Kyunghun Kim ECN101(SS1, 2014): Homework4 Answer Key Due in class on 7/28

Transcription

1 1. AS-AD Model Suppose that government spending rises in an economy. Assume that the short-run aggregate supply curve is upward sloping. a. Draw the AS-AD model to show long-run and short-run equilibria (Label the axes and curves, and mark the initial equilibrium as point 1, the short-run equilibrium as point 2, and the long-run equilibrium as point 3.) Answer) Textbook Chapter 14. Figure Figure 1 b. What happens to output and price level in the short-run equilibrium? Answer) The economy begins in a long-run equilibrium, point 1(Y = Y 1 ). In the short-run, the equilibrium moves from point 1 to point 2. The increase in aggregate demand raises the actual price level from P 1 to P 2. Because people did not expect this increase in the price level, the expected price level remains at EP 2, and output rises from Y 1 to Y 2, which is above the natural level Y. c. What happens to output and price level in the long-run equilibrium? Answer) In the long run, the expected price level rises to catch up with reality, causing the short-run aggregate supply curve to shift upward. As the expected price level rises from EP 2 to EP 3, the equilibrium of the economy moves from point 2 to point 3. The actual price level rises from P 2 to P 3, and output falls from Y 2 to Y 3 (= Y = Y 1 ). 2. Phillips Curve Suppose that an economy has the Phillips curve. π = Eπ 0.5(u 0.06) Assume the adaptive expectataion(eπ = π 1 ). Page 1 of 5

2 a. What is the natural rate of unemployment? Answer) The natural rate of unemployment is the rate at which the inflation rate does not deviate from the expected inflation rate. Here, the expected inflation rate is just last period s actual inflation rate. Setting the inflation rate equal to last periods inflation rate, that is, π = π 1, we find that u = Thus, the natural rate of unemployment is 6 percent. b. Graph the short-run and long-run relationship between inflation and unemployment. Answer) In the short run (that is, in a single period) the expected inflation rate is fixed at the level of inflation in the previous period, π 1. Hence, the short-run relationship between inflation and unemployment is just the graph of the Phillips curve: it has a slope of 0.5, and it passes through the point where π = π 1 and u = This is shown in Figure 2. In the long run, expected inflation equals actual inflation, so that π = π 1, and output and unemployment equal their natural rates. The long-run Phillips curve thus is vertical at an unemployment rate of 6 percent. Figure 2 c. How much cyclical unemployment is necessary to reduce inflaiton by 5 percentage points? Answer)To reduce inflation, the Phillips curve tells us that unemployment must be above its natural rate of 6 percent for some period of time. We can write the Phillips curve in the form π π 1 = 0.5(u 0.06) Since we want inflation to fall by 5 percentage points, we want π π 1 = Plugging this into the left-hand side of the above equation, we find 0.05 = 0.5(u 0.06) Page 2 of 5

3 We can now solve this for u. u = 0.16 Hence, we need 10 percentage points of cyclical unemployment above the natural rate of 6 percent. d. Compute the sacrifice ratio in terms of output using Okun s law(okun s law says that an increase of 1 percentage point in unemployment translates into a decrease of 2 percentage points in GDP.). Answer)Okun s law says that a change of 1 percentage point in unemployment translates into a change of 2 percentage points in GDP. Hence, an increase in unemployment of 10 percentage points corresponds to a fall in output of 20 percentage points. The sacrifice ratio is the percentage of a years GDP that must be forgone to reduce inflation by 1 percentage point. Dividing the 20 percentage-point decrease in GDP by the 5 percentage-point decrease in inflation, we find that the sacrifice ratio is 20/5 = 4. e. Suppose that people form their expectation of inflation based on rational expectations instead of adaptive expectations. How much cyclical unemployment is necessary to reduce inflaiton by 5 percentage points? Answer) Since people form their expections of inflation based on rational expectations (Eπ = π), the short-run phillips curve becomes vertical, u = To reduce inflation by 5 percentage points, unemployment does not have to be forgone (thus, the sacrifice ratio in terms of unemployment is zero). 3. Fisher Model of Consumption Jack and Jill both obey the two-period Fisher model of consumption. Jack earns $100 in the first period and $100 in the second period. Jill earns nothing in the first period and $210 in the second period. Both of them can borrow or lend at the interest rate r. a. You observe both Jack and Jill consuming $100 in the first period and $100 in the second period. What is the interest rate r? Answer)We can use Jills intertemporal budget constraint to solve for the interest rate: C 1 + C r = Y 1 + Y r r = r r = 0.1 Jill borrowed $100 for consumption in the first period and in the second period used her $210 income to pay $110 on the loan (principal plus interest) and $100 for consumption. Page 3 of 5

4 b. Suppose the interest rate increases. What will happen to Jack s consumption in the first period? Is Jack better off or worse off than before the interest rate rise? Answer) Because of the substitution effect, the rise in interest rates leads Jack to consume less today and more tomorrow. The substitution effect costs him more to consume today than tomorrow, because of the higher opportunity cost in terms of forgone interest. However, Jack s consumption in the first period can either rise of fall when we consider not only the substitution effect but also the income effect. The increase in the interest rate makes Jack better off (as reflected by the movement to a higher indifference curve) due to the income effect. The consumer s choice depends on both the income effect and the substitution effect. Because both effects act to increase the amount of second-period consumption, we can conclude that an increase in the real interest rate raises second-period consumption. But the two effects have opposite impacts on first-period consumption, so the increase in the interest rate could either lower or raise it. Hence, depending on the relative size of income and substitution effects, an increase in the interest rate could either stimulate or depress saving in the first period. Figure 3 shows just one possible case where the substitution effect dominates the income effect in the first period so that consumption in the first period falls. Figure 3 By revealed preference we know Jack is better off: at the new interest rate he could still consume $100 in each period, so the only reason he would change his consumption pattern is if the change makes him better off. c. What will happen to Jill s consumption in the first period when the interest rate increases? Is Jill better off or worse off than before the interest rate increase? Answer)Jill consumes less today, while her consumption tomorrow can either rise Page 4 of 5

5 or fall. She faces both a substitution effect and income effect. Because consumption today is more expensive, she substitutes out of it. Also, since all her income is in the second period, the higher interest rate raises her cost of borrowing and, thus, lowers her income. Assuming consumption in period one is a normal good, this provides an additional incentive for lowering it. Her new consumption choice is at point B in Figure 4. Figure 4 Page 5 of 5