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(solution) What is the answer to 1-b) group 2, what are total profits and


What is the answer to 1-b) group 2, what are total profits and how did he get MR =200-4x?


A monopolist has two sets of customers. The inverse demand for Group 1 is described by P=200-2X.

 

The monopolist faces constant marginal cost of 40.

 

a. Show that the monopolist?s total demand, if the two markets are treated as one is:

 

X=0;

 

P>/200

 

X=200-P; 100<P</100 X=300-(3/2)P; 0<P</100

 

Answer ? Substituting X =0, we will get P =200.

 

If P lies between 100 and 1/100, then X lies between 100 and 1/100.

 

In case P lies between 0 and 100, then X lies between 300 and 150.

 

Since, the range of price and quantity of demand lies between the given limits therefore the two

 

markets

 

b. Show that the monopolist?s profit maximizing price is P=120 if both groups are to be charged the

 

same price. At this price, how much is sold to members of Group 1 and how much to members of

 

Group 2? What is the consumer surplus of each group? What are total profits?

 

Answer ? MR = 200 ? 4X

 

MC =40

 

200 ? 4X = 40

 

40 = X

 

40 units will be sold to group 1.

 

P = 200- 80 = 120

 

consumer surplus for group 1 = ½*80*40 = 1600

 

profit for 1 = 80*40 = 3200 3. Now suppose that the monopolist in #3 can separate the two groups and charge separate, profitmaximizing prices to each group.

 

a. What will these prices be? What is consumer surplus? What are total profits?

 

Answer ? P = $100

 

Consumer surplus = $800

 

Total profits = $2100 b. If total surplus is consumer surplus plus profit, how has price discrimination affected total

 

surplus?

 

Answer ? Due to price discrimination, total surplus will increase because of rise in producer?s

 

profits.

 


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