Suppose households preferences are described by the utility function U(C, l) = βl1/2 + C, where β = 3.3541, andC
stands for consumption of market goods l stands for leisure. The total number of hours available to the representative consumer is 1, and the market real wage is w. Output is produced using the production function Y = (Nd ) 1/2 . For simplicity, let us assume that there is no government, that is G = 0. The firm distributes a profit π to the consumer. Note that the π and w are unknown parameters which will be determined in the equilibrium. Your answers to the following questions may depend on these two parameters. 1. Solve the consumer's problem and find the optimal values of C ? , l ? , and then deduce Ns . 2. Can the income effect ever dominate the substitution effect or not? 3. Solve the firm's problem and derive Nd . 4. Compute the competitive equilibrium wage rate (w ? ), and deduce employment (N? ), and the aggregate output (Y ? ) in this economy. 5. Compute the equilibrium profit π ? , l ? and C ? . Is it the income-expenditure identity satisfied?
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