Question

1) Company XYZ has a monopoly on a new product. The product can be manufactured in either of two factories. The costs of production for the two factories are C1 = 5Qị and C2 = 10Q2. The firm's demand for the product is P = 500- 4Q. a. (10) Find the quantity produced by factory 1, the quantity produced by factory 2, the total quantity produced, and the price that maximize profit. b. (10) There is an increase in the cost of labor in Factory 1 but the cost of labor in Factory 2 remains the same. How will this increase in labor cost affect the quantity produced in Factory 1? the quantity produced in Factory 2? Total output? Price?

Answer 1

The monopolist's demand curve is

P = 500 – 4Q

The costs of the two factories are

C₁ = 5Q²₁ and C₂ = 10Q²₂

The goal of the Monopolist is to maximize profit

Π = TR – C₁ – C₂

TR = Total Revenue

TR = PQ

TR = (500 – 4Q)Q

TR = 500Q – 4Q²

Marginal revenue (MR) = ΔTR/ΔQ = 500 – 8Q = 500 – 8(Q₁ + Q₂)

C₁ = 5Q²₁

MC₁ = ΔC₁/ΔQ₁ = 10Q₁

C₂ = 10Q²₂

MC₂ = ΔC₂/ΔQ₂ = 20Q₂

Equating each MC to the common MR

500 – 8Q₁ – 8Q₂ = 10Q₁

500 – 8Q₁ – 8Q₂ = 20Q₂

Solving for Q₁ and Q₂ we find

Q₁ = 22.72

Q₂ = 11.36

So, the total Q is 34.08 units. This total output will be sold at price P defined by

P = 500 – 4Q

P = 500 – (4 × 34.08)

P = 363.68

The Monopolit’s Profit is

Π = TR – C₁ – C₂

Π = (363.68 × 34.08) – 5(22.72)² – 10(11.36)²

Π = 12,394.21 – 2,580.99 – 1,290.50

Π = 12,394.21 – 3,871.49

Π = 8,522.73

Part b) Now it is given that the cost of labor in Factory 1 has increased while the cost of labor in Factory 2 has remained the same. Under this situation, the output at Factory 1 will decline. The quantity produced at Factory 2 will increase.

However, given the fact that while cost has increased in Factory 1 and remained same at Factory 2, so the overall cost of production has in fact increased. As a result, total output will decline. Since, we are dealing with a Monopolist who has market power to determine the price, the rise in cost will lead to increase in the price of the good.