Question

In: Economics

A monopoly can discriminate prices between its New York and Los Angeles markets. The demand functions...

A monopoly can discriminate prices between its New York and Los Angeles markets.

The demand functions are:

QNY=50−(1/3)PNY

QLA=80−(2/3)PLA

The cost function is: CT = 1000 + 30Q

Where Q=QNY + QLA

a) Determine the prices and amounts that maximize profits for the company.

b) If one can no longer discriminate and only one price has to be charged, what is the new price and quantity of profit maximizers?

c) In which situation is the company and the NY and LA consumers better?

Solutions

Expert Solution

MC = 30

Inverse demand function of New York

Total Revenue,

Now equating MR to MC

Now in case of LA market

Inverse demand function of LA market

Equate MR to MC

B. When no price discrimination is possible then PNY = PLA

Adding the QNY and QLA then we get

P = 130 - Q

TR = 130Q - Q2

MR = 130 - 2Q

Equating MR to MC we get

130 - 2Q = 30

2Q = 130 - 30 = 100

Q = 50 units

P = $ 80 per unit (=130 - 50)

C. When there is no price discrimination then NY consumer pay $ 90 per unit. So, they will get benefit by no price discrimination.

The LA consumer will be paying more in no price discrimination.

Profit of firm with price discrimination

Profit = (90*20)+(75*30)-(1000 + 30*50) = 1800 + 2250 -2500

= 4050 - 2500

= $ 1550

Now when there is no price discrimination

Profit = 80*50 - (1000+30*50) = 4000 - (1000 + 1500)

= 4000 - 2500

= $ 1500

Therefore, the firm is better off When there is price discrimination.

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