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I have a similar question to this, with different values and slightly different questions. I was able to do 1-4 without a problem but was wondering how to go about the rest of the questions? In my assignment, there is a question about how many vacancies were posted initially in the economy. Is this an equivalent question to number 4 here or is there a different number at the beginning?

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Consider a simple economy with search unemployment. The matching function is given by
M = eQ1/2 A1/2.
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. Calculate the market tightness j. Show your calculation in details.
2. What is the unemployment rate?
3. What is the vacancy rate?
4. How many vacancies are posted in the economy?
5. Provide the expression for the Beveridge curve.
6. Calculate and interpret the slope of the Beveridge curve for the current state of the economy.
7. How does a decrease in the matching efficiency e shift the beveridge curve?
8. 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.
9. Assume instead that the government wants to implement a policy that will in-
crease the vacancy rate by 25%. Compute the percentage change in b that will yield
this new target.

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