Problem Set #4: Aggregate Supply and Aggregate Demand Econ 100B: Intermediate Macroeconomics

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1 roblem Set #4: Aggregate Supply and Aggregate Demand Econ 100B: Intermediate Macroeconomics 1) Explain the differences between demand-pull inflation and cost-push inflation. Demand-pull inflation results from high aggregate demand: the increase in demand pulls prices and output up. Cost-push inflation comes from adverse supply shocks that push up the cost of production-for example, the increases in oil prices in the mid- and late-1970s. The hillips curve tells us that inflation depends on expected inflation, the difference between unemployment and its natural rate, and a shock v. The term β(u u n ) is the demand-pull inflation, since if unemployment is below its natural rate (u < u n ), inflation rises. The supply shock v is the cost-push inflation. 2) Why might inflation be inertial? Inflation is inertial because of the way people form expectations. It is plausible to assume that people s expectations of inflation depend on recently observed inflation. These expectations then influence the wages and prices that people set. For example, if prices have been rising quickly, people will expect them to continue to rise quickly. These expectations will be built into the contracts people set, so that actual wages and prices will rise quickly. In addition, both the hillips curve and the short-run aggregate supply curve show that inflation and unemployment move in opposite directions. 3) Assume the following model of the economy: Y = C + I + G C = (Y T ) I = r G = 50 and T = 40 ( ) d M = Y 20r M = 600 and = 2 a. Identify each of the variables and briefly explain their meaning. The variable Y represents real output or real income. From Chapter 2, we know that the value of the produced goods and services (real output) has to be equal to the value of the income earned in producing the goods and services (real income). The variable C represents the consumption of goods and services. The variable I represents investment by the firms. When firms purchase new capital goods, this counts as investment. When firms experience a change in their inventories, this also counts in the investment category of GD. The variable G represents the government s spending on newly produced goods and services. The variable T represents lump sum taxes, and Y T represents disposable income. The variable M represents the nominal money supply, is the price level, and M/ is the real money supply. The variable r is the real interest rate. The variable (M/ ) d represents real money demand. Consumption depends positively on disposable income, investment depends negatively on the real interest rate, and real money demand depends positively on real income and negatively on the real interest rate. b. Derive the equation for the IS curve, showing Y as a function of r alone. 1

2 The IS curve represents all combinations of the real interest rate r and real output Y such that the goods market is in equilibrium. The equation for the IS curve can be derived as follows: Y = C + I + G Y = ( (Y T )) + (100 10r) + 50 Y = ( (Y 40)) + (100 10r) + 50 Y = Y 10r 0.5Y = r Y = r c. Derive the equation for the LM curve, showing Y as a function of r alone. The LM curve represents all combinations of the real interest rate r and real output Y such that the money market is in equilibrium. The equation for the LM curve can be derived as follows: ( ) d ( ) M = M Y 20r = Y = r d. What are the equilibrium level of income and equilibrium interest rate? Y = 400, r = 5 e. Derive and graph an equation for the aggregate demand curve. What happens to this aggregate demand curve if fiscal or monetary policy changes? IS: Y = r or r = 25.05Y LM: Y = 600 ( ) + 20r s ( ) d M = M 600 = Y 20r (we need to keep in the equation) Y = r ) s AD: Y = ( 300 merge IS and LM using r Y = (25.05Y ) Y = Y 2Y = Y = An increase in decreases Y, so AD is downward slopping. Expansionary monetary or fiscal policy shift aggregate demand to the right. Contractionary monetary or fiscal policy shift aggregate demand to the left. 4) Suppose that an economy has the hillips curve A) What is the natural rate of unemployment? π t = π t 1.5(u.06) 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 period s inflation rate, that is, π t = π t 1, we find that u = Thus, the natural rate of unemployment is 6 percent. 2

