Question

Consider a simple economy with search unemployment. The matching function is given by

M = eQ^(1/2)A^(1/2)

There were initially Q = 1000 unemployed workers looking for a job. Let b = 0.5, z = 1, k = 0.1, e = 3/5 and a = 0.5, where k is the cost of creating a vacancy.

1. Provide the expression for the Beveridge curve.
2. Calculate and interpret the slope of the Beveridge curve for the current state of the economy.
3. How does a decrease in the matching efficiency e shift the beveridge curve?
4. Assume the government wants to implement a policy that will decrease the unemployment rate by 25%. Compute the percentage change in b that will help reach this target.
5. Assume instead that the government wants to implement a policy that will increase the vacancy rate by 25%. Compute the percentage change in b that will yield this new target.

Answer 1

The expression for the Beveridge curve is given by:

u= (q+n)/((q+n+v/u*m(v/u))

It shows the relationship between vacancy rate v and unemployment rate u.

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It is hyperbolic shaped and slopes downward.For example:High unemployment and low vacancies show recessionary periods shown on the lower side of 45 degree line.High vacancies and low unemployment indicate expansion period on the upper side of 45 degree line.

Let

U= no. of unemployed

v=no.of vacancies,N=No.of employed, L=labor force

Unemployment rate u=U/L

vacancy rate v=V/L,Job separation rate s results in flow sN of workers from employment to unemployment. Vice-versa there is flow pU of workers into employment through hire.

In the steady state pU=sN

h(v,u)=s(1-u)

The right hand side of equation shows matching function and whole function is Beveridge curve.

Outward shift in Beveridge curve shows deterioration in matching efficiency.Shift to right of curve shows increasing inefficiency of labor market and vice-versa.When the unfilled jobs number increase,unemployment must be relatively low otherwise unemployed people go to work in empty jobs.Job opening is to be low if unemployment is high is stated here by this.