all. (30 points) Consider an economy in which workers live for two periods and have a...

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all. (30 points) Consider an economy in which workers live for two periods and have a life-time utility U = log(c₁) — 12h² + B (log(C+1) - 1 / M ²+1) in the first period of her life and 1 Here ct is consumption and he is the number of hours an individual works in period t. The wage Ct rate is w, and the budget constraint is Ct + bt = wtht, Ct+1 = Wt+1ht+1+(1+rt)bt in the second period of her life. Here rt is the interest rate and be is the amount saved in period t. The production function is yt = Atlt, and firm profits are yt wilt. Here yt is the amount of output produced, l, is the number of hours firms hire and At is productivity. Since this is a closed economy, so bt = 0, yt = ct and the equilibrium in the labor market requires that ht=lt. Suppose that = 1.05. (a) Characterize the equilibrium in the labor market. That is, find the labor supply and de- mand curves and calculate the equilibrium wage and amount of hours worked as a function of productivity At and the other parameters of the model. [Hint: the worker's labor choice (conditional on consumption) is static. You can greatly simplify your algebra by first calcu- lating the worker's labor supply choice as a function of wt and ct and then imposing the goods market clearing condition ct=yt = Atht to calculate the equilibrium ht.] (b) Write down the Euler equation for this economy. You can state it without explicitly deriving it. Find the equilibrium interest rate as a function of the current and next period's level of productivity. (c) Consider two scenarios. In the first one, At = At+1 = 1. In the second one, At = 1.10 and At+1=1. Find the equilibrium values of all macroeconomic variables - output, interest rates, wages, hours worked in period t under the two scenarios. You will receive partial credit for providing a correct qualitative answer even if your numerical calculations are incorrect. (d) Consider two scenarios. In both A₁ = At+1 = 1. In the first scenario 3 = 105. In the second one 3 increases to 1.02. Find the equilibrium values of all macroeconomic variables – output, interest rates, wages, hours worked in period t under the two scenarios. You will receive partial credit for providing a correct qualitative answer even if your numerical calculations are incorrect. all. (30 points) Consider an economy in which workers live for two periods and have a life-time utility U = log(c₁) — 12h² + B (log(C+1) - 1 / M ²+1) in the first period of her life and 1 Here ct is consumption and he is the number of hours an individual works in period t. The wage Ct rate is w, and the budget constraint is Ct + bt = wtht, Ct+1 = Wt+1ht+1+(1+rt)bt in the second period of her life. Here rt is the interest rate and be is the amount saved in period t. The production function is yt = Atlt, and firm profits are yt wilt. Here yt is the amount of output produced, l, is the number of hours firms hire and At is productivity. Since this is a closed economy, so bt = 0, yt = ct and the equilibrium in the labor market requires that ht=lt. Suppose that = 1.05. (a) Characterize the equilibrium in the labor market. That is, find the labor supply and de- mand curves and calculate the equilibrium wage and amount of hours worked as a function of productivity At and the other parameters of the model. [Hint: the worker's labor choice (conditional on consumption) is static. You can greatly simplify your algebra by first calcu- lating the worker's labor supply choice as a function of wt and ct and then imposing the goods market clearing condition ct=yt = Atht to calculate the equilibrium ht.] (b) Write down the Euler equation for this economy. You can state it without explicitly deriving it. Find the equilibrium interest rate as a function of the current and next period's level of productivity. (c) Consider two scenarios. In the first one, At = At+1 = 1. In the second one, At = 1.10 and At+1=1. Find the equilibrium values of all macroeconomic variables - output, interest rates, wages, hours worked in period t under the two scenarios. You will receive partial credit for providing a correct qualitative answer even if your numerical calculations are incorrect. (d) Consider two scenarios. In both A₁ = At+1 = 1. In the first scenario 3 = 105. In the second one 3 increases to 1.02. Find the equilibrium values of all macroeconomic variables – output, interest rates, wages, hours worked in period t under the two scenarios. You will receive partial credit for providing a correct qualitative answer even if your numerical calculations are incorrect.

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