Question

Suppose a monopolist faces two markets with the following demand curves: Market 1: ?1 (?1 ) = 500 − ?1 Market 2: ?2 (?2 ) = 800 − 4?2 Let the marginal cost be $2 per unit in both markets.

A) If the monopolist can price discriminate, what should be ?1 and ?2 to maximize the monopolist’s profit?

B) What is the profit-maximizing price if the government requires the monopolist to charge the same price in each market?

C) How much profit does the monopolist lose from the government regulation in B), relative to the profit the monopolist would earn from being able to price discriminate in A)?

Answer 1

A)

MARKET 1

In order to maximize profit a monopoly produces that quantity at which MR(Marginal Revenue) = MC(Marginal Cost)
Here MC = 2

Q₁ = D₁ (p₁ ) = 500 − p₁ => p₁ = 500 - Q₁

Hence MR in Market 1 = d(p₁Q₁)/dQ₁ = 500 - 2Q₁

Hence MR = MC =>  500 - 2Q₁ = 2 => Q₁ = 249

=> p₁ = 500 - 249 = $251

Hence In market 1 he will charge $251

MARKET 2

In order to maximize profit a monopoly produces that quantity at which MR(Marginal Revenue) = MC(Marginal Cost)
Here MC = 2

Q₂ = D₂ (p₂ ) = 800 − 4p₂ => p₂ = 200 - 0.25Q₁

Hence MR in Market 1 = d(p₂Q₂)/dQ₂ = 200 - 0.5Q₁

Hence MR = MC => 200 - 0.5Q₂ = 2 => Q₂ = 396

=> p₂ = 200 - 0.25*396 = $101

Hence In market 2 he will charge $101

(b) Q₂ = D₂ (p₂ ) = 800 − 4p₂ and Q₁ = D₁ (p₁ ) = 500 − p₁

Hence Now he can charge same price only in both markets so, Let p₁ = p₂ = p

Now, Market demand is given by Q = Q₁ + Q₂

=> Q = 800 − 4p + 500 - p = 1300 - 5p => p = 260 - 0.2Q

Now MR = d(pQ)/dQ = 260 - 0.4Q

MC = 2

=>260 - 0.4Q = 2

=> Q = 645

Hence p = 131

the profit-maximizing price if the government requires the monopolist to charge the same price in each market = $131

(c) Profit = Total Revenue - Total Cost

Loss in profit = Profit in (a) - Profit in (b)

= p₁Q₁ - 2Q₁+ p₂Q₂ -2Q₂ - (pQ - 2Q) = 249*251 - 2*249 + 396*101 - 2*396 - (645*131 - 2*645)

= 18000

Hence loss in profit = $18000