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Economics/Finance Department
University of Scranton
Kania School of Management
Final ECO 507
Managerial Economics
Dr. Ghosh
(240 points)
Instructions: Answer all questions. Show and explain all calculations. Explain
your answers in detail.
Good Luck!!
1. Consider a market for an electronic component used in airport radar systems.
Two firms hold a patent on the component and only they can sell the product.
The market demand function is given by:
P = 100 –
2
1
Q
Where Q = Q1 + Q2, is the industry output and P the price. Q1 and Q2 are the
outputs of the two firms respectively.
The total cost functions for the two firms are given by:
Q 100
2
1
TC
TC 5Q 300
2
2 2
1 1
? ?
? ?
(a) Assume that the two firms behave as Cournot Duopolists. Explaining the
concept of “best response” or “reaction function”, determine the best
response function for each firm. Calculate the profit maximizing output
of each firm and the market price. Calculate optimal profit of each firm.
(36 points)
(b) Assume that the two firms collude and form a cartel to maximize their
joint profit. Calculate the optimal output and profit for each firm and the
market price. Also, calculate the resulting profit of cartel. Determine
whether firm 1 has any incentive to “cheat” the cartel by overproducing.
(24 points)
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(c) Suppose that firm 1 acts as a “Stackelberg” leader and sets its quantity
first to maximize its own profit. Firm 2 acts as a follower and sets its own
quantity in response to the output set by firm 1. Calculate optimal
outputs price and profits.
(20 points)
2. (i) A competitive firm’s short run total cost function is given by
TC = Q2 + 40 Q + 81
(a) Determine the range of prices for which the firm incurs a
loss but continues to produce. Also determine the range of
prices for which the firm earns a profit.
(8 points)
(b) Calculate the profit maximizing output and the resulting profit
when price is $100.
(10 points)
(ii) Propylene is used to make plastic. The propylene industry is perfectly
competitive and each producer has a long run total cost function given by
Q 6Q 40Q
3
1
LTC ? 3 ? 2 ?
Where Q denotes the output of the individual firm.
The market demand for propylene is
X = 2200 – 100P
Where X and P denote the market output and price respectively.
(a) Calculate the optimal output produced by each firm at the long run
competitive equilibrium (LRCE).
(8 points)
(b) Calculate the market price and market output at the LRCE.
(8 points)
(c) Calculate the number of firms at the LRCE.
(4 points)
(d) Suppose the demand curve shifts to
X = A – 100P
Where A is a positive number.
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Calculate how large A would have to be so that in the new LRCE, the
number of firms is twice what it was in the initial equilibrium.
(6 points)
(iii) Suppose that Saudi Arabia lets other members of OPEC sell all the oil
they want at the existing price which the Saudis set and other members
accept. The daily world demand for OPEC oil is given by:
P = 88 – 2Q
where P is the price per barrel of oil and Q the total quantity of OPEC oil
(in millions of barrels per day). The supply function for other members of
OPEC who behave like a “competitive fringe” is given by:
Qr = .6P
The Saudis’ cost of production of oil is given by:
TCs = 15Qs +20
where Qs is the daily output of oil produced by the Saudis.
Calculate the price that Saudi Arabia will set to maximize its own profit.
Also calculate the optimal output and profit of the Saudis. Determine the
output produced by other members of the OPEC as well as the total
market output.
(20 points)
(iv) A monopolist produces a product in one central production facility using
the cost structure: TC = (1/2) Q2 +300 and sells it in two different
markets with the following demand functions:
Market 1: P1 = 60 – (1/4)Q1
Market 2: P2 = 80 – (1/2)Q2
where Q =Q1 + Q2
Calculate the amounts of outputs, Q1 and Q2 that the monopolist should produce
and the prices that it should charge if it wants to maximize total profit. Calculate
the amount of total profit.
(16 points)
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3. (i) A monopolist faces the following demand and total cost functions:
TC Q 10Q 50
P
2
1
Q 65
? 2 ? ?
? ?
(a) Calculate the profit maximizing output and price of the monopolist.
Calculate the resulting profit.
(12 points)
(b) Suppose the government imposes an excise tax of $30 on the production
and sale of the product. Calculate the resulting optimal profit maximizing
output and price for the monopolist. Also determine the level of profit.
(12 points)
(c) If the government’s objective is to generate the maximum possible tax
revenue from the monopolist, what excise tax rate should the government
impose on the monopolist? Calculate the resulting optimal output, and
price of the monopolist as well as government’s tax revenue.
(16 points)
(ii) Two firms produce differentiated products and set prices to maximize
their individual profits. Demand functions for the firms are given by
Q1 = 64 – 4P1 + 2P2
Q2 = 50 – 5P2 + P1
where P1, P2, Q1, Q2, refer to prices and outputs of firms 1 and 2
respectively. Firm 1’s marginal cost is $5 while firm 2’s marginal cost is
$4. Each firm has a fixed cost of $50.
Assuming that the two firms decide on prices independently and
simultaneously, calculate the best response function of each firm in terms
of prices. Calculate the resulting equilibrium price quantity combination for
each firm. Illustrate your answer with a suitable graph. Also calculate
optimal profits of each firm.
(20 points)
(iii) Firm A and Firm B are battling for market share in two separate markets: I
and II. Market I is worth $120 thousand (per month) in revenue and market
II is worth $60 thousand (per month). Each firm has to decide how to
allocate their sales people in the two markets. Firm A has three sales
people and B has two. Each firm’s revenue share is proportional to the
number of sales people the firm assigns in that market. For example, if
firm A allocates two sales people in market I and firm B allocates one
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sales person there, then A’s revenue from market I will be [2/(2+1)]$120 =
$80 thousand, while B’s revenue share is the remaining (1/3)$120 = $40
thousand . Note that if neither firm assigns a sales person in a market,
they split a market. Each firm’s strategy describes how they allocate sales
people in the two markets. Thus firm A has four strategies:3-0, 2-1, 1-2
and 0-3, where the first number denotes the number of sales people
deployed by Firm A in market I and the second number denotes the
number of sales people deployed in market II. Similarly, B has three
strategies: 2-0, 1-1 and 0-2.
(a) Complete the payoff matrix. (Note that payoffs indicate total monthly
revenue for each firm from two markets.)
(b) Does either firm have a dominant strategy (or dominated strategies)?
Explain. Determine the Nash equilibrium of this game.
(20 points)
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