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Unformatted text preview: MM 203 Problem Set No. 5 Due: 19 September 2009, 4 PM 1. Assume that two companies (A and B) are duopolists that produce identical products. Demand for the
products is given by the following linear demand function:
P = 200 – QA – QB
where QA and QB are the quantities sold by the respective firms and P is the selling price. Total cost
functions for the two companies are:
TCA = 1,500 + 55 QA + QA
TCB = 1,200 + 20 QB + 2QB
Assume that the firms act independently as in the Cournot model (that is, each firm assumes that the
other firm's output will not change).
a. Determine the long-run equilibrium outputs and selling price for each firm.
b. Determine Firm A, Firm B, and total industry profits at the equilibrium solution found in part (a).
2. Consider Problem 1 above. Assume that the firms form a cartel to act as a monopolist and maximize
total industry profits (sum of Firm A and Firm B profits).
a. Determine the optimum output and selling price for each firm.
b. Determine Firm A, Firm B, and total industry profits at the optimal solution found in part (a).
c. Show that the marginal costs of the two firms are equal at the optimal solution found in part (a).
3. Compare the optimal solutions obtained in Problems 1 and 2 above. Specifically:
a. How much higher (lower) is the optimal selling price when the two firms form a cartel to maximize
industry profits compared with when they act independently?
b. how much higher (lower) is total industry output?
c. How much higher (lower) are total industry profits?
4. Alchem (L) is the price leader in the polyglue market. All 10 other manufacturers [follower (F) firms] sell
polyglue at the same price as Alchem. Alchem allows the other firms to sell as much as they wish at the
established price and supplies the remainder of the demand itself. Total demand for polyglue is given by
the following function (QT = QL + QF):
P = 20,000 – 4QT
Alchem's marginal cost function for manufacturing and selling polyglue is
MCL = 5,000 + 5QL
The aggregate marginal cost function for the other manufacturers of polyglue is
MCF = 2,000 + 4QF
a. To maximize profits, how much polyglue should Alchem produce and what price should it charge?
b. What is the total market demand for polyglue at the price established by Alchem in part (a)? How
much of total demand do the follower firms supply?
5. Chillman Motors, Inc. believes it faces the following segmented demand function:
P = 150 – .5Q
when 0 ≤Q ≤50
P = 200 – 1.5Q
for Q > 50
a. Indicate both verbally and graphically why such a segmented demand function is likely to exist. What
type of industry structure is indicated by this relationship?
b. Calculate the marginal revenue functions facing Chillman. Add these to your graph from part (a).
Chillman's total cost function is:
TC1 = 500 + 15Q + .5Q
c. Calculate the marginal cost function. What is Chillman's profit-maximizing price and output
d. What is Chillman's profit-maximizing price-output combination if total costs increase to
TC2 = 500 + 45Q + .5Q
e. If Chillman's total cost function changes to either
TC3 = 500 + 15Q + 1.0Q
TC4 = 500 + 5Q + 025Q
f. What price-output solution do you expect to prevail? Would your answer change if you knew that all
firms in the industry witnessed similar changes in their cost function? ...
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This note was uploaded on 09/15/2009 for the course IM MM203 taught by Professor Thirddacanay during the Summer '09 term at University of the Philippines Diliman.
- Summer '09