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EC202 – Macroeconomics

Koç University, Summer 2014

by Arhan Ertan

Study Questions - 3

1. Suppose a government is able to permanently reduce its budget deficit. Use the Solow growth

model of Chapter 9 to graphically illustrate the impact of a permanent government deficit reduction on the steady-state capital–labor ratio and the steady-state level of output per worker. Be sure to label the: a. axes; b. curves; c. initial steady-state levels; d. terminal steady-state levels; and e. the direction curves shift.

2. Suppose a government is able to impose controls that limit the number of children people can

have. Use the Solow growth model of Chapter 9 to graphically illustrate the impact of the slower rate of population growth on the steady-state capital–labor ratio and the steady-state level of output per worker. Be sure to label the: a. axes; b. curves; c. initial steady-state levels; d. terminal steady-state levels; and e. the direction curves shift.

3. Two countries, Highland and Lowland, are described by the Solow growth model. Both countries

are identical, except that the rate of labor-augmenting technological progress is higher in Highland than in Lowland. a. In which country is the steady-state growth rate of output per effective worker higher? b. In which country is the steady-state growth rate of total output higher? c. Does the Solow growth model predict that the two economies will converge to the same

steady state?

4. Based on the Solow growth model with population growth and labor-augmenting technological

progress, explain how each of the following policies would affect the steady-state level and steady-state growth rate of total output per person: a. a reduction in the government's budget deficit b. grants to support research and development c. tax incentives to increase private saving d. greater protection of private property rights

5. Explain how the Solow growth model differs from models of endogenous growth with respect to:

a. the sources of technological progress. b. returns to capital.

6. Income per person exceeds $25,000 in many countries, but it is below $1,000 per person in

many other countries. Based on the Solow growth model, suggest at least four possible explanations for this gap in living standards.

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7. The Solow model with population growth and labor-augmenting technological progress predicts balanced growth in the steady state. Growth rates of which variables are predicted to be balanced (i.e., will be equal) in the steady state?

8. What is the difference between convergence and conditional convergence with respect to

predictions of the Solow growth model? Explain. 9. Assume that the long-run aggregate supply curve is vertical at Y = 3,000 while the short-run

aggregate supply curve is horizontal at P = 1.0. The aggregate demand curve is Y = 2(M/P) and M = 1,500. a. If the economy is initially in long-run equilibrium, what are the values of P and Y? b. If M increases to 2,000, what are the new short-run values of P and Y? c. Once the economy adjusts to long-run equilibrium at M = 2,000, what are P and Y?

10. Assume that the long-run aggregate supply curve is vertical at Y = 3,000 while the short-run

aggregate supply curve is horizontal at P = 1.0. The aggregate demand curve is Y = 3(M/P) and M = 1,000. a. If the economy is initially in long-run equilibrium, what are the values of P and Y? b. Now suppose a supply shock moves the short-run aggregate supply curve to P = 1.5. What

are the new short-run P and Y? c. If the aggregate demand curve and long-run aggregate supply curve are unchanged, what

are the long-run equilibrium P and Y after the supply shock? d. Suppose that after the supply shock the Fed wanted to hold output at its long-run level.

What level of M would be required? If this level of M were maintained, what would be long-run equilibrium P and Y?

11. The principal method used by the Federal Reserve to change the money supply is through

open-market operations. Use the aggregate demand–aggregate supply model to illustrate graphically the impact in the short run and the long run of a Federal Reserve decision to increase open-market purchases. Be sure to label: i. the axes; ii. the curves; iii. the initial equilibrium values; iv. the direction the curves shift; v. the short-run equilibrium values; and vi. the long-run equilibrium values. State in words what happens to prices and output in the short run and the long run.

12. Suppose that laws are passed banning labor unions and that resulting lower labor costs are

passed along to consumers in the form of lower prices. Use the aggregate demand–aggregate supply model to illustrate graphically the impact in the short run and the long run of this favorable supply shock. Be sure to label: i. the axes; ii. the curves; iii. the initial equilibrium values; iv. the direction the curves shift; v. the short-run equilibrium values; and vi. the long-run equilibrium values. State in words what happens to prices and output in the short run and the long run.

