Question

Another monopolist has constant marginal costs of 10,000 SEK per unit, and faces two separate markets that allow price discrimination, with the (inverse) demand functions: p(a) = 40000 - 20q and p(b) = 25000 - 50Q What pricing maximizes profits?

Answer 1

MC = 10,000 SEK

In market a,

p(a) = 40000 - 20q - (1)

Multiplying above equation with q and differentiation w.r.t. q give MR of market a.

MR = 40000 - 40q

For profit maximization,

MC = MR

10000 = 40000 - 40q

q = (40000-10000)/40

q = 750 units

P(a) = 40000 - 20*750

P(a) = 25000 SEK

==

In market b:

p(b) = 25000 - 50Q

Multiplying above equation with q and differentiation w.r.t. q give MR of market b.

MR = 25000 - 100Q

For profit maximization,

MC = MR

10000 = 25000 - 100Q

Q = (25000 - 10000)/100

Q = 150 units

p(b) = 25000 - 50*150

P(b) = 17500 SEK

If different prices are used in differen markets, then:

Total profit = 25000*750 + 17500*150 - (750+150)*10000

Total profit = 12375000 SEK

===

If price of 25000 is used in both the markets:

Then,

25000 = 25000 - 50Q

Q = 0

Then, profit will not be maximized,

===

If price of 17500 is used in both the markets:

17500 = 40000 - 20q

q = (40000 - 17500)/20

q = 1125 units

So,

Total profit = 17500*1125 + 17500*150 - (1125+150)*10000

Total profit =  9562500 SER

So, the profit is maximized when different price are used in different markets. In market a, price should be 25000 SER and in market b, price should be 17500 SER.