Question

XYZ Candy makes specialty chocolate bars to distribute online, shipping across North America. XYZ has established a great deal of monopoly power in pricing given its specialty status. Let’s assume XYZ’s customers are identical with individual (inverse) demand as P = 2.50 – 0.1Q, where Q is number of bars the customer orders per month. Marginal cost to supply another bar is constant (equal to average cost) at $0.50. If XWZ acts like a single-price non-discriminating monopoly, its profit-maximizing price is $1.50 and quantity is 10 (you can check this!)

a. Suppose XYZ offers a quantity discount where it sells customers the first 10 units at $1.50 each but discounts the price for each bar ordered over 10 units (i.e., a lower price for the 11th bar and all beyond that). What will be the discounted price that maximizes profit? (Hint: The relevant portion of the demand curve for the discount pricing are quantities beyond price $1.50 and 10 units; it may help to think of this portion of the demand curve as a new demand curve beginning with the 11th unit, or a shift in the demand of 10 units for price $1.50 or below.)

b. How many bars does XYZ sell at the discounted price?

c. Compare the profit in the discounted pricing scheme to the monopoly single price of $1.50.

d. Suppose XYZ adds a three-tier pricing policy. Explain what would happen to profits.

e. Explain what happens to consumer surplus as XYZ adds more discount price points.

please help :/

Answer 1

a) Relevant portion of demand curve for discounted price is : P = 2.50 - 0.1(Q- 10) or P= 1.50 - 0.1Q

Average cost c = $ 0.5

Profit on the above demand curve = P*Q - cQ = (1.50-0.1Q )*Q - 0.5Q = Q - 0.1Q^​​​2

First order condition of profit maximisation : d(profit)/dQ = 0 OR d (Q - 0.1Q^​​​2)/dQ = 0 or 1-0.2Q = 0 or Q = 5 bars

Price = 1.50 - 0.1Q = 1 . PRICE = $1

b) At discounted price p= $1 , 5 bars are sold. This is in addition to the bars sold at monopoly price i.e., 10 bars. In total 15 bars are sold

c) Profit at monopoly price= P*Q - cQ = (P-c)Q = (1.5-0.5)*10 = $ 10

Profit at discounted price = (P-c)*Q = (1-0.5)*5 = $ 2.5

In discounted price, the Monopolist earns $2.5 in addition to what it earns by selling 10 units of goods at $1.5 ., i.e., in total $12.5

d) when three tier pricing policy is added ,the monopolist succeds in selling more goods without reducing prices for every units of good he sells. Thus profit increases further with three teir pricing policy

e) As more and more discount prices are added ,it enables the Consumer to buy more than it could have under monopoly without price discrimination. However , each time a discounted price is added , monopolist succeds in capturing a part of consumer surplus . In the figure below this part is shown by area enclosed by the square abcd. Had the price fallen to $1 , this square would have been consumer surplus. But due to discount price policy monopoly captures it

00 Price (3) P=105 a a To 10 15 quantity