13. The economy of Macroland is initially in long-run equilibrium. A severe drought causes an

adverse supply shock. a. What happens to prices and output in the short run? b. What would happen to prices and output in the long run if there is no policy

accommodation? c. If the Central Bank of Macroland wants to prevent the short-run changes in price and

output, what policy action could it take? How would the results of this policy action differ from the prices and output that would result in the long run with no policy action?

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14. A central bank reduces the money supply in an economy initially in long-run equilibrium. a. What will happen to output and prices in the short run? b. What will happen to unemployment in the short run? c. What will happen to output and prices in the long run?

15. An oil cartel effectively increases the price of oil by 100 percent, leading to an adverse supply

shock in both Country A and Country B. Both countries were in long-run equilibrium at the same level of output and prices at the time of the shock. The central bank of Country A takes no stabilizing policy actions. After the short-run impacts of the adverse supply shock become apparent, the central bank of Country B increases the money supply to return the economy to full employment. a. Describe the short-run impact of the adverse supply shock on prices and output in each

country. b. Compare the long-run impact of the adverse supply shock on prices and output in each

country.

16. An economy is initially in long-run equilibrium. The introduction of an electronic payments

system dramatically reduces the demand for money in the economy. a. What is the short-run impact on prices and output of the new system? b. What can the central bank do, if anything, to counteract the short-run changes in output

and prices? c. If the central bank does not take any policy actions, what will be the long-run impact of the

electronic payments system on prices and output?

17. Explain the meaning of monetary neutrality and illustrate graphically that there is monetary

neutrality in the long run in the aggregate demand–aggregate supply model. Be sure to label: i. the axes; ii. the curves; iii. the initial equilibrium values; iv. the direction the curves shift; v. the short-run equilibrium values; and vi. the long-run equilibrium values. Explain in words what your graph illustrates.

18. You are given information about the following leading indicators. For each indicator explain

whether the information suggests that a recession or expansion should be expected in the future. a. Average initial weekly claims for unemployment insurance rise. b. New building permits issued increases. c. The interest rate spread between the 10-year Treasury note and the 3-month Treasury bill

narrows. d. The Index of Supplier Deliveries falls.

19. Consider a closed economy to which the Keynesian-cross analysis applies. Consumption is given

by the equation C = 200 + 2/3(Y – T). Planned investment is 300, as are government spending and taxes. a. If Y is 1,500, what is planned spending? What is inventory accumulation or decumulation?

Should equilibrium Y be higher or lower than 1,500? b. What is equilibrium Y? (Hint: Substitute the values of equations for planned consumption,

investment, and government spending into the equation Y = C + I + G and then solve for Y.) c. What are equilibrium consumption, private saving, public saving, and national saving? d. How much does equilibrium income decrease when G is reduced to 200? What is the

multiplier for government spending?

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20. Assume that the consumption function is given by C = 200 + 0.5(Y – T) and the investment function is I = 1,000 – 200r, where r is measured in percent, G equals 300, and T equals 200. a. What is the numerical formula for the IS curve? (Hint: Substitute for C, I, and G in the

equation Y = C + I + G and then write an equation for Y as a function of r or r as a function of Y.) Express the equation two ways.

b. What is the slope of the IS curve? (Hint: The slope of the IS curve is the coefficient of Y when the IS curve is written expressing r as a function of Y.)

c. If r is one percent, what is I? What is Y? If r is 3 percent, what is I? What is Y? If r is 5 percent, what is I? What is Y?

d. If G increases, does the IS curve shift upward and to the right or downward and to the left?

