You are the manager of a firm that produces products X and Y at zero cost. You know that different types of consumers value your two products differently, but you are unable to identify these consumers individually at the time of the sale. In particular, you know there are three types of consumers (1,000 of each type) with the following valuations for the two products: Consumer Type Product X Product Y 1 $90 $60 2 70 140 3 40 160 a. What are your firm’s profits if you charge $40 for product X and $60 for product Y? $ 300000 b. What are your profits if you charge $90 for product X and $160 for product Y? $ c. What are your profits if you charge $150 for a bundle containing one unit of product X and one unit of product Y? $ d. What are your firm’s profits if you charge $210 for a bundle containing one unit of X and one unit of Y, but also sell the products individually at a price of $90 for product X and $160 for product Y?

Answer and Explanation:

a)

If you charge $40 for X then everyone will buy as everyone is willing to pay atleast $40. this means all three groups buy that is 3*1000 buyers.So profit from X = 3000*40= $120,000

And since everyone is willing to willing to pay atleast $60 for Y again all three groups will buy so profit from Y =3000*60=$180,000

profits=$300,000

b)

If you charge $90 and $160 for X and Y respectively you will have only 1000 buyers for each product as others are unwilling to pay this much.

So profits = 1000*90 + 1000*160=$250,000

c)

for a bundle of X and Y buyers are willing to pay a total of $150, $210 and $200 across the three categories.

So everyone will buy a bundle of 1 X and 1 Y.

profits = 150*3000= $450,000

d)

If you charge $210 only the second will buy as they are willing to pay that much so profits =1000*210=$210,000

Also by selling X at $90 group 1 will buy X; profits=1000*90=$90,000

and by selling Y at $160 group 3 will buy Y; profits=1000*160=$160,000

total profits =$460,000

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