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Competitive Markets Econ3501

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Assignment 5:
Competitive Markets
Econ3501, Spring 2020
Moritz Ritter
Temple University
Question 1.
In a perfectly competitive market, there are 2 firms with the following short run cost functions:
C1(q1) = 2q
2 + 10q + 200
C2(q2) = 0.5q
2 + 10q + 50
where q1 and q2 denote the quantity of output produced by firm 1 and firm 2 respectively. The marginal
cost functions are given by:
MC1(q1) = 4q1 + 10
MC2(q2) = q2 + 10
a. What is the lowest output price for which both firms will be active in the market in the short run?
b. What is the lowest output price for which both firms will be active in the market in the long run?
c. Assume that there are 10 firms of each type in the market. Derive the short run supply curve for this
market.
Now assume there is only one firm of each type, but there are also 2 more firms with the following marginal
cost curves:
MC3(q3) = 4q3 + 5
MC4(q4) = q4 + 5
Both firms are active in the short run if the price is at least $5.
d. Derive the new short run supply curve for this market (four firms in total) and draw into a well-labelled
diagram.
e. Assume the market demand function is given by: P = 51.25 − Q. What are the equilibrium price and
quantity in the short run? Show the equilibrium in the above diagram.
f. Is this short run equilibrium also a long run equilibrium? If not, what will happen in the long run?
Question 2.
Ten identical firms operate in the competitive market for sweaters. Each firm’s variable and marginal cost
curves are given by
V C(q) = 2q + q
2
and MC(q) = 2 + 2q,
respectively, where q denotes the quantity of sweaters produced by a single firm.
The market demand function is given by:
P = 30 − 0.5Q.
P denotes the market price and Q the quantity of sweaters demanded by the market.
a. Draw a clearly labeled diagram and derive an analytical expression for the short run supply function
of a single firm in this industry. [Remember to make sure to specify for what market prices this firm
will not produce any output.]
b. Derive an analytical expression for the short run industry supply function.
c. Calculate Consumer Surplus and Producer Surplus in the short run market equilibrium.
d. If the fixed cost are 9 for each firm, is this market in a long run equilibrium? If not, how many firms
will be in the market in the long run?
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