the female participation rate drops by 2%. Other partners increase their hours worked due to lower marginal tax rates in the higher tax brackets. This compensates for the lower participation rate so that the overall effect of the flat tax reform for the labour supply of partners is negligible. Lower marginal tax rates also encourage training by increasing income differences between skills. This raises the transition rate from low to high-skilled labour. The share of high-skilled labour supply is found to expand by 0.8%.

The equilibrium unemployment rate falls slightly. This is the result of two offsetting effects.

On the one hand, benefit recipients typically collect lower incomes than workers. Hence, the replacement rate falls. This increases job search and reduces the reservation wage in the searchmatching model. Moreover, it moderates wage claims in the bargaining model, where the lower replacement rate reduces the bargaining position of the workers due to a less attractive outside option. On the other hand, the lower marginal tax exerts upward pressure on wages in the bargaining model. On balance, the first effect dominates so that the unemployment rate falls by 0.1%. The effect is concentrated among the low-skilled where the replacement rate falls most. The favourable labour-market effects of the reform cause a broadening of the tax base so that tax revenues expand ex-post. This effect shows up in higher public consumption, which rises by 0.5% of GDP. Overall, we can conclude that the 38% flat-tax reform causes more inequality. At the same time, it reduces distortions in labour supply, training and unemployment. Hence, it illustrates the classical trade-off between equity and efficiency.

The second column of Table 4.1 shows the labour-market effects of the 43% flat-tax reform.

We see that aggregate labour supply distortions become larger, rather than smaller: labour supply falls by 0.3%. The reason is that the marginal tax burden is shifted from people at the bottom and top of the income distribution towards the middle incomes. On the one hand, the lower marginal tax at the bottom encourages non-working partners to participate in small parttime jobs. Moreover, high-skilled primary earners who face a lower marginal tax rate raise their hours worked. On the other hand, the higher marginal tax on middle incomes exerts negative effects on hours worked. This latter distortion is relatively large for two reasons. First, it affects the more densely populated group of middle incomes, which renders the distortions larger.

Second, it affects secondary earners and singles who feature larger elasticities than male breadwinners. Indeed, the simulations suggest a fall in labour supply of partners and singles of 0.1% and 1.1%, respectively. By construction, the 43% flat tax reform does not increase overall income inequality: the Theil coefficient does not change. Also the effects on human capital formation and the share of high-skilled labour supply are negligible. Due to the fall in hours worked, aggregate employment falls by 0.3%. Hence, while the 43% flat-tax reform avoids an increase in aggregate inequality, it fails to yield positive labour market effects. In fact, the reform comes along with negative effects on labour supply and employment. It suggests that the 43% flat tax achieves redistributive goals in a less efficient way than the current Dutch tax system. The third column of Table 4.1 shows the effects of the 29% flat-tax reform. It moves in opposite direction compared to the second column, i.e. it benefits the higher incomes who gain relatively much from the lower income tax rate, at the expense of lower incomes who currently benefit relatively much from the general tax credit. This reform thus further reduces the progression of the tax system and moves the income tax towards a proportional income tax. As a result, the inequality index rises sharply by more than 20%. At the same time, labour supply expands by 4%, and the share of high-skilled labour rises by 1.7% due to improved learning incentives. It shows the same equity-efficiency trade-off as in the first column of the table, but in a more extreme form.

The simulation results with MIMIC match with the insights from optimal tax literature. That literature suggests that a non-linear tax structure is typically more efficient than a linear (flat) tax system in reducing inequality because it better exploits information about the variation in income densities and elasticities. In fact, the general tax credit appears to be too crude an instrument to achieve the desirable degree of equality. In MIMIC, a flat tax fails to improve labour-market performance if income inequality is to be maintained. In the model, not only income densities and the variation in elasticities matter, but distortions are reinforced through endogenous human capital formation but mitigated by pre-existing distortions on the labour market.

Tax arbitrage and simplification

Flat tax proposals have also been motivated by other arguments than their labour-market implications. In this section, we discuss these arguments and explore whether they can validate the introduction of a flat tax.

Under a flat income tax, the government requires only information about aggregate labour income to determine tax liabilities. Indeed, there is no need for an individualised tax rate so that the tax can be levied simply as a payroll tax on employers. This may save on administrative and compliance costs. However, these savings on administrative costs evaporate if the government still needs to collect information on household or individual incomes for the determination of means-tested benefits, tax credits, subsidies or tax exemptions. Related to this is the argument of increased transparency of a flat tax for taxpayers. Also this ignores the income dependent schemes. In fact, the complexity and lack of transparency of the tax system is not caused by the rate structure, but by the determination of taxable income, which is complicated due to exemptions, deductions and credits to e.g. housing, pensions, schooling, children, cars, traveling costs, and the like. Removing these parts of the tax code can simplify the system and broaden the tax base considerably, but this is different from the adoption of a flat tax rate.

Another possible advantage of the flat tax is that it reduces tax arbitrage. For instance, the flat tax is neutral with respect to the division of lifetime income across years and thus reduces intertemporal tax arbitrage. However, the opportunities for intertemporal arbitrage are already mitigated as in the current system people have the option to divide their income equally across three subsequent years. Still, intertemporal arbitrage remains important as the Dutch tax system applies a tax rate that is 17.9%-points lower for people above 65 than for people below 65. This encourages postponement of income to the old age. Yet, this form of intertemporal arbitrage does not depend on the progressive tax structure, but on the low tax on elderly. There are also other forms of tax arbitrage, e.g. between corporate and personal income or between labour and capital income. As long as the flat tax applies only to labour income and different tax rates apply to different sources of income, these forms of arbitrage will not disappear, however.

