Reference no: EM131392543

Consider the Robinson Crusoe Economy in the Post-Walras Arrival Age. Robinson’s utility function over yams (y) and leisure (l) is U ( y , l )= √2 y +l . Robinson’s endowment of time is L. The production function for yams is y = h where h is the amount of labor used. Let yams be dy =¿ ; the marginal the numeraire. Useful information: (i) the marginal product of labor is dh dU 1 = utility of yams is ; the marginal utility of leisure is 1; and the marginal disutility of dy √ 2 y labor is 1. (a) Find the supply curve of yams for Robinson the Manager. (b) What does the supply curve mean for the equilibrium wage rate and profits? (c) Find the demand curve of yams for Robinson the Consumer. Illustrate with a diagram. [Hint: What are the two constraints that restrict the choices of Robinson the Consumer?] (d) Explain the conditions required for general equilibrium and illustrate with a diagram. (e) What are the general equilibrium prices? [Hint: This is very simple if you think about your answer in (a) and understand that competition and the special nature of the production function means that wage rate is determined only by costs of production. Why?] (f) Suppose that Friday introduces a flat tax on labor income, i.e., for every hour that Robinson works he pays the government t∗w and receives ( 1−t )∗w . The entire proceeds of the tax are rebated back to Robinson as a lump sum (LS). Using a diagram illustrate the new general equilibrium. [Hint: Robinson the consumer does not realize that the lump sum rebate depends on how much he works.] (g) Explain why the equilibrium without a tax is Pareto Optimal but the equilibrium with a tax is not. (h) Find the general equilibrium allocation for a tax equal to t: yams, labor, profits, and Robinson’s income.