Frisch elasticity of labor supply

The Frisch elasticity of labor supply captures the elasticity of hours worked to the wage rate, given a constant marginal utility of wealth. Marginal utility is constant for risk-neutral individuals according to microeconomics. In other words, the Frisch elasticity measures the substitution effect of a change in the wage rate on labor supply. This concept was proposed by the economist Ragnar Frisch after whom the elasticity of labor supply is named.
The value of the Frisch elasticity is interpreted as willingness to work when wage is changed. The higher the Frisch elasticity, the more willing are people to work if the wage increases.
The Frisch elasticity can be also refers as “λ-constant” elasticity, where λ denotes marginal utility of wealth, or also in some macro literature it is referred to as “macro elasticity” as macroeconomic models are set in terms of the Frisch elasticity, while the term “micro elasticity” is used to refer to the intensive margin elasticity of hours conditional on employment.
The Frisch elasticity of labor supply is important for economic analysis and for understanding business cycle fluctuations. It also controls intertemporal substitution responses to fluctuations of wage. Moreover it determines the reaction of effects to fiscal policy interventions, taxation or money transfers.
Lets denote the Frisch elasticity as FE. Then "formula_1"|λ=const.
This is formula for overall Frisch elasticity, where h and w denote hours of work and wage, respectively.
The overall effect of the Frisch elasticity, however, can be distinguished into extensive and intensive. The extensive effect can be explained as a decision whether to work at all. The intensive effect refers to a decision of an employee on the number of hours to work..
Under certain circumstances, a constant marginal utility of wealth implies a constant marginal utility of consumption. Also the Frisch elasticity corresponds to the elasticity of substitution of labor supply.