In class we have discussed unemployment. In this exercise, unemployment will be introduced explicitly into the model. Start with the production function:

Y = AK ^a L1-a

The variable L is labour input and is defined as the fraction of work force (Ns) that is employed. The workforce is the sum of those working and those unemployed. Thus:

L = (1- u)N s

Labour supply is a simple function of the wage rate:

N s= w

a)Start by using the production function to find an expression for the demand for labour (Ld). Then using the second and third equation, find an equation for the wage rate as it relates to A, K and u. Finally, based on your wage equation, write out an expression for the unemployment rate as it relates to A, K and w.

b)You are given the following values:

A =204.8, K = 25 and = 0.5

Assume for the moment that there is no unemployment; that is, set u equal to zero. Use your model to find the equilibrium wage rate, employment and output.

c)Now assume that, after extensive lobbying from labour groups, the government introduces a minimum wage that is 1.72 per cent above the wage rate you found on part b. Calculate the effect that this policy has on the demand for labour, output and the unemployment rate. In percentage terms, how much have output and employment changed?

In this part you will be using the model for a business cycle and its relationship to unemployment. Note that you may find it helpful to use Excel. Assume the wage rate remains fixed at the minimum you found in part c. As well, assume that the unemployment rate you found there is the natural rate of unemployment, u and that the level of output you found is the full-employment level.

d)

Suppose that there is a one percentage point negative shock to total factor productivity and then, separately, a one-percentage point negative shock to the capital stock. You can assume that these shocks are temporary and accordingly the supply of labour remains constant. Calculate the effect of each shock separately on the cyclical unemployment rate, u -u , and the

output gap, 100 (ln(Y ) - ln(Y )), where "ln" is the natural logarithm. Which

shock has the largest effect and why?

e)Next assume that the shocks you saw in part c are now positive; that is, productivity and the capital stock each experience separately a one- percentage point increase. In addition, suppose that in response to these changed circumstances, the wage rate does not adjust. Calculate the effect on the cyclical unemployment rate and the output gap. Can you think of reasons why wages might not adjust upward in the short run?

f)Finally, plug in the values you calculated for the output gap and cyclical unemployment into the table below. Is there a relationship between the output gap and cyclical unemployment that you found in parts d and e? Does this results conform to Okun's Law? Using your four observations, plot the relationship between each variable in an Excel spreadsheet. What is the slope of your relationship?