Prof. Gustavo Indart
Department of Economics
University of Toronto
ECO 100Y
INTRODUCTION TO ECONOMICS
Problem Set 8
1. This question traces some of the long-run adjustments that take place in a perfectly
competitive market in response to a change in demand. Each firm currently in the
industry, as well as each potential entrant, has the cost structure depicted in the left
panel below. The right panel shows the industry's short-run supply curve and the
current market demand curve D0.
a) At the initial equilibrium,
i) What are equilibrium price and output?
ii) What is the output and profit of each firm in the industry?
iii) How many firms are operating in this industry?
d) Is the industry in long-run equilibrium? Explain.
b) Suppose demand shifts to D1. At the new short-run equilibrium
i) What are the equilibrium market price and quantity?
ii) What is the output of each firm in the industry?
iii) What is each firm's profit?
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c) Explain the changes in the industry's short-run supply curve after sufficient time has
elapsed for entry and exit to occur given a constant cost industry in the long-run?
d) At the new long-run equilibrium,
i) What are the market price and quantity?
ii) What is the output and associated profit of each firm?
iii) How many firms will be active in this industry?
2. X is produced by a perfectly competitive constant cost industry. The diagram to the
right shows the long-run cost curves of one of the firms and also the short run costs
associated with two alternative plants.
a) If the price of X is
$12, what is the
profit-maximizing
output in the shortrun for a firm which
has the larger of the
two plants with
SAC2 and SMC2?
b) The owner of this
firms wishes that
she had built the
smaller plant with
cost curve SAC1.
The plant manager
doesn't agree; he says that the firm earns larger profits with the bigger plant than
it would be earning with the smaller plant. What is your advice?
c) Draw the long-run supply curve of the X industry in a second diagram if these are
the only two possible plant sizes. (Remember that it is a constant cost industry).
If Demand (D0) for X is P = 24 - Q/1000, how much does the industry produce in
long-run equilibrium? Plot D0 in your second diagram.
d) Given the equilibrium from c) and the elimination of firm 2 and its plant size,
sketch the short-run supply curve of the industry in your second diagram.
e) Suppose that this equilibrium in disturbed by a shift in demand to P = 22 Q/2000. Specify the short run i) price; ii) industry output; iii) output of one firm;
and iv) profit of one firm.
f)
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Given the new demand in e), specify the long-run i) price; ii) industry output; iii)
output of one firm; iv) profit of the firm; and v) number of firms.
3. A perfectly competitive industry is in long-run equilibrium. At this point, there are
10,000 firms in the industry. The industry has a constant cost long-run supply curve.
The government now decides to stimulate the industry by a large lump sum reduction
in the licensing fee imposed on each firm to operate in this industry.
Illustrate the effect of this licensing fee reduction in the short-run and in the long-run
on the firm and the industry by graphing the firm's cost diagram and the industry's
supply and demand diagram. Clearly label each of the relevant curves and the
changes in price, cost, and quantity, using the subscripts 0, s, and 1, to designate the
original, the short-run, and the final long-run situations respectively. Provide a brief
written analysis to explain the changes in your diagrams.
4. A perfectly competitive firm is in long-run equilibrium with initially "n" identical firms.
The industry has a constant cost long-run supply curve.
Shock: Energy costs decrease such that the average variable cost curve for each
potential plant size decreases by exactly $2.00 per unit of output.
Assessment Statement: As a result of this cost shock in the long run adjustment
period, the industry price would decrease by $2.00; industry output would stay the
same; each firm would produce a higher output and more firms would enter the
industry.
5. A perfectly competitive firm is in long run equilibrium with initially "n" identical firms.
The industry has a constant cost long run supply curve.
Shock: The government introduces a specific commodity tax of exactly $2.00 per unit
of output in the long-run.
Assessment Statement: As a result of this tax on the industry and each firm, in the
long run, the consumer price will increase by exactly $2.00; the industry output will
decrease; the full burden of the tax will be imposed on the industry; each firm will
produce an unchanged output and firms will leave the industry.
6. Demonstrate that competition without technological change will produce perfect
competition, i.e., competition will eliminate all firm sizes except the capital that
provides mimimum long-run average cost.
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a. Draw a firm diagram with a long-run average cost curve and a short-run average
cost curve tangent to minimum long-run average cost and another short-run
average cost curve tangent somewhere above minimum long-run average cost.
b. Draw an industry diagram with Supply and Demand intersecting above minimum
average cost for both the short-run average cost curves.
c. Prove diagrammatically that only the firm with capital giving mimimum long-run
average cost will survive in the long-run.