21. Assume that the equilibrium in the money market may be described as M/P = 0.5Y – 100r, and

M/P equals 800. a. Write the LM curve two ways, expressing Y as a function of r and r as a function of Y. (Hint:

Write the LM curve only relating Y and r; substitute out M/P.) b. What is the slope of the LM curve? c. If r is 1 percent, what is Y along the LM curve? If r is 3 percent, what is Y along the LM

curve? If r is 5 percent, what is Y along the LM curve? d. If M/P increases, does the LM curve shift upward and to the left or downward and to the

right? e. If M increases and P is constant, does the LM curve shift upward and to the left or

downward and to the right? f. If P increases and M is constant, does the LM curve shift upward and to the left or

downward and to the right?

22. a. Suppose Congress decides to reduce the budget deficit by cutting government spending.

Use the Keynesian-cross model to illustrate graphically the impact of a reduction in government purchases on the equilibrium level of income. Be sure to label: i. the axes; ii. the curves; iii. the initial equilibrium values; iv. the direction the curve shifts; and v. the terminal equilibrium values.

b. Explain in words what happens to equilibrium income as a result of the cut in government spending and the time horizon appropriate for this analysis.

23. a. Use the Keynesian-cross model to illustrate graphically the impact of an increase in the

interest rate on the equilibrium level of income. Be sure to label: i. the axes; ii. the curves; iii. the initial equilibrium values; iv. the direction the curve shifts; and v. the terminal equilibrium values.

b. Explain in words what happens to equilibrium income as a result of the increase in the interest rate.

24. a. Graphically illustrate the impact of an open-market purchase by the Federal Reserve on the

equilibrium interest rate using the theory of liquidity preference and the market for real money balances. Be sure to label: i. the axes; ii. the curves; iii. the initial equilibrium values; iv. the direction the curve shifts; and v. the terminal equilibrium values.

b. Explain in words what happens to the equilibrium interest rate as a result of the open-market purchase.

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25. a. As an economy moves into a recession, income falls. Illustrate graphically the impact of a decrease in income on the equilibrium interest rate using the theory of liquidity preference and the market for real money balances. Be sure to label: i. the axes; ii. the curves; iii. the initial equilibrium values; iv. the direction the curve shifts; and v. the terminal equilibrium values.

b. Explain in words what happens to the equilibrium interest rate as a result of the fall in income.

26. Two identical countries, Country A and Country B, can each be described by a Keynesian-cross

model. The MPC is 0.9 in each country. Country A decides to increase spending by $2 billion, while Country B decides to cut taxes by $2 billion. In which country will the new equilibrium level of income be greater?

27. a. The interest rate affects which variable in: (1) the market for goods and services and (2) the

market for real money balances? b. The level of income affects which variable in: (1) the market for goods and services and (2)

the market for real money balances?

28. Compare the predicted impact of an increase in the money supply in the liquidity preference

model versus the impact predicted by the quantity theory and the Fisher effect. Can you reconcile this difference?

29. Assume the following model of the economy, with the price level fixed at 1.0:

C = 0.8(Y – T) T = 1,000 I = 800 – 20r G = 1,000 Y = C + I + G Ms/P = Md/P = 0.4Y – 40r Ms = 1,200 a. Write a numerical formula for the IS curve, showing Y as a function of r alone. (Hint:

Substitute out C, I, G, and T.) b. Write a numerical formula for the LM curve, showing Y as a function of r alone. (Hint:

Substitute out M/P.) c. What are the short-run equilibrium values of Y, r, Y – T, C, I, private saving, public saving,

and national saving? Check by ensuring that C + I + G = Y and national saving equals I. d. Assume that G increases by 200. By how much will Y increase in short-run equilibrium?

What is the government-purchases multiplier (the change in Y divided by the change in G)? e. Assume that G is back at its original level of 1,000, but Ms (the money supply) increases by

200. By how much will Y increase in short-run equilibrium? What is the multiplier for money supply (the change in Y divided by the change in Ms)?

