Econ2123 Self-practice 1 Ch1-5

Econ2123 Self-practice 1 Ch1-5 Instructor: Prof. Wenwen Zhang TA: Mr. Ding Dong Chapter 2 1. Suppose you are measuring annual U.S. GDP by adding up the final value of all goods and services produced in the economy. Determine the effect on GDP of each of the following transactions. a. A seafood restaurant buys $100 worth of fish from a fisherman. b. A family spends $100 on a fish dinner at a seafood restaurant. c. Delta Air Lines buys a new jet from Boeing for $200 million. d. The Greek national airline buys a new jet from Boeing for $200 million. e. Delta Air Lines sells one of its jets to Jennifer Lawrence for $100 million. a. No change. This transaction is a purchase of intermediate goods. b. +$100: personal consumption expenditures c. +$200 million: gross private domestic fixed investment d. +$200 million: net exports e. No change. The jet was already counted when it was produced, i.e., presumably when Delta (or some other airline) bought it new as an investment. 2. An economy produces three goods: cars, computers, and oranges. Quantities and prices per unit for years 2009 and 2010 are as follows: 1

a. What is nominal GDP in 2009 and in 2010? By what percentage does nominal GDP change from 2009 to 2010? b. Using the prices for 2009 as the set of common prices, what is real GDP in 2009 and in 2009? By what percentage does real GDP change from 2009 to 2010? c. Using the prices for 2010 as the set of common prices, what is real GDP in 2009 and in 2010? By what percentage does real GDP change from 2009 to 2010? d. Why are the two output growth rates constructed in (b) and (c) different? Which one is correct? Explain your answer. a.2009 GDP: 10($2,000) + 4($1,000) + 1000($1) = $25,000 2010 GDP: 12($3,000) + 6($500) + 1000($1) = $40,000 Nominal GDP has increased by 60%. b. 2009 real (2009) GDP: $25,000 2010 real (2009) GDP: 12($2,000) + 6($1,000) + 1000($1) = $31,000 Real (2010) GDP has increased by 24%. c. 2009 real (2010) GDP: 10($3,000) + 4($500) + 1,000($1) = $33,000 2010 real (2010) GDP: $40,000. Real (2010) GDP has increased by 21.2%. d. The answers measure real GDP growth in different units. Neither answer is incorrect, just as measurement in inches is not more or less correct than measurement in centimeters. 3. Consider the economy described in Problem 2. a. Use the prices for 2009 as the set of common prices to compute real GDP in 2009 and in 2010. Compute the GDP deflator for 2009 and for 2010, and compute the rate of inflation from 2009 to 2010. b. Use the prices for 2010 as the set of common prices to compute real GDP in 2009 and in 2010. Compute the GDP deflator for 2009 and for 2010 and compute the rate of inflation from 2009 to 2010. c. Why are the two rates of inflation different? Which one is correct? Explain your answer. a. 2009 base year: Deflator(2009) = 1; Deflator(2010) = $40,000/$31,000 = 1.29 Inflation = 29% 2

b. 2010 base year: Deflator(2009) = $25,000/$33,000 = 0.76; Deflator(2010) = 1 Inflation = (1 0.76)/0.76 =.32 = 32% c. Analogous to 2d. Chapter 3 1. Balanced budget versus automatic stabilizers It is often argued that a balanced budget amendment would actually be destabilizing. To understand this argument, consider the economy with following behavioral equations: C = c 0 + c 1 Y D T = t 0 + t 1 Y Y D = Y T. a. Solve for equilibrium output. b. Solve for taxes in equilibrium. Suppose that the government starts with a balanced budget and that there is a drop in c 0. c. What happens to Y? What happens to taxes? d. Suppose that the government cuts spending in order to keep the budget balanced. What will be the effect on Y? Does the cut in spending required to balance the budget counteract or reinforce the effect of the drop in c 0 on output? (Don t do the algebra. Use your intuition and give the answer in words.) a. Y = [1/(1 c 1 + c 1 t 1 )][c 0 c 1 t 0 + I + G] b. T = t 0 + t 1 [1/(1 c1 + c1t1)][c 0 c 1 t 0 + I + G] c. Both Y and T decrease. d. If G is cut, Y decreases even more. A balanced budget requirement amplifies the effect of the decline in c 0. Therefore, such a requirement is destabilizing. 2. Taxes and transfers 3

