Question

Consider a static, one-per Static One Period Model of the Eco iod model of the economy. There 1s a representative household who can choose how much to consume and how much to work. There is no saving since the model is static. The household problem is C,N I have dropped the t subscripts since there is only one period. Here N is hours of labor, C is consumption, D is a dividend received from ownership of the firm, and w is the real wage. The parameter θ governs the disutility from working. Higher values of θ make the household want to work less. You could also think about θ as corresponding to the utility from leisure, since if you are not working we treat that as leisure. A firm produces duction technology according to the following pro This is different than the production function in class. Here only labor is used (no capital) and there are no diminishing returns to labor. We can still analyze the problem with F(K, N)- N, but the conclusions may be different. The firm's dividend is m's objective is to pick N to maximize D: max AN -wN. Use the household (flow) budget constraint to substitute out for C in the utility function. Then use calculus to derive a first order condition characterizing optimal behavior for the household Solve this equation for N in terms of objects that the household treats as given. These may be exogenous or endogenous but treated as fixed by the household. Use calculus to derive a first order condition characterizing optimal behavior by the firm.

Answer 1

In a static, one-period model of the economy, a representative household maximizes a dividend received from the firm while considering disutility of working. The optimal behavior for the household and the firm can be derived using calculus and solved for the optimal labor choice.

Step-by-step explanation:

In the static, one-period model of the economy, a representative household must make choices about consumption and work. The household's problem can be summarized as maximizing the dividend received from the firm, D, subject to the disutility of working, θ. By using the household's budget constraint and substituting for consumption, we can derive a first-order condition that characterizes the optimal behavior for the household. This equation can be solved to find the optimal labor choice, N, in terms of other given variables.

The firm's objective is to maximize its production, represented by AN, while minimizing the wage cost, wN. By using calculus, we can derive a first-order condition that characterizes the optimal behavior for the firm. This equation can also be solved to find the optimal labor choice for the firm.