Problem 1. A buyer's RP for a total of q copies of Moby Dick is given by 10q-(q^2/2)
For example, the RP for one copy of the Moby Dick is $9.5, the RP for 2 copies of the Moby Dick is $18. If copies of Moby Dick are sold at $4 a copy, how many (whole) copies should the buyer purchase to maximize his consumer surplus?
Problem 2 You face a market of 30,000 buyers divided into 2 segments (A and B). From each segment you have picked a random sample and offered them a price. Here are the results.
1. Segment A: A random sample of 1000 from a population of 10,000 was offered a price of $20. Of the sample, 200 indicated they would buy at this price and the remainder said they would not.
2. Segment B: A random sample of 15,000 from a population of 20,000 was offered a price of $60. Of the sample 4,000 indicated they would buy at this price and the remainder said they would not.
The unit cost of production is $15. Is there sufficient data to determine profit maximizing price? If not, in what way is the data deficient? Reasons specific to the problem rather than generic are preferred.
Problem 3. You are the monopoly supplier of laptops to a market consisting of four segments: A, B, C and D. Individuals within a segment share the same RP for laptops. The RPs of each segment and their fraction of the market are shown in the table below:
Segment A B C D
Proportion 25% 25% 30% 20%
RP $800 $950 $1100 $1500
Draw the demand curve for your product (market share vs. price). If a segment is indifferent between buying and not buying, assume they will buy.
Now suppose there is a competitor supplying its own laptop at a price of $1100. The RP of each segment for the competitor's laptop are $1000, $1200, $1500 and $1350 respectively.
Draw the demand curve for your product in this case. In this case if at a particular pair of prices a segment is indifferent between brands, assume that half the segment buy one brand and the other half of the segment purchase the other brand.