Recall that we define taxes, T, as net of transfers. In other words, T = Taxes - Transfer Payments a. Suppose that the government increases transfer payments to private households, but these transfer payments are not financed by tax increases. Instead, the government borrows to pay for the transfer payments. Show in a diagram (similar to Figure 3-2) how this policy affects equilibrium output. Explain. b. Suppose instead that the government pays for the increase in transfer payments with an equivalent increase in taxes. How does the increase in transfer payments affect equilibrium output in this case? c. Now suppose that the population includes two kinds of people: those with high propensity to consume and those with low propensity to consume. Suppose the transfer policy increases taxes on those with low propensity to consume to pay for transfers to people with high propensity to consume. How does this policy affect equilibrium output? d. How do you think the propensity to consume might vary across individuals according to income? In other words, how do you think the propensity to consume compares for people with high income and people with low income? Explain. Given your answer, do you think tax cuts will be more effective at stimulating output when they are directed toward high-income or toward low-income taxpayers? Answers: a. In the diagram representing goods market equilibrium, the ZZ line shifts up. Output increases. b. There is no effect on the diagram or on output. c. The ZZ line shifts up and output increases. Effectively, the income transfer increases the propensity to consume for the economy as a whole. d. The propensity to consume is likely to be higher for low-income taxpayers. Therefore, tax cuts will be more effective at stimulating output if they are directed toward low-income taxpayers. 3. Investment and income This problem examines the implications of allowing investment to depend on output. 4

Chapter 5 carries this analysis much further and introduces an essential relation - the effect of the interest rate on investment - not examined in this problem. a. Suppose the economy is characterized by the following behavioral equations: C = c0 + c 1 Y D Y D = Y T I = b 0 + b 1 Y Government spending and taxes are constant. Note that investment now increases with output. (Chapter 5 discusses the reasons for this relation.) Solve for equilibrium output. b. What is the value of the multiplier? How does the relation between investment and output affect the value of the multiplier? For the multiplier to be positive, what condition must (c 1 + b 1 ) satisfy? Explain your answer. c. What would happen if (c 1 + b 1 ) 1? (Think about what happens in each round of spending). d. Suppose that the parameter b 0, sometimes called business confidence, increases. How will equilibrium output be affected? Will investment change by more or less than the change in b 0? Why? What will happen to national saving? a.y = C + I + G Y = [1/(1 c 1 b 1 )] [c 0 c 1 T + b 0 + G] b. Including the b 1 Y term in the investment equation increases the multiplier. Increases in autonomous spending now creates a multiplier effect through two channels: consumption and investment. For the multiplier to be positive, the condition c 1 + b 1 < 1 is required. c. When c 1 +b 1 is greater than one there is no multiplier effect. When total spending exceeds one the formula is nonsensical. The multiplier should be 1/(1 c 1 b 1 ). So, when c 1 + b 1 is greater than one the multiplier is negative, which does not make sense. Another way of looking at this concept is saving must equal investment so in a closed economy c 1 + b 1 can never be greater than one. d. Output increases by b 0 times the multiplier. Investment increases by the change in b 0 plus b 1 times the change in output. The change in business confidence leads 5

