M.A in Economics (with specialisation in World Economics) JNU

[Chandrani Sarma]

Entrance Exam 2008.
Q.2 (b) A natural monopolist has total cost C(Q)= 400 + 25Q and faces the market demand Q=200 - 2P. Solve for the monopolist's profit, output and consumer's surplus when price is set equal to average cost.
(c) there is 'two-part pricing'. That is, the monopolist sets the price equal to marginal cost and charges a fixed participation fee per consumer. Assume that the demand comes from 10 identical consumers. What participation fee would a profit maximising monopolist set?

[priyanka]

1) C(Q)=400+25Q
AC = C(Q)/Q =400/Q + 25

P = AC
=> P =400/Q +25   ...(i)

Q = 200 - 2P
=> Q =200 -2 (400/Q +25)    ....(FROM (i))
=> Q^2 -150Q +800 = 0
=> Q = 144.6, 5.54
When Q = 144.6, P = 22.77, TR = 22.77*144.6= 4011.65
PROFIT= TR - C(Q) = 0
CONSUMER SURPLUS = 1/2*(100-27.77)*144.46 = 5217.17

When, Q = 5.54, P = 97.2, TR = 97.2*5.54 = 538.49
PROFIT = TR - C(Q) = 538.49 - (400 + 25*5.54) =0
CONSUMER SURPLUS = 1/2 *(100- 97.2)*5.54=7.756

MONOPOLIST SHOULD PRODUCE Q = 5.54 AS HE CAPTURES MAXIMUM AMOUNT OF CONSUMER SURPLUS

2) c(Q) = 400+ 25Q  
MC = 25
SO, P = 25 (AS PER QUESTION)
=> q = 150
Monopolist should charge the entire consumer surplus as participation fee. and in this case consumer surplus is equal to 1/2*(100-25)*150 = 5625 (this is same for all cosumers as they have identical demand curves)
so, monopolist should charge 5625 as particapation fee.