Assume that a firm has a production function Y = 1,000L1/2, where Y is output and L is labour. Labour demand is Ld = 250,000(P/W)2 and labour supply is Ls = 31,250(w=2). Initially, there is an equilibrium in which output is 250,000, employment is 62,500, the nominal wage is 20, and the price level is 10. Demand for output is 250,000 at the given price, so all output is sold. Suddenly, demand at the given price drops to 200,000, but the firm does not lower its price. It lowers output and lays off workers.
a.
Assuming that the firm cannot produce for inventory, how much will the firm want to produce?
b.
Assuming output equals the amount given under part a, what employment force will the firms want to hire?
c.
If the firm continues to pay the same nominal and real wage, how much more labour will workers wish to supply than the firm will want to hire?
2.
Assume that an economy is governed by the Phillips curve p = pe – 0.5(u – 0.06), where p = (P – P–1)/P–1, pe = (Pe – P–1)/P–1, and 0.06 is the natural rate of unemployment. Further assume pe = p–1. Suppose that, in period zero, p = 0.03 and pe = 0.03—that is, that the economy is experiencing steady inflation at a 3-percent rate.
a.
Now assume that the government decides to impose whatever demand is necessary to cut unemployment to 0.04. Suppose the government follows this policy for periods 1 through 5. Create a table of p and pe for these five periods.
b.
Assume that, for periods 6 through 10, the government decides to hold unemployment at 0.06. Create another table of p and pe for these five periods. Is there any reason to expect the inflation rate to go back to 0.03?
c.
If the government persisted in its behavior under part a, do you think the public would continue for long forming expectations according to pe = p–1? Why?
3.
Assume that an economy operates according to the sticky-wage model. The nominal wage was set to make labour supply and labour demand equal when the expected price level equaled 120 (as measured by the consumer price index).
a.
Use a graph of the labour market to illustrate and explain what happens to the quantity of labour employed if the actual price level over the time period when wages are stuck equals 110.
b.
Use a graph of the production function to illustrate and explain how the quantity of output produced changes if the actual price level equals 110 when the expected price level is 120.
c.
Given the unexpectedly low price level, will this economy be operating above, below, or at the natural rate?
4.
Consider two economies: one operates according to the sticky-wage model and one operates under the sticky-price model. Aggregate demand unexpectedly falls in both countries, leading to a recession and an unexpected decline in price level and the demand for output.
a.
Use a graph of the labour market in each country to illustrate and explain the impact of the recession on the level of employment and the real wage.
b.
In which country is the real wage procyclical? In which country is the real wage counter-cyclical?
5.
Assume that an economy is initially operating at the natural rate of output. Use the model of aggregate demand and aggregate supply (using the upward-sloping short-run aggregate supply curve) to illustrate and explain graphically the short-run and long-run effects on price and output of a reduction in government spending that produces a budget surplus.
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