Optimal control problems from second-order difference equations
Abstract We examine solutions x ϵ l ∞ ( R n ) of the equations F t ( x t−1 , x t , x t+1 ) = 0 and derive conditions for the existence of objective functions G t so that x solves max xϵl ∞ ΣG t ( x t , x t +1 ). We specialize the conditions to time autonomous equations and apply them to a competitive industry in temporary equilibrium. The objective function in the example is of the cost-benefit form: consumer surplus minus opportunity cost of labor minus industry-wide cost of investment.