Midterm Exam 1. Tuesday, September hour and 15 minutes. Name: Answer Key

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1 Macroeconomics ECON 302 San Francisco State niversit Michael Bar Fall 2011 Midterm Eam 1 Tuesda Setember 27 1 hour and 15 minutes Name: Answer Ke Instructions 1. This is closed book closed notes eam. 2. No calculators of an kind are allowed. 3. Show all the calculations. 4. If ou need more sace use the back of the age. 5. Full label all grahs. Good uck

2 1. 15 oints. The net grah shows the ln of the.s. national debt over the 30 ears eriod a. Based on the above grah circle the correct answer: i. The ln of debt growing at constant rate ii. The debt is growing at increasing rate iii. The debt is growing at constant rate iv. The debt is growing at decreasing rate b. Provide a brief one sentence elanation for our chosen answer in the revious section. The lndebt is a linear function of time. c. Based on the above grah what is the aroimate average growth rate of the debt over the given eriod? Show our calculations The sloe of lndebt is aroimatel equal to the growth rate of the debt: g DEBT % er ear

3 2. 15 oints. Suose that GDP in the.s. is twice a large as that of China. Also suose that the.s. GDP is not growing at all while Chinese GDP grows at 7% er ear. a. How man ears would it take China to catch u with the.s. in terms of GDP? Instructions: simlif our equations u to the oint when ou must use a calculator. GDP 2GDP 2 1 t t 1 0 GDPCHN t GDPCHN t 0.07 ln2 t ln1.07 t S CHN ln2 ln1.07 b. sing the "rule of 70" give aroimate answer to the revious question. 70 t 10 7 ears c. sing the "rule of 70" again how man ears aroimatel would it take China to catch u with the.s. if the.s. GDP grows at 3.5% er ear? 70 t ears Now China is catching u with the.s. at 3.5% rate. 2

4 3. 10 oints. The net table rovides data on rices and outut in some artificial econom for the ears The goods are labeled 1 and 2 so that P P Q Q are rices and quantities of the two goods resectivel Year P 1 Q 1 P 2 Q a. Calculate the growth rate of real GDP between the ears 2000 and 2001 using 2000 as the base ear. RGDP The net growth rate is zero: RGDP RGDP RGDP g RGDP RGDP 2001 RGDP 1 0 Notice that this result is not surrising since there is no growth in outut of the two goods b. Calculate the inflation rate between the ears 2000 and 2001 using 2000 as the base ear. Nominal GDP in 2001: GDP Price level in 2001: GDP P 2001 RGDP Price level in 2000: P rice level in the base ear is alwas 1 Inflation between 2000 and 2001: P % P

5 4. 10 oints. The net table resents data from the National Income and Product accounts of some countr. Personal Consumtion Eenditures 6000 Gross Investment 2000 Government Consumtion Eenditures 1500 Eorts 500 Imorts 1000 Comensation of Emloees 5000 Net Interest 1000 Rental Income 500 Prorietors income 500 Cororate rofits 600 Indirect business ta net of subsidies 500 Consumtion of fied caital 1000 Statistical Discreanc -100 a. Based on the above data calculate the GDP using the eenditure aroach. GDP EX C I G X IM b. Calculate the GDP using the Income aroach. Self check: I rovided the number for the statistical discreanc so ou can check that our calculations are correct. The statistical discreanc is the difference between the GDP calculated b eenditure aroach and the GDP calculated b the income aroach. GDP INC W Int Re nt Ti De P B 4

6 oints. Suose that consumer derives utilit from two goods X and Y and has a utilit function u. The rices of goods are P P and his income is I. a. Write the consumer's otimization roblem. I s t u.. ma b. Write the agrange function associated with the consumer's otimization roblem. I u c. Derive the mathematical condition for otimal consumtion bundle assuming that indifference curves are conve. The first order conditions for the above agrange function: 0 0 Dividing the two conditions: d. Give a verbal interretation of the above condition. Interretation 1: The left hand side is the sloe in absolute value of the indifference curve and the right hand side is the sloe in absolute value of the budget constraint. Thus at the otimum the indifference curve is tangent to the budget constraint. Interretation 2: The above condition can be written as P The left hand side is the utilit generated b etra dollar sent on X and the right hand side is the utilit from etra dollar sent on Y. The otimal allocation of income between the two goods requires that those should be the same.

7 e. Illustrate the condition ou derived in art c with a grah of the budget constraint and indifference curve. Otimal consumtion Bundle f. Suose that the utilit function is consumer's demand functions u. Write the * * 0.5 I I 0.5 g. Suose that the utilit function is v 40. This consumer sends 40 ercent of his income on good X and 60 ercent of his income on Y regardless of the rices of these goods and regardless of his income. True/False circle the correct answer and rovide a brief elanation. This utilit function is obtained b aling a monotone increasing transformation to u which we know leads to the demand in the last section and imlies 2 sending 50% of income on each good. The transformation is: v 40u Thus the utilit functions u and v 40 ield the same demand functions and iml sending equal fractions of income 50% on each good. 6

8 6. 15 oints. Suose that a firm oerates a technolog given b the following roduction function F K 100K. a. Prove that this technolog ehibits constant returns to scale. F K 100 K 100 K 100K F K b. Derive the marginal roducts of caital and labor. MP MP K F K K F 100K 1 K 1 100K c. Prove that in erfect cometition if being a rice taker the above firm as 30% of it's outut to caital and 70% of it's outut to labor. A rice-taking firm as the inuts their marginal roduct r MPK w MP 1 The ament to caital: r K 100K K 100K 0. 3Y 1 The ament to labor: w 100K 100K 0. 7Y 7