Indeed, it would require an integrated approach along the lines of the Hall-Rabushka proposal for a flat tax, not just a flat rate on labour income, to alleviate this arbitrage.

A flat rate is also argued to be more neutral with respect to the division of labour between partners in a household. Rising marginal tax rates give excessive incentives to men to engage in household production compared to women --given that men earn more than women. Under a flat tax, in contrast, the marginal tax rate will be equal for both partners. This form of neutrality is, however, inefficient when differences in labour elasticities between men and women are taken into account. Indeed, Ramsey principles suggest that elastic tax bases should be taxed less than inelastic ones so that marginal tax rates for women should be lower than for men (Boskin and Sheshinsky, 1983). Accordingly, the government needs to trade off distortions in the division of labour within families and distortions in the labour market. A flat tax is sometimes said to reduce political opportunism, which arises due to special interests and lobby groups. This argument is flawed because not the rate structure serves special interest groups, but the myriad of exceptions, exemptions and deductions does. Changing the rate structure is not a targeted policy to serve the special interest groups, too costly in budgetary terms and completely transparent to the general public. A flat tax is therefore unlikely to fundamentally affect political distortions.

Conclusions

Should countries with a grown-up welfare state follow the example of Central and Eastern

European countries and adopt an income tax structure with a single, flat tax rate? This paper analyzes different versions of a flat tax in the Netherlands by looking at their effects on the income distribution and labour-market performance, using an applied general equilibrium model combined with a microsimulation model for households. We find that flat tax reforms have the potential to stimulate labour supply and reduce unemployment. For instance, a 29% flat tax with no general tax credit is found to raise aggregate employment by 5.3%. A less extreme 38% flat tax that leaves the general tax credit at its current level raises employment by 1.1%. Such proposals, however, come at the expense of more inequality. Thus, they illustrate the classical trade-off between equity and efficiency. If we construct a flat tax that does not affect aggregate income inequality, our simulations suggest that it will not alleviate labour market distortions. Instead, labour supply and employment will decline. The reason is that the flat tax shifts the marginal tax burden towards the densely populated middle groups and to partners and singles who feature relatively high elasticities of labour supply. For Western European countries that are unwilling to sacrifice in terms of equity, flat tax reforms are thus unlikely to improve efficiency.

  German electoral campaign of 2005, Paul Kirchhof of the Christian Democratic Party promoted the flat tax for Germany. In the Netherlands, proposals for a flat income tax have been suggested by e.g. the Christian Democrats in 2001, the Liberal Party in 2005 and the Council of Economic Advisors in 2005. In promoting them, proponents generally advocate flat taxes for being simple and transparent.

  government should put much effort in the redistribution of incomes from high to low-ability agents. The social benefits from equality should be weighed against the efficiency losses induced by redistribution. These efficiency costs are determined by the following two factors: (i) elasticity of labour supply of various agents; (ii) population density at various

  participate or are eligible for social benefits, and age. Overall, the model distinguishes 40 different household types.

  Wages are obtained from a right-to-manage model. In bargaining over wages, trade unions exploit their monopsony power to reap part of the rents earned in production. However, by setting wages above the market clearing level, trade unions create unemployment which they value negatively. Unions thus face a trade off between high wages and low unemployment. An important specification in the right-to-manage model is the fall-back position of the trade union.

Figure 4

 4 Figure 4.1 shows the income effects of the 38% flat income tax reform. Households are distinguished in four groups: one-earner couples, two-earner couples, single workers and single benefit recipients. The figures show the results from simulations for 40.000 households, where

Figure 4 .

 4 Figure 4.3 shows the distributional effects of the 29% flat tax in which the general tax credit is abolished. The scale on the vertical axis in Figure 4.3 differs from that in Figures 4.1 and 4.2

Figure

  Figure 4.1 Income effects according to household type of a 38% flat tax in 2006 (% changes)

  .B., 1997, Public finance solutions to the European unemployment problem?, Economic Policy, 12, 221-264. Tuomala, M. (1990), Optimal Income Tax and Redistribution, Oxford: Clarendon Press. Tyrvainen, T., (1995), "Real Wage Resistance and Unemployment: Multivariate Analysis of Cointegrating Relations in 10 OECD Countries", OECD Working Paper No. 10, Paris.

Table Error !

 Error Style not defined..1 Income

taxation in the Netherlands in 2006 (excluding employee insurances)

	a
		Bracket length	Tax rate c	Tax payers	Taxable income
		euro	%	1 000 persons	bln euro
	Personal income tax (Box1) b
	First bracket	17 046	34.15	5 174	158.5
	Second bracket	13 586	41.45	4 069	62.4
	Third bracket	21 598	42.00	2 171	24.8
	Open bracket		52.00	425	8.7
	General tax credit			1 990
	Earned income tax credit		Maximum 1 357
	a Projection, CPB Macro Economic Outlook 2006, September 2005.
	b Box 1 contains income from labour and housing. Income from capital is taxed separately.
	c The tax rates of the first two brackets comprise social security contributions at a rate of 31.70% for state old-age pension (aow:
	17.90%), exceptional medical expenses (awbz: 12.55%) and survivor benefits (anw: 1.25%). Taxpayers over the age of 65 are not
	required to pay aow contributions and face a tax rate in the first two brackets of 16.25 % and 23.55 % respectively.

Table Error !

