# Shapiro-Sitglitz 1984 Model Essay Example

• Category:
Marketing
• Document type:
Math Problem
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1
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339
1. [Shapiro-Sitglitz 1984 Model]

In the context of the shirking model presented in topic 6: suppose that the facts are as follows: ν = \$8 and b = \$2; G = \$2.5 and q = 0.5; s(u) = (a constant) = 0.5; and the marginal revenue product of labor (MRP) is MRPL = 100 − 100∙e, where e is the employment rate:

a) Temporarily assume that q = 1, so there is perfect monitoring. What is the equilibrium employment rate,? Is any unemployment that arises involuntary?

When q = 1, equilibrium wage rate w* = v + b = u

We know that u = 1 – e

Therefore, u/100 = MRPL/100 = 1 – e

10/100 = 1 – e

e = 1 – 0.1

Therefore, the equilibrium employment rate is 90%

There is an involuntary unemployment of (100 — 90) = 10%

b) Now assume that the detection probability is q = 0.5. What is the no-shirking wage? Determine the equilibrium employment (e*1) and unemployment (u*1) rates. Is this unemployment involuntary?

WNSC = 1 – q/q * (G/s(u)) + (v + b)

q = 0.5; G = 2.5; s(u) = 0.5; v = 8; and b = 2

= 1 * (2.5/0.5) + 10

Therefore, non-shirking wage = \$15

U*1 = (1 — q)(w + G) + q[ s(u).(v + b) + (1 – s(u).w)]

= (0.5(17.5) + 0.5 [5 — 6.5)

= 8.75 – 0.75 = 8

Therefore unemployment rate = 8%

e*1 = 1 – 8% = 92%

Therefore, employment rate is 92%

The unemployment reported here is not involuntary

c) Suppose that the government increases the value of unemployment benefits to b = \$7. What happens to the equilibrium unemployment rate?

U*1 = (1 — q)(w + G) + q[ s(u).(v + b) + (1 – s(u).w)]

Then, equilibrium unemployment rate = 0.5(17.5) + 0.5 (7.5 – 6.5)

= 8.75 + 0.5 =9.25

Therefore, the equilibrium unemployment rate will also increase by 1.25%
Hint: Use the no-shirking condition (NSC), on slide 4 of topic 6 — part II