Question

The cost of producing y is c(y) 5 +7y. Demand for y is given by 0 if p > 10 y(p) - -10 if p E (8,10 20 if p E [0,8 a) What are the monopoly price, quantity, profit, and total surplus? b) Suppose the monopoly can price discriminate between the two following sub-markets: 0 if p>10 0 if p >10 7 ifpE (8,10] 10 if p e [0, 8] Y2(p) 3 if pE (8,10 if p E [0,8] = 10 Find the prices, profit, and total surplus.

Answer 1

a) The marginal cost of production is 7. So, the price has to be more than 7. If the price is greater than 10, the demand is 0.

So, price belongs to [8,10]

If the price is 8, the demand is 20.

If the price is 9, demand is 10

If price is 10, demand is again 10. So, we need to compare the profits of P=8 and P=10 to decide.

When P =10

π=10 * y(10)-c(y) = 10 * 10-(5+7+10)-100 -75-25

When P =8

π = 8 * y(8)-e(y)-8 * 20-(5 7 * 20) 160-145 15

Monopolist earns more profit when P = 10. Therefore,

Price, P = 10

Quantity, y = 10

Profit = 25

Surplus = consumer surplus + producer surplus = 0 + 25 = 25

(Consumer surplus is 0, because 10 is the maximum they are willing to pay and they are paying 10.)

b) We will not consider the fixed cost (5 units) in the analysis to find optimal pricing. While calculating the profits and surplus, we will consider that also.

Submarket 1

When P = 8,

πο = 8 * yi (8) _ vc(y! ) = 8 * 10-7*10=80-70 10

When P =10,

ΠΟ 10 * yi( 10) _ ue( yi) = 10 * 7-7 * 7 = 70-49-21

That is, operating margins is higher when P =10 for the submarket 1.

Submarket 2

When P =8,

πο = 8 * y2(8)-ve(Y2) = 8 * 10-7*10=80-70 10

When P=10,

по-10 * y-( 10) _ ue(y-) = 10 * 3-7 * 3 = 30-21-9

Operating margins are higher when P = 8 for submarket 2

Answers

Price, P₁ = 10 (For submarket 1)

Price, P₂ = 8 (For submarket 2)

Profit = sum of profits of each market - fixed cost = 21 + 10 - 5 = 26

Surplus = producer surplus + consumer surplus = 26 + 6 = 32

(There is no consumer surplus in submarket 1. In submarket 2, consumer surplus = 6 because, there is a demand for 3 units at price equals 10. But, this is being fulfilled at price of 8. Hence, 3*(10-8) is surplus for consumers)