 Error Style not defined..1 Long

-term effects of two flat tax proposals on the labour market

  The 38% flat tax involves a revenue-neutral replacement of the existing tax structure by a single rate; The 43% flat tax is accompanied by a rise in the general tax credit of 1 400 euro. The 29% flat tax is accompanied by an abolishment of the general tax credit. The rate for elderly people is 17.9% lower in the current first two tax brackets. All figures are expressed in relative changes unless indicated otherwise.

	5
	F o r
	P
	e
	Flat tax 38% Tax credit 2000 euro e r	Flat tax 43% Tax credit 3400 euro	a Flat tax 29% Tax credit zero
	Inequality index (Theil coefficient) Labour supply in hours primary earners secondary earners single persons	6.4 0.9 1.2 0.3 0.8 R e v	0.0 0.3 0.1 0.1 1.1	20.6 4.0 2.8 4.2 4.7
	Female participation rate Share of high-skilled labour supply Employment low skilled high skilled	2.0 0.8 1.1 2.1 2.4	1.5 0.0 0.3 0.4 0.2 w i e	1.9 1.7 5.3 2.0 8.2
	Unemployment rate (absolute change)	0.1		0.1	0.3
	Production	1.2		0.1	5.1
	Public consumption in % GDP (closure rule)	0.5		0.2	1.8
	Source: MIMIC simulations.
					17

a

See Bovenberg et al.,

for a core version of MIMIC. A description of the full model and its calibration can be found inGraafland et al.,

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

[START_REF] Rym | Average marginal tax rates in the UK economy[END_REF] discuss alternative methods to compute the average marginal tax rate. We take the weighted mean of all working individuals, where gross incomes are used as weights.

Acknowledgements

We are grateful to Nicole Bosch and Joke Goes for preparing figures 4.1, 4.2 and 4.3 and two anonymous referees for their valuable comments on an earlier draft.


Laurent Granier
email: laurent.granier@univ-montp1.fry

Sébastien Trinquard
email: sebastien.trinquard@univ-montp1.fr

Entry Deterrence and Mergers under Price Competition in Pharmaceutical Markets

Keywords: barriers, endogenous mergers, limit-pricing, pharmaceuticals, pseudo-generics I11, L12 barriers, endogenous mergers, limit pricing, pharmaceuticals, pseudo-generics

published or not. The documents may come

corroborate the Ferrandiz theoretical model. In a complementary approach, [START_REF] Kong | Pseudo-genenric products and barriers to entry in pharmaceutical markets[END_REF] use a two-stage game model with product di¤erentiation and show the central role of cross price-elasticity in using pseudo-generic products to deter entry. Pseudo-generics drugs, by raising competitive pressure on the generic …rm, make entry deterrence easier. From this perspective, [START_REF] Granier | Pseudo-generics products and mergers in pharmaceutical markets, Working Paper, Cahier LASER 18.01.06, Université Montpellier I. versus trade-name prescription decision[END_REF] show that this increase in competitive pressure facilitates the generic …rm's purchase by the brand-name laboratories. This justi…es our present study i.e. the trade-o¤ between mergers and barriers to entry in pharmaceutical markets.

Regarding barriers to entry, this model considers the limit-pricing strategies that consist of …xing the highest price that insures that the entrant realizes no pro…t 4 . A basic defect in the Bain/sylos limit-pricing model of entry deterrence stems from its assumption that the potential entrant believes that the established …rm would maintain its output constant if entry occurred. The problem is that if entry did occur it would not generally be rational for the established …rm to carry out this threat; thus the threat is not credible (see, e.g., Sherer, 1980, pp.246-48). Considering asymmetric information in a Bayesian game, Milgrom and Roberts (1982) solves the credibility problem. Even if this new model can qualify the e¢ cacy of the limit-pricing strategy, in a compromise between generality and tractability, we assume generic …rms are myopic producers. Regarding mergers, we construct a model of endogenous mergers (see, e.g., [START_REF] Kamien | The limits of monopolization through acquisition[END_REF][START_REF] Kamien | Monopolization by sequential acquisition[END_REF][START_REF] Granier | Endogenous mergers and cost heterogeneity[END_REF] to better consider merger dynamics. More exactly, we study preemptive mergers. These are F o r P e e r R e v i e w initiated to prevent an unfavorable future event such as certain rival mergers (Brito, 2003, Fridolfsson and[START_REF] Fridolfsson | Why mergers reduce pro…ts, and raise share prices -A theory of preemptive mergers[END_REF], or in our case, such as the generic entry.

The purpose of this paper is to study the trade-o¤ between a limit-pricing strategy and a merger strategy. To achieve this aim, we develop a simple model in which a brand-name laboratory and a generic one compete à la Bertrand-Stackelberg in a therapeutic market with vertically di¤erentiated goods. We …nd two main results. The limit-pricing strategy is always preferable to accommodating entry but the generic …rm myopic assumption quali…es this result.

Secondly, merger is preferable to entry deterrence depending on the entrant setup cost level and to the discount rate. Our paper extends [START_REF] Kong | Pseudo-genenric products and barriers to entry in pharmaceutical markets[END_REF], and [START_REF] Granier | Pseudo-generics products and mergers in pharmaceutical markets, Working Paper, Cahier LASER 18.01.06, Université Montpellier I. versus trade-name prescription decision[END_REF] models. Indeed, it studies the trade-o¤ between entry deterrence and merger, also taking into account the possibility of pseudo-generic production. Moreover, it di¤ers from these two models by assuming price competition. The rest of the paper is organized as follows. Section 2 sets out the model. In section 3, we analyze limit-pricing strategies. Section 4 is devoted to merger analysis and to its comparison with that of limit-pricing strategies. We conclude in section 5.