30. Suppose Congress wishes to reduce the budget deficit by reducing government spending. Use

the IS–LM model to illustrate graphically the impact of the reduction in government spending on output and interest rates. Be sure to label: i. the axes; ii. the curves; iii. the initial equilibrium values; iv. the direction the curves shift; and v. the terminal equilibrium values.

31. Use the IS–LM model to illustrate graphically the impact on output and interest rates of a

one-time increase in the price level due to a large increase in oil prices. Be sure to label: i. the axes; ii. the curves; iii. the initial equilibrium values; iv. the direction the curves shift; and v. the terminal equilibrium values.

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32. Use the IS–LM model to illustrate graphically the impact of the Pigou effect on the equilibrium level of income and interest rate during the Great Depression, when prices were falling.

33. Assume that initially everyone expects the price level to stay the same. Now the Federal

Reserve announces that it will increase the rate of money growth in one year. People now expect inflation. Use the IS–LM model to illustrate graphically the impact of expected inflation on the level of output and on the real and nominal interest rates.

34. Two identical countries, Alpha and Beta, can be described by the IS–LM model in the short run.

The governments of both countries cut taxes by the same amount. The Central Bank of Alpha follows a policy of holding a constant money supply. The Central Bank of Beta follows a policy of holding a constant interest rate. Compare the impact of the tax cut on income and interest rates in the two countries.

35. Compare the impact of a tax cut on consumption, investment, output, and interest rates in the

classical model of Chapter 3 versus the IS–LM model. 36. a. An economy is initially at the natural level of output. There is an increase in government

spending. Use the IS–LM model to illustrate both the short-run and long-run impact of this policy change. Be sure to label: i. the axes; ii. the curves; iii. the initial equilibrium, iv. the short-run equilibrium, and v. the terminal equilibrium.

b. Explain in words the short-run and long-run impact of the change in government spending on output and interest rates.

37. Assume the economy is initially in a short-run equilibrium at a level of output below the natural

rate. a. Use the IS–LM model to graphically illustrate: (1) how the economy will adjust in the

long-run if the no policy action is taken; and (2) the long-run equilibrium if fiscal policy is used to return the economy to the natural rate of output.

b. Explain how investment, the interest rate, and the price level differ in the new long-run equilibrium in the two cases.

38. Use the IS–LM model to predict the short-run impact on the interest rate and output if the Fed

pushes interest rates down at the same time that both consumption and investment fall due to a financial crisis. Illustrate your answer graphically. Be sure to label: i. the axes; ii. the curves; iii. the initial equilibrium; and iv. the direction the curves shift. Explain your answer in words.

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Answer Key

1.

2.

3. a. The steady-state growth rate of output per effective worker is zero in both countries.

b. The steady-state growth rate of total output will be higher in Highland because of the higher rate of technological progress.

c. No, the Solow growth model predicts that the economies will converge to different steady states because they have different rates of technological progress.

4. a. The reduction in the budget deficit increases the saving rate, which will increase the steady-state level of output per person, but not alter the steady-state growth rate of output per person.

b. Grants to support research and development may improve the rate of technological progress, which will increase the steady-state level and growth rate of output per person.

c. Greater private saving increases the saving rate, which will increase the steady-state level of output per person, but not alter the steady-state growth rate of output per person.

d. Greater protection of property rights may be an institutional improvement that improves the rate of technological progress, which will increase the steady-state level and growth rate of output per person.

5. a. The Solow growth model assumes technological growth exists, while endogenous growth models try to explain where technological progress comes from.

b. The Solow growth model assumes diminishing returns to capital, while endogenous growth models assume constant returns to capital.

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6. Possible explanations include: richer countries have higher saving rates, lower population growth rates, lower capital-depreciation rates, higher rates of technological progress, or institutions that better facilitate economic growth.

7. Output per worker, capital per worker, and the real wage will all grow at rate g, the growth rate of technological progress in the steady state. Output per effective worker, capital per effective worker, the capital–output ratio, and the real rental return on capital will all be constant in the steady state.

