ECON 23950 Economic Policy Analysis Practice Midterm #1
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ECON 23950 Economic Policy Analysis
Practice Midterm #1
Part I. TRUE-FALSE Questions (23 points)
Please answer the following questions as TRUE or FALSE, and provide a justification using at most 3-4 sentences for each of the questions. The questions should be answered in the context of the theory and materials discussed in class or done in homework. A good answer often involves identifying a particular theoretical concept related to the question. No points will be given for an answer without a justification.
(5pts) 1. The national debt to GDP ratio is over 100% while the government continues to run
deficit by about 10% of GDP. This is clearly unsustainable.
(5pts) 2. The Ramsey optimal policy problem we studied in class assumes away the government commitment problem.
3. Assuming that Ricardian equivalence holds and that all taxation is lump-sum, con- sumption will fall in the future if the government announces a spending increase that will be financed by a current increase in taxes.
(5pts) 4. A country that has constant output expects a large temporary increase in government
expenditures sometime in the future, say due to an imminent overseas war. Optimal taxation implies that the level of the overall tax rate in the pre-war years is higher than its level in the war and post war years. (Assume that the government is collecting its revenue through proportional taxes and that output always remains constant.)
(8pts) 5. Earlier in 2012, Newt Gingrich said ”We want to have zero capital gains tax.” Addition-
ally he said he would cut the corporate income tax to 12.5%. Gingrich claims that this will surely create jobs and increase tax revenues. Your reaction? (Both theoretically and empirically)
Part II. Problem (50 points) Please solve the following problem.
(50pts) 1. Consider an infinitely lived household whose preferences are given by
with
u(ct , lt ) = 2 √ct - Q log lt
where ct is the household’s consumption in period t, lt is the household’s labor supply in period t, 0 < β < 1, and Q > 0.
If the household supplies lt units of labor in period t, the household gets wt lt units of income, where {wt } ∞t=0 is a sequence of real wage rates which the household takes as given (exogenous).
The income of the household in period t is taxed at rate τt. The household has access to a perfect credit market, on which it can save and borrow at a constant interest rate r. We also assume that β(1 + r) = 1.
(A) Denoting the amount of savings in period t by bt , state the household’s period-t budget constraint.
(B) Using the period-t budget constraint from above, derive the household’s lifetime budget constraint and specify the transversality condition that you used to derive it. Assume that b-1 = 0.
(C) Set up the household’s maximization problem using λ to denote the Lagrange mul- tiplier on the lifetime budget constraint and calculate the relevant FOC(s).
(D) Solve for optimal consumption and labor supply, as functions of τt , wt , and model parameters.
(E) Is consumption constant over time? How about labor supply? Briefly explain.
Now let’s add the government. Suppose that the government in this economy has to finance a stream of expenditures {Gt } ∞t=0. It has access to a perfect credit market where it can borrow and lend at the same rate r as the household.
The government is benevolent and will choose the sequence of taxes {τt } ∞t=0 to max- imize the household’s total utility.
(F) Denoting the amount of government borrowing in period t by Bt , state the govern- ment’s period-t budget constraint.
(G) Using the period-t budget constraint from above, write down the government’s life- time budget constraint and specify the transversality condition that you used to derive it. Assume that B-1 = 0.
(H) Set up the government’s maximization problem using μ to denote the Lagrange multiplier on the lifetime budget constraint and calculate the relevant FOC(s).
(Hint: What is the government maximizing? Reread the problem!)
(I) Solve for the level of the optimal tax rate τ * , as a function of the exogenous model parameters.
(J) Is the optimal tax rate constant over time? Briefly explain.
2024-06-14