Question

1. Barnes and Nobles has a local monopoly on the provision of books in Westford but faces a perfect competitive labor market. The inverse demand curve for books is given by: P = 100 – 0.4Q. The production function is given by: Q=5E . The daily wage that the stores take as given is W= $60

a. Find Barnes and Nobles’ Total Revenue function.

b. Using Barnes and Nobles’ production and total revenue functions and applying calculus we can derive the marginal product and marginal product functions which are given by MPe = 5 and MR= 100-.08Q . Find Barnes and Nobles’ Marginal Revenue Product of Labor.

c. Find Barnes and Nobles’ profit maximizing level of employment, and the corresponding level of output.

d. Find Barnes and Nobles’ monopolistic exploitation.

Answer 1

1)

P = 100-0.4Q

Total Revenue = P*Q = (100-0.4Q)*Q = 100Q - 0.4Q²

b)

MP = 5

MR = 100 - 0.8Q

Marginal Revenue Product of Labor = Marginal Product*Marginal Revenue = 5*(100-0.8Q)

c)

Profit maximizing employment:

The marginal Revenue product of labor = wage

5*(100-0.8Q) = 60

500 - 4Q = 60

4Q = 440

Put Q = 5E

20E = 440

E = 22

Output Q = 5E = 5*22 = 110

Price P = 100 - 0.4Q = 100-0.4*110 = 56

d)

Under perfect competition MR = P

Ideally, a unit of labor should be paid equal its value of marginal product

Value of Marginal Product = MP*P = (100 – 0.4Q)*Marginal Product = 280

But under monopolistic competition the labor is paid as per its Marginal Revenue product

Marginal Revenue Product = MP*MR = 5*(100-0.8Q) = 60

Exploitation = 280-60 = 220