Question

Your firm produces two products, and has three consumer types, each of which represent 1/3 of the market. Each consumers’ willingness to pay for each good is given in the following table:

Consumer:	GOOD 1	GOOD 2
A	$600	$100
B	$1000	$50
C	$350	$150

A) Suppose both goods are produced at zero marginal cost. If the goods cannot be bundled, what is the optimal price to charge for each good?

B) If the goods can be bundled, what is the optimal price to charge for each bundle? What is the total profit? Should your firm bundle or not?

C) Suppose the production of each good entails a marginal cost of $90 (so the MC of the bundle is $180). How would this this change your answers to a. and b. above?

Answer 1

(A) Here the marginal production cost is zero therefore, the producer will charge that price at which its total revenue (TR) is highest. Consider the case, of good 1, when the price is $600 then there is the only consumer; therefore, TR = $600, when the price is $1000, there is are two consumers; therefore, TR = $2000, and when the price is $350 then there are three consumers; therefore, TR = $1050. Hence, the optimal price for a good 1 is $1000.

Similarly for good 2, when the price is $100 then there is the only consumer; therefore, TR = $100, when the price is $50 there is are two consumers; therefore, TR = $100, and when the price is $150 then there are three consumers; therefore, TR = $450. Hence, the optimal price for good 2 is $150

(B) Now, if the goods are bundled the consumer A's willingness to pay is $700, consumer B's willingness to pay is $1050, and consumer C's willingness to pay is $500. Then again the above procedure is followed wherein when the price is $700, there is one consumer; therefore, TR = $700, when the price is $1050, there are two consumers; therefore, TR = $2100, and when the price is $500, there are three consumers; therefore, TR = $1500. Henceforth, the optimal price charge would be $1050. total profit = 4 units*1050 = $4200

(C)

Now, it is given that the marginal cost of a product is $90 rather than zero; therefore, considering part (a), there are 5 units of goods are produced. Thus, the total profit of the firm will become $2000 ($2450 - $90*5).

Similarly, for part (b), there are 6 units of goods are produced. Thus, the total profit of the firm will become $1980 ($2100 - $30 *4)