1 Class 4. Aggregate Supply 1) Consider the following aggregate demand and supply model: a) Aggregate demand: Y = F 2P (1) b) Aggregate supply: Y = Y + β ( P P) (2) c) Find out the equilibrium level of output and the equilibrium price level. d) To what extent are these solutions short or long run solutions? Do they depend on the parameter β? For what values of β will the solution represent the short or long run equilibrium of the economy? 2) Suppose that in the model described in Problem 1, F=400, Y =300 and P=50. a) Work out the short run equilibrium of this economy and represent it graphically. b) Work out the long run equilibrium of this economy and represent it graphically. 3) Suppose that the economy represented by the model considered in the previous problem suffers a transitory supply shock so that P = 100. a) Can you think of a real world example of a shock of this characteristics? b) Work out the new short run equilibrium and represent it graphically. Discuss the economic effects of a negative supply shock.
c) What should the government do to reduce the negative effects of this shock? 4) Go back to the economy represented in Problem 2. Suppose that now this economy suffers a permanent supply shock so that Y = 250. a) Can you think of a real world example of a shock of this characteristics? b) Work out the new long run equilibrium and represent it graphically. Discuss the economic effects of a negative supply shock. c) What should the government do to reduce the negative effects of this shock? 2 5) Consider the following production and labour supply functions: 2 s Y = 20L 0.01 L and L = 50( W P) Given this information, work out: a) The labour demand function. b) The labour market equilibrium. c) The level of output. d) Work again the equilibrium of the market if the labour supply function is s L = 46.15( W P) 6) An economy with a rigid nominal wage equal to 80 and a price level equal to 2, produces output
according to the following aggregate production function 2 Y = 500L L a) Work out the real wage and the employment level. b) Suppose there is an increase in the price level ( P = 4). Work out the new equilibrium and depict it graphically. 7) Consider the following changes in the sticky wage model. a) Suppose that labour contracts specify that the nominal wage be fully indexed for inflation. That is, the nominal wage is to be adjusted to fully compensate for changes in the consumer price index. How does full indexation alter the aggregate supply curve in this model? b) Suppose now that indexation is only partial. That is, for every increase in the CPI, the nominal wage rises, but by a smaller percentage. How does partial indexation alter the aggregate supply curve in this model? 8) The aggregate production function is 2 Y = 180L 0.5L a) Labour supply is s W L = 3 e P 3
b) W Calculate the real wage and the level of occupation in the long run. What is the potential level of output? c) What is the equilibrium real wage if P = 3 and e P = 2. Show the equilibrium graphically. What model of the labour market are we using? d) What is the equilibrium price level in the long run if G=1,000 (G is government expenditure) and the aggregate supply and demand curves are s e Y = 16,000 + 50( P P ) d Y = 10,000 + 6.5G 250P e) Starting from the equilibrium position in c), what would be the short and long run effect of an increase in G of 46? Represent graphically and relate your results to those in a) and b) above. 9) Consider the following aggregate supply and demand functions s e Y = 1,500 + 2( P P ) Y d = 3,500 4P a) Work out, both numerically and graphically, the equilibrium level of output and the price level in the long run. b) Suppose there is an unexpected disturbance from the demand side so that the new aggregate d demand curve is Y = 4,100 4P. Work out the 4
new equilibrium level of output and price level in the long run. 10) With the same aggregate supply and demand functions as in the previous problem, what are the equilibrium output and price level in the short run (2 periods) if agents form their expectations according to the following rules e t 1 P = P e t 1 P = 0.3 P+ (1 0.3) P e P = P a) What rule involves the shortest time to reach the long run equilibrium? Why? b) In the sticky price model, describe the aggregate supply curve in the following special cases. How do these cases compare with the short run aggregate supply curve used in Lesson 4? c) No firms have flexible prices (s=1). d) The desired price does not depend on aggregate output (a=0). 11) Suppose that an economy has the Phillips curve π = π 1 0.5( u 0.06) a) What is the natural rate of unemployment? b) Graph the short-run and long-run relationships between inflation and unemployment. 5
c) How much cyclical unemployment is necessary to reduce inflation by 5 percentage points? Using Okun s Law, compute the sacrifice ratio. d) Inflation is running at 10 percent. The Central Bank wants to reduce it to 5 percent. Give two scenarios that will achieve that goal. 6
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