Question

Exercise 4 Let us consider a monopolist with cost unction function C = 12000 + 30q that serves 1000 consumers with individual demand functions q = 60 - p. - Compute the quantity Q the monopolist decide to produce, the price pQm), and the total profits. -If the monopolist has complete information about each consumer determine the the quantity that she decide to produce in order to maximize profits? Compute the profits. -Let assume that 500 new consumers enter in the market and have individual demand function qn = 130 - 2p. (Denote with "N" the new consumers and with "0" the old ones). What is the new total market demand? - If the monopolist cannot distinguish any of the consumers (new or old) he has to charge the same price, compute the optimal quantity and the price. -Now imagine that all the new consumers have a common feature that distinguish them from the others. What would be the optimal strategy of the monopolist? (Notice that here we assume that you can discriminate consumers between the two groups but not within the same group)

Answer 1

A)

C= 1200+30q

MC=30

Demand ;,q=60-p{ individual demand}

Q=1000(60-p){ market demand}

Q=60,000-1000p

P=60-0.001Q

TR=60Q-0.001Q^2

MR=60-0.002Q

MR=MC{ profit Maximizing condition}

60-0.002Q=30

Q=30/0.002=15,000

P=60-0.001*15,000=60-15=45

Profit=(45-30)*15,000=15*15,000=225,000

B)

If monopolist has the complete information about CONSUMER then he will the the highest price that CONSUMER is Willing to pay for each quantity.by doing this,he can acquire entire CONSUMER surplus.

And the quantity he will produce will be that where CONSUMER is Willing to pay equal to Marginal cost.

MC=30

Q=60,000-1000*30=60,000-30,000=30,000

The profit of monopolist will be equal to consume surplus.

Profit/ CS=1/2*30,000*(60-30)=15*30,000=450,000

C) New market demand= demand of 'O' type of CONSUMER+ demand of 'N' type of CONSUMER

QN=(130-2p.) { Individual demand}

QN=500(130-2p)=65,000-1000p{ market demand of N type of CONSUMER}

New entire Market demand;Q=60,000-1000p+65,000-1000p=125,000-2000p

Inverse demand;p=62.5-0.0005Q

D)Q=125,000-2000p

Profit=TR-TC=125,000p-2000p^2-12000-30(125,000-2000p)

DERIVATIVE profit function with respect to P and put equals to zero to obtain profit Maximizing price.

125,000-4000p+60,000=0

185,000/4000=p

P=46.25

QN=65,000-1000*46.25=18,750

Qo=60,000-1000*46.25=13,750

E)for New CONSUMER,

P=65-0.001q

MR=65-0.002q

MR=MC

65-0.002qn=30

Qn=35/0.002=17,500

P=65-0.001*17,500=65-17.5=47.5

For old CONSUMER,{ same as part a)}