Model

We consider a drug market where the patent has expired. Thus, generic laboratories are able to produce. We take into account the fact that the brand-name …rm can equally produce a pseudo-generic. Consumers may choose between a brand-name product and a generic product. The brand-name producer, threatened by the generic entry, may adopt three alternative strategies: either accommodate entry or deter entry or merge as soon as a generic …rm enters the market. We de…ne a game in which these three strategies are available. By comparing pro…ts associated with these three strategies, we compute the Nash equilibrium of the game (see …gure 1). First, we present the model assumptions. Second, we establish existence conditions of the benchmark in which the three strategies can be analyzed.

Insert Figure 1 2

.1 Assumptions

The physician is considered as a perfect agent of the patient. In this context, the physician's utility and the patient's utility are one and the same. Their utility function is linear since we assume risk-neutral consumers. The absence of an insurance market is also assumed, which means that consumers pay their drugs bill in full and there is no public intervention in the market5 . We assume a vertical product di¤erentiation because of brand loyalties6 and uncertainty The variable u is the drug quality, p b the brand-name price and p g the generic price. Each consumer is characterized by a value of . This parameter is the subjective cost of switching from the branded to the generic drug. Here, it is modeled as a probability. It is the perceived probability that the generic drug is of the same quality as the brand-name one. Consumption decisions are trade-o¤s between the perceived quality of a drug and its price. The parameter is assumed to be uniformly distributed over the interval [0; 1]. Let F ( ) be the distribution function. A patient purchases the brand-name drug if the following is true:

u p b u p g ) 1 p b p g u , (1)
u p b 0 ) p b u. (2)
From this, we compute market shares. Let s g be the generic market share and s b the brand-name one:

s g = 1 F (1 p b p g u ) = p b p g u , (3)
s b = F (1 p b p g u ) = 1 p b p g u . ( 4
)
The literature on the pharmaceutical market usually assumes negligible marginal cost and focuses on sunk costs of R&D. Here, we leave aside these sunk costs since we do not consider innovation issues. However, the generic laboratory pays a setup cost to enter the pharmaceutical market. Let F denote the setup cost in the rest of the paper. This is not the case for the brandname …rm when it produces its pseudo-generic drug because the pseudo-generic good may be manufactured on the same production lines as its brand-name equivalent (Kong and Seldon, 2004, footnote 2). Furthermore, we assume the brand-name producer can act as a Stackelberg leader because of brand loyalties. Moreover, the brand-name …rm and the generic …rm compete à la Bertrand 7 . We assume also the brand-name …rm has no incentive to produce several di¤erent pseudo-generic drugs 8 . Now we have de…ned the benchmark conditions, we can to study the trade-o¤ between entry deterrence, accommodation of entry and merger.

Benchmark conditions

In order to study the trade-o¤ between accommodating entry, deterring entry, or purchasing the generic …rm, we de…ne a benchmark for which entry is profitable. To elucidate the topic, we restrict the study to the case in which entry is pro…table if and only if the industry is monopolistic and there is only one entry at any time 9 . To check this assumption, a second entrant must realize no 7 Because of the …xed market demand (i.e. covered market and unit density), we assume price competition and we consider limit pricing strategy. 8 There are two justi…cations to this assumption. On one hand, brand-name laboratories have a reluctance to produce several types of pseudo-generic drugs so as not to degrade brand-loyalties from which they bene…t. Indeed, for a given therapeutic class, the generics proliferation decreases the switching cost from the brand to the generic drug [START_REF] Hurwitz | Persuasion or information? Promotion and the shares of brand name and generic pharmaceutical[END_REF]. On the other hand, we note the absence of such pseudo-generic duplication in stylized facts. 9 Results are not qualitatively modi…ed if there are several entrants at the same time.

Indeed, if several …rms simultaneously enter the market, these share equally the generic market among themselves. Therefore, merger and entry deterrence strategies are una¤ected. pro…t. Therefore, we have to compare a duopolistic industry with a triopolistic one. Given that the brand-name …rm can produce two goods, we must determine which strategy this …rm follows, whether to produce only pseudogeneric drugs or not. First, we determine if it produces pseudo-generics when there is only one entrant. Second, we make the same study when there are two entrants. The comparison of these two studies determines the benchmark conditions where there is only one potential entrant at any one time.

Stackelberg duopoly vs Stackelberg pseudo-duopoly

To know if the brand-name laboratory has an incentive to produce a pseudogeneric when there is only one entrant, we compare its pro…ts with and without a pseudo-generic drug. We call "pseudo-duopoly" the duopoly in which pseudo-generics are produced. We start by analyzing the Stackelberg duopoly before analyzing the Stackelberg pseudo-duopoly.

Stackelberg duopoly Let D b and D g be brand-name and generic …rms duopoly pro…ts. These pro…ts are as follows:

D b = s b p b , ( 5
) D g = s g p g F . ( 6
)
Since the brand-name laboratory acts as a Stackelberg leader, we substitute the generic …rm's reaction function into the brand-name …rm's pro…t function to compute equilibrium prices and pro…ts. Thus, we obtain the following equilibrium pro…ts: …rms'duopoly pro…ts. These pro…ts are then given by:

D b = u 2 , ( 7
) D g = u 4 F . (8)
P D b = s b p b + 1 2 s g p g , (9)
P D g = 1 2 s g p g F . ( 10
)
As the two generic drugs are homogeneous, the Bertrand competition leads to a unique price on this market. Thus, the two producers share the generic market equally among themselves. Since the brand-name laboratory acts as a

Stackelberg leader, we substitute the generic …rm's reaction function into the brand-name …rm's pro…t function to establish equilibrium prices and pro…ts.

