ECO 325 – Suppose that a consumer has income y

ECO 325 – Suppose that a consumer has income y

Subject: Economics    / General Economics
Question
University of Maryland
Department of Economics
Economics 325
Spring 2017
PROBLEM SET 3
50 POINTS
Please be kind to your TAs: Type or otherwise neatly write your answers. Make LARGE diagrams
and label everything clearly. Use colors if necessary. You can’t get points if the TAs can’t
understand your answers.
Due in class on Wednesday, Mar 15. No late submissions are accepted. Solutions will be posted
on Elms after the due date.
1. 15 POINTS. Suppose that a consumer has income y in the current period and income y’ in the future
period, and faces proportional taxes on income in both periods. That is, the consumer pays a tax ty
in the current period and t’y’ in the future period. The government wishes to collect tax revenue to
finance its spending g in the current period and g’ in the future period. The real interest rate is r.
a. Derive the consumer’s inter-temporal budget constraint.
b. Derive the government’s inter-temporal budget constraint.
c. Suppose that the government’s total spending does not change, but the government changes
the way it finances this spending, by increasing t and reducing t’. What effect, if any, does
the change in the tax rates have on the consumer’s choice of current and future
consumption, and on savings? Does Ricardian equivalence hold? Explain why or why not.
2. 15 POINTS. A consumer’s income in the current period is y=60, and income in the future period is
y=100. He pays lump-sum taxes of T=20 in the current period and T’=20 in the future period. His
utility function is u(c,c’ )=logc+?logc’. For simplicity, ?=1 and the real interest rate is r=0.
a. Set up and solve the consumer’s problem and find optimal c and c’, assuming that the
consumer is not credit constrained, i.e. he can borrow or save as much as he wants in the
current period: what are the expressions and numerical values for consumption today,
savings today and consumption tomorrow?
b. Suppose that government decides to give a tax cut on current taxes so that T decreases to 15
and T’ increases to 25. Redo the computation in part (a). Do optimal c and c’ change?
Explain why or why not with reference to Ricardian Equivalence.
c. Now suppose that consumers are credit constrained so that they can save as much as they
want in the current period but are unable to borrow at all (we must satisfy s>=0). Redo
parts (a) and (b). Are optimal c and c’ different? Explain why or why not with reference to
Ricardian Equivalence. 1 3. 20 POINTS. A consumer maximizes utility u(c, c’) by choosing c and c’, where c is the amount of
consumption in the current period, and c’ is the amount of consumption in the future period. The
consumer’s income in the current period is y, and income in the future period is y’. The consumer
pays lump-sum taxes T in the current period, and T’ in the future period. The real interest rate at
which the consumer can save is r>0.
The consumer is given two options. First, he can borrow at the interest rate r but can only borrow
up to a maximum amount x, where
x = we-y+T, where we = lifetime wealth.
Second, he can borrow an unlimited amount at the interest rate r’ > r.
This problem contrasts two alternative forms of credit market imperfections. As one possibility,
consumers may either borrow or lend at the same real interest rate r, but face a maximum amount
of borrowing. The alternative possibility allows unlimited borrowing, but the interest rate paid on
borrowing exceeds the interest rate earned from lending, r’ > r.
Clearly, consumers who choose to be lenders are unaffected by such constraints. We therefore only
need to be concerned about the behavior of borrowers.
Use diagrams to determine which option a borrower would choose, and explain your results. 2