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594-problems - Collection of Practice Problems Econ 204A...

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1 Collection of Practice Problems Econ 204A Henning Bohn * In previous years, students have often asked me about practice problems in addition to the problem sets. Here is a collection. A subset will be assigned for the weekly problem sets. I hope the others are useful for practice. Request : Please tell me about errors or ambiguities. Many of the questions below are old exam problems. As I am updating the course over the years, the notation, references, and sequencing has changed, which means that some old problems may have lost educational value without me noticing immediately. So if a problem seems obscure to you, please let me know. (Your incentive: your problem set might shrink if you convince me a problem is unclear.) Part 1 : 1. Consider the two-period consumption model: Individuals have initial assets A, earn interest r on assets, and earn wage income ( w 1 , w 2 ) . They maximize utility U = u ( c 1 ) + β u ( c 2 ) . a. Assume u ( c ) = ln( c ) . i. Solve for optimal consumption and period-1 asset holdings as functions of wage income, the interest rate, and the time-discount factor β . Discuss under what conditions higher interest rates reduce consumption. [Discuss means: Interpret the solution. Conditions may be exact, or necessary, or sufficient. Hint: Distinguish cases with w 2 = 0 vs. w 2 > 0 .] ii. Show that the dependence of period-1 consumption on ( y 1 d , y 2 d ) can be expressed in terms of permanent income. b. Assume u ( c ) = 1 1 γ c 1 γ where γ > 0, γ 1 . Do the same as in (a). In the discussion, identify which results apply for all γ , and which ones only for γ greater or less than one. 2. Consider the permanent income model with n periods. Assume β =1/(1+r). Assume initial assets are zero (A=0). To answer questions about taxes, interpret w as wage income net of taxes. This question is intended to give you a quantitative perspective. (Hint: Use a spreadsheet.) a. Assume the real interest rate is 3% per year. Assume the time horizon is n=50 years (about the life expectancy of males age 25 or females age 30). Determine the marginal propensity to consume (MPC=dc/dw) from (i) a one-year wage increase; (ii) an increase in wages that lasts 5 years; (iii) and a wage increase that last for 35 years * Provided online for use by UCSB students. (C) Copyright 2009 Henning Bohn
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2 [intuition: until about retirement]; (iv) a tax reduction for one year followed by a tax increase of the same size in the next year. Discuss: How do the results compare? Do you find them surprising? Realistic? Why or why not? b. Assume the real interest rate is again 3% per year. Determine the impact of a one-year tax cut for consumers with alternative planning horizons of, respectively, n=1 year; n=2 years; n=10 years; n=50 years; the limiting case of n=infinity. Discuss: How do the results compare? Do you find them surprising? Realistic? Why or why not?
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