In: Economics
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?
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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