Thus, the equilibrium pro…ts are:

P D b = 5 8 u, (11)
P D g = 1 8 u F . ( 12
)
Proof. see appendix B.

Conclusion: which structure? The brand-name laboratory compares its pro…ts in the two structures to decide whether or not to produce pseudogenerics.

P D b D b = u 8 > 0. ( 13
)
The brand-name …rm, in competition with a generic …rm, produces pseudogenerics. We deduce from that the generic …rm enters the market if and only if it recovers its setup cost, that is if F < u 8 . Now, we study the case for which there are two entrants to de…ne the conditions under which a sole entry is pro…table.

Stackelberg triopoly vs Stackelberg pseudo-triopoly

We call "pseudo-triopoly" the triopoly in which pseudo-generics are produced.

Proceeding in the same way as in section 2.2.1 but with two potential entrants, we study the brand-name …rm's decision to produce pseudo-generics. We start by analyzing the Stackelberg triopoly before analyzing the Stackelberg pseudotriopoly.

Stackelberg triopoly Let T b , T g1 , and T g2 be brand-name and generic …rms'triopoly pro…ts. These pro…ts are as follows:

T b = s b p b , ( 14
) T g1 = T g2 = 1 2 s g p g F . ( 15
)
Subsequently, the equilibrium pro…ts are:

T b = u 2 , ( 16
) T g1 = T g2 = u 8 F . ( 17
)
Proof. see appendix C.

Stackelberg pseudo-triopoly Let P T b , P T g1 , and P T g2 be brand-name and generic …rms'triopoly pro…ts. These pro…ts are given by:

P T b = s b p b + 1 3 s g p g , (18)
P T g1

= P T g2 = 1 3 s g p g F . ( 19
)
The generic market is divided into three equal shares because of the reasons mentioned in section 2.2.1. Subsequently, the pro…ts are the following: Conclusion: which structure? The brand-name laboratory compares its pro…ts in the two structures in order to decide whether or not to produce pseudo-generics.

P T b = 7 12 u, (20)
P T b T b = u 12 > 0. ( 22
)
The brand-name …rm, in competion with two generic …rms, produces the pseudo-generic. We deduce from this that two generic …rms enter the market simultaneously or sequentially if and only if they recover their setup costs, that is if F < u 12 . The pseudo-duopoly and the pseudo-triopoly are the market structures preferred by the brand-name …rm in the case of a sole competitor or of two competitors respectively. By assumption, entry is pro…table if and only if the initial structure is a monopolistic one and if there is an only one entry at a time. To check this assumption, the second entrant must realize no pro…t. By comparing the two structures, we ascertain the condition under which entry is pro…table for one …rm but not for two:

u 12 < F < u 8 . ( 23
)
The benchmark conditions having been studied, we focus on the deterrence of the entry of the generic …rm.

Entry deterrence

In this Bertrand competition context, the brand-name …rm may have an incentive to use a limit-pricing strategy to deter entry. This strategy consists in …xing the highest price which deters entry. Since the brand-name …rm can produce pseudo-generics, two sub-strategies exist. On one hand, to deter entry by producing only the brand-name good. On the other hand, to deter entry by producing the two drugs. We compare these two sub-strategies to ascertain the optimal strategy. We begin with the case in which the brand-name …rm produces only its princeps. Second, we study the case in which it produces pseudo-generics also.

Limit-pricing strategy and Stackelberg duopoly

The limit-pricing strategy consists in determining the price which maximizes the brand-name …rm's pro…t under the assumption that the generic producer realizes no pro…t:

max p b LD b = s b p b (24) s=t LD g = s g p g F 0
Since the brand-name laboratory acts as a Stackelberg leader, we substitute the generic …rm's reaction function into the brand-name …rm's pro…t function to establish equilibrium prices and pro…ts. The reaction function is:

RF (p b ) : p g (p b ) = p b 2 . ( 25
)
The pro…t of the generic producer must be non-positive to deter entry.

Since the brand-name …rm's pro…t function is concave, we saturate the constraint so as to establish the equilibrium brand-name good price p LD b :

LD g = s g p b 2 F = p 2 b 4u F = 0 ( 26
)
) p LD b = 2 p F u.
Given that the generic …rm does not enter the market, the brand captures price exceeds the consumer's willingness to pay. The …rm cannot …x this price, but in this case, the generic …rm does not enter (see section 2.2.1). Thus, the equilibrium brand-name …rm's pro…t is:

the whole demand if p LD b < u, that is F < u 4 . Note that if F > u 4 ,
LD b = s b p LD b = 2 p F u. ( 27
)
Under the benchmark conditions, the brand-name laboratory can deter entry without pseudo-generics production by …xing the equilibrium price p LD b .

Limit-pricing strategy and Stackelberg pseudo-duopoly

Proceeding in the same way as in the previous section, the maximization problem becomes:

max p b LP D b = s b p b + 1 2 s g p g (28) s=c LP D g = 1 2 s g p g F 0
Inserting (25) and saturating the constraint, we deduce the equilibrium brand-name good price p LP D b :

LP D g = 1 2 s g p b 2 F = p 2 b 8u F = 0 ( 29
) ) p LP D b = 2 p 2F u.
Given that the generic …rm does not enter the market, the brand captures

the whole demand if p LP D b < u, that is F < u 8 . Note that if F > u 8 , the limit
price exceeds the consumer willingness to pay. The …rm cannot …x this price, but in this case, the generic producer does not enter (see section 2.2.1). Thus, the equilibrium brand-name …rm's pro…t is: This strategy is pro…table if the brand-name pro…t is positive, that is the case if F < 2u. So, the benchmark holds if F < u 8 . Thus, under the benchmark conditions, the brand-name …rm can deter entry by producing its pseudogeneric good by …xing the equilibrium price p LP D b .