8. Convergence applies to economies with the same saving rate, population growth rate, depreciation rate, rate of technological progress, and production function. These economies will converge to the same steady state according to the Solow growth model, with the same level of output per worker, capital per worker, and growth rates (even if the levels were initially different). Conditional convergence applies to economies with different saving rates, population growth rates, depreciation rates, rates of technological progress, and/or production functions. These economies will move to different steady state equilibria with different levels of output per worker, capital per worker, and growth rates determined by the key variables.

9. a. P = 1.0; Y = 3,000 b. P = 1.0; Y = 4,000 c. P = 1.333; Y = 3,000

10. a. P = 1.0; Y = 3,000 b. P = 1.5; Y = 2,000 c. P = 1.0; Y = 3,000 d. M = 1,500; P = 1.5; Y = 3,000

11.

In the short run, output increases, while the price level remains unchanged. In the long run, prices increase and output returns to the full-employment level.

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12.

In the short run output increases, while the price level decreases. In the long run, prices increase and output returns to the full-employment level.

13. a. In the short run, prices increase and output decreases. b. With no policy accommodation, both output and prices would return to their initial

long-run equilibrium levels. c. The central bank could increase the money supply to return output to full employment, but

this would result in a long-run equilibrium at a higher price level than the initial long-run equilibrium.

14. a. In the short run, output would decrease with little change in prices. b. In the short run, unemployment will increase. c. In the long run, output will return to the full-employment level at a lower price level.

15. a. In both Country A and Country B, output will decline and the price level will rise. b. In the long run, output in both Country A and Country B will return to the full-employment

level, but the price level will be higher in Country B than in Country A because of the policy accommodation.

16. a. In the short run, output will increase as the reduction in money demand (increase in velocity) shifts the aggregate demand curve out to the right. There will be an increase in output and little change in prices in the short run.

b. The central bank could counteract the decline in money demand by reducing the money supply, shifting the aggregate demand curve back to the left.

c. In the long run with no central bank stabilizing action, output will return to the full-employment level with a higher price level.

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17.

Monetary neutrality is the property that changes in money do not change real variables. Graphically starting from long-run equilibrium at A, an increase in the money supply shifts the AD curve rightward. There is a short run equilibrium at B with higher real output, but in the long run, prices increase, shifting the SRAS upward until the new long-run equilibrium is reached at C, where there is a higher price level, but no change in real GDP. This illustrates that in the long-run the change in the money supply does not change the real variable (real GDP).

18. a. Recession. More workers eligible for unemployment insurance benefits indicate that firms are laying off workers and cutting back on production.

b. Expansion. Planned investment is increasing. c. Recession. Future interest rates are not expected to rise, which typically occurs in a

recession. d. Recession. Few firms are experiencing slow deliveries, indicating that output and

production is slow.

19. a. Planned spending is 1,600. Inventory de-cumulation is 100. Equilibrium Y should be higher than 1,500.

b. Equilibrium Y is 1,800. c. Consumption is 1,200, private saving is 300, public saving is 0, and national saving is 300. d. Equilibrium Y decreases by 300. The multiplier is 3.

20. a. Y = 2,800 – 400r or r = 7 – 0.0025Y. b. The slope of the IS curve is –0.0025. c. If r is 1 percent, I is 800 and Y is 2,400. If r is 3 percent, I is 400 and Y is 1,600. If r is 5

percent, I is 0 and Y is 800. d. IS shifts upward and to the right.

21. a. Y = 1,600 + 200r, or r = –8 + 0.005Y. b. The slope of the LM curve is 0.005. c. If r is 1 percent, Y is 1,800. If r is 3 percent, Y is 2,200. If r is 5 percent, Y is 2,600. d. The LM curve shifts downward and to the right. e. The LM curve shifts downward and to the right. f. The LM curve shifts upward and to the left.

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22. a.

b. The equilibrium level of income falls. This analysis is appropriate in the short run when

prices and the interest rate are constant.

23. a.

b. The equilibrium level of income falls.

