ShapiroSitglitz 1984 Model Essay Example
 Category:Marketing
 Document type:Math Problem
 Level:Undergraduate
 Page:1
 Words:339

[ShapiroSitglitz 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 noshirking wage? Determine the equilibrium employment (e*1) and unemployment (u*1) rates. Is this unemployment involuntary?
W^{NSC} = 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, nonshirking 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 noshirking condition (NSC), on slide 4 of topic 6 — part II