Econ 509
Econ 509 Spring 2014 S. Parente Final Exam Part I. Labor- Leisure Decision (15 pts) 1. Consider the following static economy given by the following equations. Utility ln(c H ) ln(l ) where H stands for the household Production: c f Ah f where f stands for the firm Time Endowment of Household l h H 100 Suppose the government taxes the output of the firm at rate, τ, and uses the tax revenues to buy a good that provides no value to society. a) Show algebraically that this type of policy has no effect on work hours by solving for the equilibrium (10 pts) b) In words explain, why this policy has no effect on equilibrium work effort. (5 pts) Part II. Savings and Government Finance (50pts) All of the questions in Part II use the Overlapping Generations model where people live two periods. Each generation has the same number of people. Preferences are ln(c y ) ln(cold ) . Each agent is endowed with ey units of output when young and eold units of output when old. 1. Suppose there is a lump-sum tax/transfers when the agent is young equal to Txy and a lump-sum tax/transfer implemented when the agent is old equal to Txold. The first period budget constraint is c y s e y Tx y . The second period budget constraint is cold eold Txold (1 r )s where s is savings and r is the real interest rate. a. Derive the Intertemporal budget constraint (3 pts) b. Derive the utility maximization condition (3 pts) c. Use (a) and (b) to derive the savings function. Verify that savings will not decrease if the real interest rate increases. Assume eold-Txold ≥ 0 (4 pts) 2. Solve out the equilibrium where there is no government policy. Give the condition for which the competitive equilibrium is not Pareto optimal. Provide some intuition for this result. (10 pts) 3. Assume the conditions exist in Question 2 above so that the equilibrium under autarky is not Pareto Optimal. Further, assume the government implements a pay as you go pension system that allows each generation to enjoy the same level of consumption when young and old, i.e., cy = cold. Solve out the equilibrium for this economy (10 pts) 4. What is Ricardian Equivalence? Use the results in questions (2) and (3) to determine whether Ricardian Equivalence holds in this economy. Explain why Ricardian Equivalence either holds or fails to hold in this economy. (10 pts) 5. What is a fully funded pension system? Use the Overlapping Generations model to explain why it is better than a pay as you go system in terms of equilibrium outcomes. (Note: You do not need to compute equilibrium in the OG model when a fully funded and pay as you go systems are implemented. Instead, you are being asked to report and interpret the findings from class.) (10 pts). IV. Business Cycles (35 points) 1. Explain how Kydland and Prescott (1986) document the business cycle facts/regularities. Why do they conclude, that business cycles are a monetary myth? (8 pts) 2. What are some similarities and differences between New Keynesian Economics and Real Business Cycle Theory? In your answer, be sure to comment on why monetary policy is neutral in the Real Business Cycle whereas it has real effects in the New Keynesian model. (7 pts) 3. Consider the Neoclassical Growth Model without leisure in the utility. The model is given by Preference t 0 t ln(ct ) Production: yt A(1 ) t (1 ) k t ht1 (these are per capita variables with h being work hours, and k being capital per person.) Resource constraint: ct k t 1 yt (1 )kt a. What are the utility maximizing condition(s) for the household? (2 pts) b. What are the profit maximizing conditions for the firm? (2 pts) c. What is the relation between the rental price of capital and the interest rate from the banking sector zero profit condition? (1 pts) d. Solve for the balanced growth path capital stock for this economy (5 pts) e. Explain how you would assign parameter values to β, δ, θ, γ and A in matching the model’s balanced growth properties to the long-run US growth experience. (5 pts) 4. Explain how Kydland and Prescott determine how much of US business cycles over the postwar period can be accounted for by TFP shocks. (5 pts)
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