to an increase in output, which induces an additional increase in investment. Since investment increases, and saving equals investment, saving must also increase. The increase in output leads to an increase in saving. Chapter 4 1. Suppose that a person s yearly income is $60,000. Also suppose that this persons money demand function is given by M d = $Y (0.35 i) a. What is this person s demand for money when the interest rate is 5%? 10%? b. Explain how the interest rate affects money demand. c. Suppose that the interest rate is 10%. In percentage terms, what happens to this persons demand for money if the yearly income is reduced by 50%? d. Suppose that the interest rate is 5%. In percentage terms, what happens to this persons demand for money if the yearly income is reduced by 50%? Answers: a. i=0.05: money demand = $18,000 i=0.10: money demand = $15,000. b. Money demand decreases when the interest rate increases because bonds, which pay interest, become more attractive. c. The demand for money falls by 50%. d. The demand for money falls by 50%. 2. Suppose that money demand is given by M d = $Y (0.25 i) where $Y is $100. Also, suppose that the supply of money is $20. a. What is the equilibrium interest rate? b. If the Federal Reserve Bank wants to increase the equilibrium interest rate i by 10 percentage points from its value in part (a), at what level should it set the supply of money? 6

a. 20 = 25 100i Therefore, i=.05 or 5% b. M s = $10 = 100(0.25 0.15). Chapter 5 1. Consider first the goods market model with constant investment that we saw in Chapter 3. Consumption is given by C = c 0 + c 1 (Y T ) and I, G, and T are given. a. Solve for equilibrium output. What is the value of the multiplier? Now let investment depend on both sales and the interest rate: I = b 0 + b 1 Y b 2 i b.solve for equilibrium output. At a given interest rate,is the effect of a change in autonomous spending bigger than what it was in part (a)? Why? (Assume c 1 + b 1 < 1.) Next, write the LM relation as: M/P = d 1 Y d 2 i c. Solve for equilibrium output. (Hint: Eliminate the interest rate from the IS and LM relations.) Derive the multiplier (the effect of a change of one unit in autonomous spending on output). a. Y = [1/(1 c 1 )][c 0 c 1 T + I + G]. The multiplier is 1/(1-c1). b. Y = [1/(1 c 1 b 1 )][c 0 c 1 T + b 0 b 2 i + G] The multiplier is 1/(1 c 1 b 1 ). Since the multiplier is larger than the multiplier in part (a), the effect of a change in autonomous spending is bigger than in part (a). An increase in autonomous spending now leads to an increase in investment as well as consumption. c. Substituting for the interest rate in the answer to part (b), Y = [1/(1 c 1 b 1 + b 2 d 1 /d 2 )][c 0 c 1 T + b 0 + (b 2 /d 2 )(M/P ) + G]. 7

The multiplier is 1/(1 c 1 b 1 + b 2 d 1 /d 2 ). 2.Consider the following IS-LM model: C = 200 + 0.25Y D ; I = 150 + 0.25Y 1000i G = 250; T = 200 M d = 2Y 8000i; M s = 1600 a. Derive the IS relation. b. Derive the LM relation. c. Solve for equilibrium output. d. Solve for the equilibrium interest rate. e. Solve for the equilibrium values of C and I; and verify the value you obtained for Y by adding C, I, and G. f. Now suppose that the money supply increases to M/P = 1,840. Solve for Y, i, c, and T, and describe in words the effects of an expansionary monetary policy. g. Set M/P equal to its initial value of 1,600. Now suppose that government spending increases to G = 400. Summarize the effects of an expansionary fiscal policy on Y, i, and C. a. Y=C+I+G=200+.25(Y-200)+150+.25Y-1000i+250;; Y=1100-2000i; b. M/P=1600=2Y-8000i i=y/4000-1/5. c. Substituting from part (b) into part (a) gives Y=1000. d. Substituting from part (c) into part (b) gives i=5%. e. C=400; I=350; G=250; C+I+G=1000. f. Y=1040; i=3%; C=410; I=380. A monetary expansion reduces the interest rate and increases output. Consumption increases because output increases. Investment increases because output increases 8

and the interest rate decreases. g. Y=1200; i=10%; C=450; I=350. A fiscal expansion increases output and the interest rate. Consumption increases because output increases. Investment is affected in two ways: the increase in output tends to increase investment, and the increase in the interest rate tends to reduce investment. In this example, these two effects exactly offset one another, and investment does not change. THIS IS THE END OF SELF-PRACTICE QUESTION 1. 9