Consider the demand for cupcakes in Problem 17. Suppose Elaine decides to sell cupcakes only in packages of 20.
a. How much would customers be willing to pay to obtain a 20-pack of Elaine's cupcakes? (Hint: Remember that the value of each cupcake is given by the corresponding point on the demand curve. Add up those values for cupcakes 1-20.)
b. How much profit will Elaine earn from each customer?
c. How does the profit from this scheme compare to the profit Elaine earned in part (f) of Problem 17?
Problem 17:
Elaine makes delicious cupcakes that she mails to customers across the country. Her cupcakes are so delicious that she has a great degree of pricing power. Elaine's customers have identical demands for cupcakes. A representative customer's demand is shown in the diagram below. Elaine can make a cupcake for a constant marginal and average total cost of $0.50.
a. If Elaine is an ordinary monopolist, what price should she charge for cupcakes? How many will each customer order? How much profit will Elaine earn? How much consumer surplus will the buyer get?
b. Suppose that Elaine decides to offer a quantity discount according to the following terms: The first 10 cupcakes can be bought for $1.50 each; any cupcake over 10 will be offered at a discounted price. What discount price will maximize Elaine's profit from this pricing scheme? (Hint: Draw a new demand curve for Elaine's customers' demand, but since her customers have already purchased 10, begin your demand curve at the 11th unit. Alternatively, shift the vertical axis to the right by 10 units.)
c. How many cupcakes will customers order at full price? How many at the discounted price?
d. What will Elaine's profit be? How does this scheme compare to the profit she earned as an ordinary monopolist?
e. Suppose that Elaine gets super-greedy and decides to implement a three-tiered pricing system. What three prices should she choose to maximize her profit? At what quantities will the price points change? What will her profit be?
f. Suppose Elaine decides to charge $2.40 for the first cupcake, $2.30 for the second, and so on. How many cupcakes will she sell, and what will her profit be?
g. What happens to consumer surplus as Elaine adds more price points? Where does it go?