Question 1: Consider a closed, representative agent economy in which the household lives for two periods, youth and old age. The household has 40 units of endowment when young and 0 units when old. Suppose that there is a firm in this economy, which produces output in the second period from investment done in the second period according to the technology 10 I1/2. Household's preferences are represented by the utility function U(C1,C2) =
ln (C1)+(1/3)ln(C2), where C1 is the first period consumption and C2 is the second period consumption.
(a) Find the optimal consumption levels and the optimal savings for this household.
(b) Write down the investment demand function for the firm.
(c) Find the equilibrium in the capital market and the output.
Question 2:
Consider a representative agent economy in which agents live for two periods. The agents earn 30 units of commodities when s/he is young and 0 units when s/he is old. There is no production in the economy and the real interest rate is %10 percent. The preferences of the agent is represented by the discounted utility function U(C1,C2) = ln(C1)+(1/(1+r))ln(C2) where C1 is the consumption when young and C2 represents the consumption when old.
a) Write down the budget constraints of the household by using the specific numbers given above
b) Find the optimal consumption levels for the agent
c) Find the optimal saving levels for the agent
d) Suppose that the agent pays 6 units of taxes from his/her income when young and receives 6 units of subsidies when old. What are the new budget constraints?
e) Find the optimal consumption levels for the agents in part d
f) Find the optimal savings levels for the agents in part d
g) Write a couple of sentences about the intuition at the back of intertemporal consumption smoothing decision of agents at the first part of the problem and the effect of tax/subsidies on these decisions that is the second case in our problem.