Question

Q4. There are four consumers A, B, C and D who can potentially buy three goods—1, 2, and 3. All three goods are made by a monopolist who incurs a production cost of $40, $40 and $80, respectively, for these goods. Consumers’ reservation prices for these goods are as shown in the following table:

1 2 3

A 150 90 60

B 90 90 90

C 60 80 100

D 80 60 120

(a) [3] What are the optimal prices under a la carte pricing?
(b) [2] What is the optimal price under pure bundling?
(c) [8] What are the optimal prices under mixed bundling?
(d) [6] Calculate Total Consumer Surplus in each of (a), (b) and (c)
(e) [6] Between (a), (b) and (c) which creates the highest total surplus?

Answer 1

a)

Under la carte pricing, monopolist can sell each product separately to any consumer. Given perfect information and no competition, monopolist will sell the product at reservation price of the consumer (for maximum profit). Under la carte, it would sell each product to that consumer which has its highest reservation price.

So i will sell Good 1 to consumer A at its reservation price (150). It will sell good 2 to consumer B at its reservation price (90). Finally, it will sell good 3 to consumer D, at its reservation price (120). This will maximize his profits.

Optimal Prices: Good 1= 150, Good 2= 90, Good 3= 120.

Consumer surplus in this case would be 0. Since each consumer will be buying at its reservation price.

b)

Under Pure bundling, monopoly can sell all 3 goods, as a bundle to any consumer. We have to find to which consumer monopolist should sell for maximum profits. Prices of the goods will be equal to reservation price of that consumer of all the goods, since that would be the optimal price for monopolist. Monopoly would have same cost, irrespective it sell to any consumer. His revenue would be different, depending to which consumer he sells. Revenue is nothing but the price, which we know should be equal to reservation price for maximum profits. So revenue would be maximized when reservation prices are maximized.

Consumer A total reservation price of all goods = 150+90+60 = 300

Consumer B total reservation price of all goods = 90+90+90 = 270

Consumer C total reservation price of all goods = 60+80+100 = 240

Consumer D total reservation price of all goods = 80+60+120 = 260

Since Consumer A has the highest total of reservation price, monopoly will sell the bundle to consumer A at its each good reservation price.

Optimal Prices: Good 1= 150, Good 2= 90, Good 3= 60.

Consumer surplus in this case would be 0. Since consumer A will be buying all goods at its reservation price.

c)

Under mixed bundling, monopoly can sell in any combination ie may 2 goods to one consumer and 1 good to another, or all three to separate or all 3 to same. Its free to use any bundling strategy.

So since consumer A has the highest reservation price of goods 1 and 2, monopoly should bundle good 1 and 2 together at reservation price of A, so that only he can buy. So monopoly should sell good 1 and good 2 as a bundle at price (150, 90). Good 3 monopolist should trying selling to consumer D as he has its highest reservation price. So monopoly should keep price of good 3 at 120.

Optimal Prices: Good 1= 150, Good 2= 90, Good 3= 120.

Consumer surplus in this case would be 0. Since each consumer will be buying at its reservation price.

d)

Like shown above, consumer surplus in each case would be 0.

e)

All a,b,c creates same consumer surplus of 0.

But producer surplus is highest in a and c, as compared with b. In a and c, producer surplus is (360- 160)= 200. (Summation of prices- summation of costs)

In b the producer surplus will be (300- 160) = 140

So Total surplus is highest in a and c and lowest in b.