24. a.

b. The equilibrium interest rate falls.

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25. a.

b. The equilibrium interest rate falls.

26. Income in Country A will increase more. The government-spending multiplier in Country A equals 10, so income in Country A will increase by $20 billion. The tax multiplier in Country B equals 9, so income in Country B will only increase by $18 billion.

27. a. The interest rate affects (1) investment in the market for goods and services, and (2) the demand for money in the market for real money balances.

b. The level of income affects (1) consumption in the market for goods and services, and (2) the demand for money in the market for real money balances.

28. The liquidity preference model predicts that an increase in the money supply will decrease interest rates. The quantity theory predicts that an increase in the money supply will increase inflation, which, via the Fisher effect, will increase the nominal interest rate. The liquidity preference model emphasizes the short-run effect when prices are fixed, while the quantity theory and Fisher effect are long-run effects when prices are flexible.

29. a. Y = 5,000 – 100r. b. Y = 3,000 + 100r. c. In the short-run equilibrium, Y = 4,000; r = 10; Y – T = 3,000; C = 2,400; I = 600; private

saving is 600; public saving is 0; and national saving is 600. d. Y increases by 500. The government spending multiplier is 2.5. e. Y increases by 250. The multiplier for money supply is 1.25.

30.

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31.

32.

Income increases because the falling prices increase money balances, thus making consumers feel wealthier. The increase in wealth causes consumers to consume more, thereby shifting the IS curve to the right. Income also increases because the decrease in prices increases real money balances, which shifts the LM curve to the right. The impact on interest rates is indeterminate.

33.

The increase in expected inflation increases output and the nominal interest rate, and lowers the real interest rate.

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34. The interest rate will increase in Alpha, but remain constant in Beta. The increase in output will be larger in Beta because the Central Bank of Beta will increase the money supply to keep the interest rate constant in the face of the tax cut. Thus, there will be no crowding out of investment in Beta, but there will be crowding out in Alpha because of the higher interest rate.

35. Output increases in the IS–LM model, but it is fixed at the natural level in the classical model because it is determined by the factors of production and technology. In both models, consumption increases because the tax cut increases disposable income. The interest rate increases in both models. In the classical model, the tax cut reduces saving, which increases the interest rate and reduces the equilibrium quantity of investment. In a closed classical economy, since income is fixed, the increase in consumption exactly offsets the decrease in investment. In the IS–LM model, the increase in income increases money demand, which results in a higher interest rate to bring money demand into equilibrium with the constant money supply. The higher interest rate partially crowds out investment in the IS–LM model (for the usual interest sensitivities of investment and money demand).

36. a.

b. The economy is initially at output Yn and interest rate r1. As a result of the increase in

government spending in the short run, output increases to Y1 and the interest rate increases to r2 as the IS curve shifts from IS1 to IS2. In the long run, the price level increases, shifting the LM curve from LM1 to LM2. Output returns to Yn and the interest rate eventually increases to r3 in the long run.

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37.

a. The economy starts in equilibrium at A. (1) With no policy change the price level will

eventually fall, shifting LM1 to LM2. The new long-run equilibrium will be at B. (2) If fiscal policy is used to restore the natural rate, IS1 will shift to IS2 and the new equilibrium will be a C.

b. If no policy is used to restore full employment, the interest rate and the price level fall. Since the long-run interest rate will be lower, investment will be larger. If fiscal policy is used, the IS curve will shift to the right. The price level will not change, but the long-run interest rate will increase. This will reduce the amount of private investment at the new equilibrium, C.

38.

Starting from A with interest rate r1 and income Y1, the reduction in interest rates by the Fed moves the LM curve to the right. The fall in consumption and investment spending moves the IS curve to the left. At the new equilibrium the interest rate will be lower, but the impact on output will depend on the relative magnitudes of the shifts. If the IS curve shifts relatively more than the LM curve, output will be lower. If the LM curve shifts relatively more than the IS curve, output will increase.