3 B) Graph the short-run and long-run relationships between inflation and unemployment. 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 t 1. Hence, the short-run relationship between inflation and unemployment is just the graph of the hillips curve: it has a slope of -0.5, and it passes through the point where π t = π t 1 and u = This is shown in Figure In the long run, expected inflation equals actual inflation, so that π t = π t 1, and output and unemployment equal their natural rates. The long-run hillips curve thus is vertical at an unemployment rate of 6 percent. C) How much cyclical unemployment is necessary to reduce inflation by 5 percentage points? Using Okun s law, compute the sacrifice ratio. To reduce inflation, the hillips curve tells us that unemployment must be above its natural rate of 6 percent for some period of time. We can write the hillips curve in the form π t π t 1 = 0.5(u0.06). Since we want inflation to fall by 5 percentage points, we want π t π t 1 = lugging this into the left-hand side of the above equation, we find 0.05 = 0.5(u 0.06). We can now solve this for u: u = Hence, we need 10 percentage points of cyclical unemployment above the natural rate of 6 percent. Okun s law says that a change of 1 percentage point in unemployment translates into a change of 2 percentage points in GD. 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 year s GD that must be forgone to reduce inflation by 1 percentage point. Dividing the 20 percentage-point decrease in GD by the 5 percentage-point decrease in inflation, we find that the sacrifice ratio is 20/5 = 4. D) Inflation is running at 10 percent. The Fed wants to reduce it to 5 percent. Give two scenarios that will achieve this goal. One scenario is to have very high unemployment for a short period of time. For example, we could have 16 percent unemployment for a single year. Alternatively, we could have a small amount of cyclical unemployment spread out over a long period of time. For example, we could have 8 percent unemployment for 5 years. Both of these plans would bring the inflation rate down from 10 percent to 5 percent, although at different speeds. 3

4 5) Suppose the economy is initially at a long-run equilibrium. Then the Fed increases the money supply. A) Assuming any resulting inflation was unexpected, explain changes in GD, unemployment, and inflation. Explain using three diagrams: IS-LM model, AD-AS model, and the hillips curve. Beginning in long-run equilibrium, where output is at the natural level, if the Federal Reserve increases the money supply, this will cause the economy to go through an expansionary phase. Starting with the ISLM model in Figure 14-2A, an increase in the money supply will shift the LM curve to the right, resulting in a lower interest rate and higher level of output at point B. In the long run, the price level will rise, real-money balances will decline, and the LM curve will shift back to its original position. There is no long-run change in the real interest rate or the level of output. Moving to the ADAS model in Figure 14-2B, an increase in the money supply will shift the AD curve to the right, resulting in a higher level of output and a higher price level at point B. In the long run, expected inflation will rise, shifting the SRAS curve upward. The economy ends up at point C with output back at its natural level and the price level at a higher level. Moving to the hillips curve graph in Figure 14-2C, the economy starts at point A, where unemployment is at the natural rate. The increase in the money supply pushes output above its natural level, and as a result, the unemployment rate falls below its natural level. This causes a movement along the short-run hillips curve to point B, where inflation is higher and unemployment is lower. In the long run, expected inflation will rise, causing the hillips curve to shift upward. The economy ends up at point C with higher inflation and no change in the unemployment rate. The economy moves through this expansionary cycle because the increase in the money supply does not immediately cause expected inflation to rise. 4

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6 B) Assuming instead that any resulting inflation is expected, explain any changes in GD, unemployment, and inflation. Explain using three diagrams: IS LM model, AD AS model, and the hillips curve. Beginning in long-run equilibrium with output at its natural level, if the Federal Reserve increases the money supply and people immediately expect inflation to rise, then nothing changes except for the price level and the inflation rate. In the ISLM model, the increase in the money supply will cause the price level to rise at the same rate as the money supply such that there is no change in real balances. The economy stays at point A, as illustrated in Figure 14-3A. Moving to the ADAS model, the increase in the money supply shifts the AD curve to the right, but at the same time, the increase in expected inflation shifts the SRAS curve up and to the left. The economy remains at the natural level of output and the price level is higher, as illustrated in Figure 14-3B. Moving to the hillips curve, the immediate increase in expected inflation shifts the short-run hillips curve upward, causing the inflation rate to rise with no change in the unemployment rate, as illustrated in Figure 14-3C. When the money supply increases and the public immediately expects higher inflation, the economy does not move through an expansionary cycle. 6

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