LP D b = s b p LP D b + s g p LP D g (30) = 2 p 2F u 2F .

Optimal limit-pricing strategy

In order to determine the optimal limit-pricing strategy, we compare brandname …rm's pro…ts in the two sub-strategies: to produce or not pseudogenerics. By assumption, only one generic …rm has an incentive to enter the market if condition (23) holds. Moreover, the two sub-strategies are applicable if condition ( 23) holds. The di¤erence between the two pro…ts is:

LP D b LD b = 2 p 2F u 2F 2 p F u. ( 31
)
This expression is a trinomial which admits two roots F 1 and F 2 10 . The benchmark conditions are between these two roots. We deduce from this:

LP D b LD b > 0. (32)
Therefore, the optimal limit-pricing strategy is that in which the brandname …rm produces pseudo-generics. In this case, brand and generic prices . We determine if it is pro…table for the brand-name …rm to deter entry. Therefore, we compare the brand-name …rm's pro…ts in the case of limit-pricing strategy and in the case of accommodation strategy. This di¤erence is analyzed for setup cost values in line with condition (23). Indeed, this condition makes the entry of only one generic …rm pro…table at one time. The pro…t di¤erence is given by:

LP D b P D b = 2 p 2 p F u 2F 5 8 u > 0.
(33)

Proposition 1 The limit-pricing strategy dominates the accommodation strategy.

Proof. see appendix E.

As we have already said, this result assumes a myopic generic …rm, since by entering the market, this …rm incites the brand-name …rm to modify its strategy by …xing competitive prices.

4 Deter entry or merge?

The previous section underlines that entry deterrence strategy dominates accommodation strategy. The merger strategy is equivalent to the entry deterrence strategy. Indeed, it prevents the generic …rm from producing. After studying the merger path, we analyze the relative pro…tability of the two strategies.

An alternative to entry deterrence: the "anticipative" merger

In the benchmark, we consider one potential entry in each period. Thus, we study the merger in a dynamic context. The brand-name …rm must purchase one …rm in each period. As the generic …rm is bought before entering the market, this merger is called "anticipative" merger 11 . This merger is equivalent 1 1 This idea belongs to a broader concept called preemptive merger. This is studied in endogenous merger literature. These mergers are initiated to prevent an unfavorable future event such as certain rival mergers (see, e.g., Brito, 2003, Fridolfsson and[START_REF] Fridolfsson | Why mergers reduce pro…ts, and raise share prices -A theory of preemptive mergers[END_REF]. In our case, the unfavorable event is a generic entry. to a premium paid by the brand-name …rm to prevent competition. The merger allows the brand-name producer to realize a monopoly pro…t. On the other hand, this …rm has to purchase each entrant. We deduce a net merger gain.

Monopolization

Therefore, we study the brand-name monopoly, achieved by merger. Let M b be the monopoly pro…t. This pro…t is the gross merger gain for one period.

M b = s b p b + 1 2 s g p g . ( 34
)
The monopoly can extract the whole consumer surplus by selling the most valued drug to each consumer since the brand-name …rm need not sell pseudogeneric drugs. Therefore, the branded good is not in competition with a generic which it would realize by refusing to be sold, it gives a reservation price 13 equal to this pro…t. By anticipating this, the brand-name …rm bids at this level, called generic …rm's buying price. We consider the auction mechanism as an instantaneous one. This mechanism takes place at the moment of the generic entry. Thus, no other …rm has an incentive to enter the market since there is already an entry at this period. Therefore, the buying price is the actualized in…nite ‡ow of gross pro…t the generic …rm would realize by entering the market. Let be the discount rate with 0 < < 1 and let BP (u; ) be the buying price:

BP (u; ) = P D g + F (1 ) = u 8
(1 ) . ( 35)

Net merger gain

Let G(F; u; ) be the net merger gain. It is equal to the gross merger gain minus the buying price. As the game horizon is in…nite, the gross merger gain is an actualized in…nite ‡ow of monopoly pro…t. The buying price is paid in each period because there is an entrant to purchase in each period.

G(F; u; ) = M b 1 BP (u; ) 1 (36) = 1 8 u ( 1) 2 (8 7) .
We …nd the net merger gain is positive for < and negative for > with = 7 8 .

Page

"Anticipative" merger strategy vs limit-pricing strategy

To solve the game, we compare two strategies: to merge with each entrant or to deter entry ad vitam aeternam. We compare the net merger gain with the actualized in…nite ‡ow of limit-pricing pseudo-duopoly pro…t. Let M LI(F; u; ) be the di¤erence between these payments. If M LI(F; u; ) is positive, then the merger path is the Nash equilibrium of the game.

M LI(F; u; ) = u 1 1 8 u (1 ) 2 2 p 2 p F u 2F 1 (37) = 1 8( 1) 2 h ( 16F 8u + 16 p 2F u) + 16F + 7u 16 p 2F u i .
Let (F; u) be the level for which M LI(F; u; ) = 0:

(F; u) = 16F + 7u 16 p 2F u 16F + 8u 16 p 2F u . ( 38
)
Proposition 2 The entry deterrence by the limit-pricing strategy is the Nash equilibrium of the game if > (F; u). By contrast, the merger strategy is the Nash equilibrium of the game if < (F; u). Moreover, (F; u) (see …gure 2) is decreasing in F and 0:5 < (F; u) < 0:643 for the setup cost values allowing the benchmark existence.

