Bus 207: Assignment #07
Textbook Ch. 9 Discussion Qs 10, 11.
Q1. A monopolist produces a single homogeneous good, which she sells in two distinct markets
between which price discrimination is possible. Her total cost function is:
TC = 1/3 Q - 7.5Q + 370Q + 100
The demand curves in the two markets are given by:
q1= 80 - 0.2p 1 and q2= Ap 2
The monopolist achieves a profit-maximizing equilibrium at which her total output (Q = q + q ) is 1 2
10 and she charges a price of $360 in market 1.
(a) What is the profit-maximizing output in markets 1 and 2?
(b) Calculate marginal revenue in either market.
(c) What is the cost of producing an extra unit at the profit maximizing output?
(d) What price is charged in market 2?
Q2. Consolidated Sugar Company sells granulated sugar to both retail grocery chains and
commercial users (e.g., bakeries, candy makers, etc.). The demand function for each of these
Retail grocery chains: P = 10 - 4q 1
Commercial users: P2= 50 - 2q 2
where P a1d P are 2he prices charged and q and q ar1 the qu2ntities sold in the respective
markets. Consolidated's total cost function (which includes a "normal" return to the owners) for
granulated sugar is
TC = 25 + 10(q + q1) 2
(a) Determine Consolidated's total profit function.
(b) Assuming that Consolidated is effectivelyable to charge different prices in the two markets,
what are the profit-maximizing price and output levels for the product in the two markets? What is
Consolidated's total profit under this condition?
(c) Assuming that Consolidated is required to charge the same price in each market, what are the
profit-maximizing price and output levels? What is Consolidated's total profit under this condition?
Q3. A monopolist produces a single homogeneous good, which he sells in two markets between
which discrimination is possible. His total cost function is:
TC = Q /3 - 40Q + 1800Q + 5000
where annual total cost is in dollars and annual output in tons. The demand curves in the two
markets are given by the equations
q1= 320 - 0.4 p an1 p2= A - Bq 2
The monopolist achieves a profit-maximizing equilibrium at which his total output (Q = q + q ) is 1 2
60 tons per annum and his annual pure profit is $5,000.
(a) What is the marginal cost at the profit maximizing output?
(b) What are the values of q an1 p at t1is output?
(c) What are the values for total cost and total revenue at this output?
(d) What are the individual values for total revenue in each of the markets?
(e) Having calculated all of the above, it is now easy to calculat