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!)

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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 complete all parts

thats all information given.

Answer 1

a) The remaining demand curve for applying discounted price will be P = 2.50 - 0.1*(Q-10) = 2.50-1-0.1Q or P= 1.50 - 0.1Q , where Q, P$\geq$0

Profit = revenue - total cost = P*Q - Average cost*Q = (1.50 - 0.1Q)Q - 0.5Q = Q - 0.1Q​​​²

Profit = Q - 0.1Q^​​​2

First order Condition of profit maximisation d(profit)/dQ = 0 or 1-0.2Q = 0 or Q= 5

P= 1.50 - 0.1Q = $1 should be the discounted price

b) At discounted price , a monopolist would sell 5 units.

c) Profit at discounted price $1= revenue - cost = 1*5 - 0.5*5 = $2.5

This is in addition to the profit which the monopolist earns without discount i.e., at $2.5

Profit at $2.5 = PQ - average cost* Q = 1.5*10 -0.5*10 = $10

In discount price monopolist in total earns = $12.5

The monopolist surely earns additional profit by 2 layer pricing .

d) Remaining demand after first discount will be P= 2.50 - 0.1*(Q-10-5) = 1 - 0.1Q ; P, Q$\geq$0

Profit = P*Q - average cost*Q = (1-0.1Q)Q - 0.5Q = 0.5Q - 0.1Q^​​​2 = 0.5*5 - 0.1*25 = 2.5 - 2.5 = 0

First order condition of profit maximisation gives : d(profit)/dQ = 0 or 0.5 - 0.2Q = 0 or Q = 2.5 units

P= 1- 0.1Q = $ 0.75

Profit from three layer pricing = 0.75*2.5 - 0.5*2.5 = 0.625

Monopolist earns in total 10+2.5+0.625 = $ 13.125

Hence monopolist increases his profile by three layer pricing

e) Above is the case of second degree price discrimination. Purpose of price discrimination is to capture market consumer surplus.

Consumer is surely able to buy more goods as layers in pricing increases, but everytime price is discounted, a part of consumer surplus is captured by the monopolist. As shown in fig 1 , after price drops, consumer is able to claim an additional surplus by being able to buy some more goods at prices lower than the highest she would have paid for it( consumer surplus is shown by shaded region) but a part of it square abcd is captured by the monopolist.

00 Pri ($) P=105 a a To 10 15 quantity

Fig 1: Second Degree price discrimination.