Proof. see appendix G.

Insert Figure 2 The interpretation of proposition 2 is as follows. There is a trade-o¤ between the two strategies that depends on the discount rate level. If this is low ( < (F; u)), it reduces the value of future payments in the merger path.

The merger tends to be more pro…table. If this is high ( > (F; u)), it raises the value of future payments in the merger path. The merger tends to be less pro…table. Moreover, the higher the setup cost is, the lower the discount factor threshold (F; u) is. Therefore, the area of pro…tability of entry deterrence increases. This is due to the fact that the increase in setup cost makes the deterrence of a generic competitor easier. Note also that if > , the net merger gain is non-positive and the entry deterrence strategy is always preferred. For (F; u) < < , the net merger gain is positive but not enough to o¤set the pro…tability of the entry deterrence strategy. For < (F; u) < , the net merger gain is positive and exceeds the entry deterrence gain.

Concluding remarks

The entry of generic drugs in the pharmaceutical market encourages brandname laboratories to use anti-competitive practices to stay in a monopolistic industry. More precisely, this article analyzes two anti-competitive practices:

the "anticipated" merger strategy and the limit-pricing strategy. Each strategy may be implemented with or without pseudo-generics production. This topic is analyzed in a vertical di¤erentiation model, in which laboratories compete à la Bertrant-Stackelberg. As to the pro…tability of the two strategies, we report the following …ndings: …rst, the entry deterrence is always preferable to entry accommodation. This result must be quali…ed by the credibility problem associated with the limit-pricing strategy. Secondly, "anticipated" merger is preferable to entry deterrence depending on the setup cost level and on the rate of discount level. (1982), would re…ne our results. Next, one of the results obtained is the mono-product monopoly persistence. Nevertheless, an insurance market could incite the monopoly also to produce pseudo-generics if we assume a non-covered drug market 14 . This scenario would be closer to the empirical reality (e.g, [START_REF] Hollis | The importance of being …rst : evidence from canadian generic pharmaceutical[END_REF][START_REF] Hollis | The anti-competitive e¤ects of brand-controlled 'pseudogenerics' in the canadian pharmaceutical market[END_REF].

Moreover, competition authorities could block the merger. However, taking synergies into account could modify this decision, all the more so since the monopoly may produce pseudo-generics. Finally, to explain the presence of only one pseudo-generic product, we might consider the fact that the switching cost from the brand to the generic drug decreases with generic proliferation.

This assumption could be endogenized in the model. Thus, the brand-name …rm's pro…t can be rewritten:

D b = s b p b (A.4) = (1 p b p b 2 u )p b = 1 2u p 2 b 2up b .
The …rst order condition of the brand-name …rm's pro…t function determines the branded good equilibrium price:

@ D b @p b = @( 1 2u p 2 b 2up b ) @p b = 1 u (u p b ) = 0. (A.5)
The second order condition holds since:

@ 2 D b @p 2 b = @( 1 u (u p b )) @p b = 1 u < 0. (A.6)
We deduce the following equilibrium prices and market shares:

p D b = u, (A.7) p D g = u 2 , s D b = s D g = 1 2 .

Appendix B

Proceeding in the same way as in the appendix A, the brand-name …rm's pro…t can be rewritten:

P D b = s b p b + 1 2 s g p g (B.1) = (1 p b p b 2 u )p b + p b p b 2 2u p b 2 = 1 8u p b (3p b 8u) .
The price maximizing the pro…t function is: = u. We report the following equilibrium prices and market shares:

p P D b = 4u 3 . (B.
p P T b = u, (D.3) p P T g = u 2 , s P T b = s P T g = 1 2 . Appendix E LP D b P D b = 2 p 2F u 2F 2 p F u. (E.1)
This di¤erence is a trinomial admitting two roots: The benchmark conditions are between these two roots. Therefore, we obtain:

F 3 = 1 4 p 2(2 p 2 p
LP D b P D b > 0. (E.2)
Appendix F

We study the sign of the net merger gain. We derive the net merger gain function in .

@G(F; u; ) @ = 1 4 u ( 1) 3 (4 3) 8 > > < > > : > 0 pour < 3 4 , < 0

Appendix G

We search for M LI(F; u; ) sign. This one is the same than the sign the function numerator. Thus, we derive this numerator in .

@( 16F 8u + 16 p 2F u) + 16F + 7u 16 p 2F u) @ = 16F 8u + 16 p 2F u. (G.1)
This derivative is a trinomial admitting two roots:

F 5 = u 16 4 p 2 9 ' 0:209u, (G.2) F 6 = u 16 4 p 2 + 9 ' 0:916u.
The benchmark conditions imply the negativity of M LI(F; u; ) derivative (in ). We compute the M LI(F; u; ) root in :

(F; u) = 16F + 7u 16 p 2F u 16F + 8u 16 p 2F u . (G.3)
Under the benchmark conditions, we study this root:

@( (F; u)) @F = 1 8 ( 2 p F u + p 2u)u 2F + u 2 p 2F u < 0 pour F 2 h u 12 ; u 8 i . (G.4) (F; u) F = u 12 = 25u 4 p 24u 28u 4 p 24u ' 0:643 2 [0; 1] . (F; u) F = u 8 = 1 2 2 [0; 1] .
Under the benchmark conditions, (F; u) is decreasing in F from 0:643 (approximatively) to 1 2 . As 0 < 1 2 < 0:643 < 1, whatever the setup cost level, there are discount factor values lower or higher than (F; u). (F; u)

F = u 8 = 1 2 2 [0; 1] .
Under the benchmark conditions, (F; u) is decreasing in F from 0:643 (approximatively) to 1 2 . As 0 < 1 2 < 0:643 < 1, whatever the setup cost level, there are discount factor values lower or higher than (F; u).

  in drugs. Consumers'utility function is assumed to be: consumes the brand-name drug, if the patient consumes the generic drug, otherwise.

