San Francisco State University Michael Bar ECON 302 Fall 206 Midterm Exam 2 Tuesday, November hour and 5 minutes Name: Instructions. This is closed book, closed notes exam. 2. No calculators of any kind are alloed. 3. Sho all the calculations, and explain your steps. 4. If you need more space, use the back of the page. 5. Fully label all graphs.
. (50 points. Consider the Classical model studied in class, and briefly described as follos. The consumer derives utility from consumption C and leisure l according to U ( C, l α lnc + ( α lnl. He is endoed ith h hours hich he can allocate beteen leisure and ork S. The real age is. The consumer ons a firm and receives dividend income (profit. The firm produces output Y using technology Y, here A is productivity parameter (TFP, K is the capital oned by the firm, and is labor employed by the firm. The government taxes labor income at the rate of t and dividend income at the rate of t, and spends its tax revenue on consumption G. a. Write the consumer s utility maximization problem. Consumer s problem maxα ln C + ( αln l C, l s. t. C ( h l( t + ( t b. erive the consumer's demand for consumption and leisure using the results from Microfoundations. Explain your steps briefly. We rerite the budget constraint in the form of px x + py y I : C + t l h( t + ( t ( Explanation: From Microfoundations, e kno that consumers ith these Cobb-ouglas preferences, spend a fraction α of their income on C and a fraction a of their income on l. Thus, the demand is: emand for consumption: C α[ h( t + ( t ] emand for leisure: l ( α [ h( t + ( t ] ( t ( t ( α h + ( t
c. Based on your results from the previous section, rite the consumer s labor supply. abor supply: or S S h l h ( α ( t αh ( α ( t ( t h + ( t d. Illustrate graphically the impact on the labor supply curve of an increase in real age (, and provide economic intuition for it. S Real after-tax age, ( t, is the price of leisure, hich had gone up. As a result, the consumer ants to consume less leisure, i.e. ork more. 2
3 e. Write the firm s profit maximization problem. max f. Solve for the firm s demand for labor and the firm s profit. The first order necessary condition for profit maximization: 0 ( Thus, / ( ( The profit: (
g. Illustrate graphically the impact on the labor demand curve of an increase in real age, and provide economic intuition for it. With higher age, the firm ants to employ less labor. Remember that competitive firm employs labor up to the point here the marginal product of labor is equal to the age. Since the marginal product is decreasing, higher age can be paid only hen feer orkers are employed. 4
h. Suppose that the economy of Haiti is described by the classical model. Using fully labeled graphs of the production function and labor market, illustrate the effect of destruction of physical capital by a Hurricane Matthe ( K on equilibrium output ( Y, equilibrium real age ( and equilibrium employment (. Y Y Production function Y 2 S abor market 2 5
i. Continuing ith the givens in previous section, hat is the predicted impact of the hurricane on unemployment rate in Haiti? Briefly explain your anser. The classical model assumes that labor supply labor demand at all times, and therefore, by assumption, the unemployment rate is alays zero (before and after the hurricane. 6
2. (20 points. Consider the Keynesian model discussed in class. Suppose that the economy is characterized by the folloing behavioral functions: Consumption: C C0 + MPC( Y T Investment: I I0 Government spending: G G0 Taxes: T T 0 + ty In all the questions belo, assume that Y < Y f. a. Solve for the Keynesian equilibrium in the goods market. Y E Y C0 + MPC( Y T0 ty + I 0 + G 0 C Y MPC( t Y C0 MPC T C0 MPC T0 + I0 + G0 Y MPC( t I 0 G + I 0 + G 0 b. Suppose that the Keynesian multiplier is m k 3. Find the change in equilibrium output resulting from a decrease in investment by 30 units. In your anser you must sho the formula used, before plugging the numbers. Y mk I 0 3 ( 30 90 7
c. Suppose that the Keynesian multiplier is m 4 and the proportional tax rate is t 0.25. The government is planning to stimulate the economy through higher spending G 00. The opposition leader claims that such spending ill lead to tremendous increase in government budget deficit. o you agree? In your anser calculate the effect of the proposed policy on the government budget deficit ( ef G T. k ef G T G t Y G t mk G 00 0.25 4 00 0 The opposition leader is rong. ue to the large multiplier, the government policy ill increase the equilibrium output by 400, and as a result, its tax revenue ill increase as ell (by 25% of output. Thus, the net effect on deficit is zero. Remark: the above results are based on the specific version of the Keynesian model, ith madeup numbers. If the multiplier as smaller, the opposition leader ould have been right. d. On a fully labeled graph illustrate the Keynesian equilibrium in the goods market before and after the fiscal policy in the last section. E E Y E C + I + G 45 0 Y 8
3. (5 points. The folloing table contains data from the labor market of some country (in millions. Civilian noninstitutional population 40 Civilian labor force 00 Employed 90 Unemployed 0 Not in the labor force 40 a. Complete the above table. b. Find the percentage unemployment rate in this country. # Unep 0 Unemp. Rate 0% # abor Force 00 c. Suppose that half of the unemployed in this economy decided to stop searching for jobs. As a result, the unemployment rate ill increase/decrease. Circle the correct anser and provide a brief proof. Both the unemployed and labor force decrease by 5. Thus, # Unep 5 Unemp. Rate < 0% # abor Force 95 Proof of the last inequality. 0% unemployment rate ould mean 9.5 unemployed, and 5 < 9.5. Another ay to prove that unemployment rate declined is to state that the numerator decreased by 50% (from 0 to 5, hile the denominator decreased only by 5% (from 00 to 95, so the fraction must decline. 9
4. (5 points. Consider the search model of unemployment, briefly described as follos. Unemployed Employed Fraction in population U U Utility V u ( b, p, t b V e (, s, t + b unemployment insurance benefit p probability of receiving a job offer t tax on b b + + real age s separation rate (probability of loosing the job t tax on The symbols + under variable of the utility function indicates the assumption that the utility is increasing in that variable, and under a variable indicates that the utility is decreasing in that variable. istribution of age offers: H ( gives the probability that an offer is at least. a. Illustrate ith 3 fully labeled graph the impact of an increase in probability of getting a job offer ( p on: ( reservation age, (2 probability of acceptance of job offers H (, and (3 steady-state unemployment rate U. 0
U t i l i t y s? U
b. Briefly discuss the economic intuition of the results you presented in the previous section. Higher probability of accepting an offer is an incentive for the unemployed to stay unemployed and ait for higher age offer. This leads to higher reservation age. Thus, there are to opposite effects on equilibrium unemployment rate: (i more unemployed receive offers, and (ii feer of them accept offers. Which effect is stronger is a quantitative question. 2