Gokhale doubt

[Diksha]

You are trying to evaluate whether the labor market for computer scientists is competitive or
monopsonistic. You know that the production function for computers depends only on labor
input: Y = -0.5 L2 + 10L, where Y is the output of computers and L is the quantity of labor
used. The price of a computer is p = 2. You also know that the labor supply, as a function of
the wage, for computer scientists is the following, where w is the wage per unit of labor:
L = -10 + w.
Based on the information given above please solve the questions no. 29,30,and 31
29. If the market for computer scientists were competitive, what would be the demand function
for labour?
a) L = 10- 0.5w
b) L= 10 –w
c) L= 5 – 2w
d) L=10 + 0.5w
30. What is the equilibrium wage rate that would prevail if the market for computer scientists
were competitive?
a) 20
b) 13.33
c) 31.5
d) 12.59
31. What is the equilibrium employment that would prevail if the market for computer scientists
were competitive?
a) 5
b) 11
c) 3.33
d) 17

[Sumit]

In a competitive industry firm hire until MPL=real wage rate(i.e MPL=w/p)
So MPL=-L+10 n real wage rate=w/2 by equating this two you will get L=10-0.5w(this is labor demand fn).
So,Q29. option a).

Now, Equate Labor supply=Labour demand

-10+w=10-0.5w you will get w=13.333
so, Q30 option b).

Now, put w=13.33 in labor demand fn you will get L=3.33.
So, Q31 option c).

[Diksha]

Got it. Thanks sumit :)