.

  The brand-name …rm, preventing its competitor from entering the market, realizes a pro…tLP D b

1 0 F1

 0 = 0 and F2 = 2u p 2 + 3u '

  good. It …xes the branded good price level at the maximum price allowing to sell the drug to each consumer, that is at p M b = u. Thus, s M b = 1. The brand-name …rm's pro…t, which is then a mono-product monopoly pro…t 12 , is M b = u.4.1.2 Buying priceAccording to the benchmark, only one generic …rm has an incentive to enter the monopolistic market at each period. Such an entrant must, to set up in the market, invest in a production unit represented by a setup cost F . As soon as the potential entrant invests, the brand-name …rm tries to purchase it to stay in a monopolistic situation. The repurchase process is a simultaneous auction brand-name …rm bids for the generic producer and the generic …rm gives a reservation price. As the generic …rm cannot hope to earn more than the Bertrand-Stackelberg gross pro…t (without deducting the setup cost)

  Figure 1. Game Tree

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  Three research perspectives appear in this simple model. First, we assume a myopic generic …rm. Taking into account a Bayesian reasoning to elabo-

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	rate the limit-pricing strategy, as Milgrom and Roberts
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In particular, the limit-pricing strategy is empirically validated by[START_REF] Sengupta | A limit-pricing model for US computer industry : an application[END_REF] for US computer industry.

« Price regulation is mainly concerned with the trade-o¤ between R&D and cost containment, while insurance is concerned with moral hazard and adverse selection problems»[START_REF] Brekke | Direct to consumer advertising in pharmaceutical markets[END_REF]. Our purpose is a very di¤erent one. We examine the trade-o¤ between entry deterrence and mergers. Therefore, we do not take account of health insurance and price regulation. Therefore, we do not take account of health insurance and price regulation. However, there are papers focused on price regulation e¤ects in pharmaceutical markets (e.g.Jones, Potashnik and Zhang,

2001).6 The empirical studies of[START_REF] Hudson | Pricing dynamics in the pharmaceutical industry[END_REF], Hellerstien (1998), or[START_REF] Kong | The price premium of generic to brand-names and pharmaceutical price index[END_REF] show the existence of brand loyalties. These studies explain swithching costs by the search costs and the uncertainty about the relative quality of the entrant.

2 The monopoly is a mono-product one but this must be nuanced because there is no insurance market. Such a market would incite the monopoly to produce pseudo-generics because of the reimbursement di¤erential if we assume a non-covered drug market. This scenario would be more in accordance with empirical reality.

3 This reservation price makes the generic …rm indi¤erent between producing and being sold.

4 To simplify the model, we ignore the insurance market. However, the higher incentive to produce generics induced by an insurance market does not a¤ect qualitatively our trade-o¤ between mergers and entry deterrence.

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

Appendix A

The generic …rm's reaction function is given by the …rst order condition:

The generic …rm's pro…t function is concave in p g since the second order condition is checked:

Therefore, the generic …rm's reaction function is:

Appendix C

Proceeding in the same way as in the appendix A, the brand-name …rm's pro…t can be rewritten:

We deduce the following equilibrium prices and market shares:

Appendix D

Proceeding in the same way as in the appendix A, the brand-name …rm's pro…t can be rewritten:

Appendix A

The generic …rm's reaction function is given by the …rst order condition:

The generic …rm's pro…t function is concave in p g since the second order condition is checked:

Therefore, the generic …rm's reaction function is:

Thus, the brand-name …rm's pro…t can be rewritten:

The …rst order condition of the brand-name …rm's pro…t function determines the branded good equilibrium price:

The second order condition holds since:

Appendix B

The generic …rm's reaction function is given by the …rst order condition:

The generic …rm's pro…t function is concave in p g since the second order condition is checked:

Therefore, the generic …rm's reaction function is:

Thus, the brand-name …rm's pro…t can be rewritten:

The …rst order condition of the brand-name …rm's pro…t function determines the branded good equilibrium price:

The second order condition holds since:

Appendix C

The generic …rms'reaction function is given by the …rst order condition:

The generic …rms' pro…t function is concave in p g since the second order condition is checked:

Therefore, the generic …rms'reaction function is:

Thus, the brand-name …rm's pro…t can be rewritten:

The second order condition holds since:

We deduce the following equilibrium prices and market shares:

Appendix D

The generic …rms'reaction function is given by the …rst order condition:

The generic …rms'pro…t functions are concave in p g since the second order condition is checked:

Therefore, the generic …rms'reaction function is:

Thus, the brand-name …rm's pro…t can be rewritten:

Appendix F

We study the sign of the net merger gain. We derive the net merger gain function in .

@G(F; u; )

Therefore, the net merger gain is increasing for < 3 4 and decreasing for >

Appendix G

We search for M LI(F; u; ) sign. This one is the same than the sign the function numerator. Thus, we derive this numerator in .