Equilibrium in a competitive industry Suppose you are given the following inform
ID: 1123472 • Letter: E
Question
Equilibrium in a competitive industry
Suppose you are given the following information about a particular industry:
QD = 6500-100P Market demand
QS = 1200P Short run market Supply
C(q) = 784 + q2 /400 Firm total cost function
Assume that all firms are identical and that the market is characterized by perfect competition.
a) Using the demand and supply curves above find the short run equilibrium price and quantity in the industry.
b) Using the total cost function derive the marginal cost function for firms in the industry.
c) Using your answers to parts a) and b) find the quantity produced by each firm in a short run competitive equilibrium. Find the profit of each firm in the short run equilibrium.
d) Using your answers to parts a) and c) find the number of firms in a short run equilibrium.
e) Would you expect to see entry into or exit from the industry in the long run? Explain. What effect will entry or exit have on market equilibrium (market price and quantity)?
f) Given the cost curve above, what is the long run equilibrium price in the industry?
Explanation / Answer
a). Solution :- At an equilibrium, Market demand = Market supply.
6500 - 100 P = 1200 P
6500 = 1200 P + 100 P
6500 = 1300 P
P = 6500 / 1300
P = $ 5.
Q = 6500 - 100 * 5 (Put the value of P = $ 5 in the market demand equation).
Q = 6500 - 500
Q = 6000 units.
Conclusion :-
b). Solution :- C(q) = 784 + q2 / 400 [ C(q) denotes the total cost function.]
C(q) = 784 + 0.0025 q2 (1 / 400 = 0.0025)
MC(q) = 0 + 2 * 0.0025 q [ MC(q) denotes the Marginal cost function.]
MC(q) = 0.005 q
Conclusion :- Marginal cost function [ MC (q) ] = 0.005q.
Note :- Marginal cost function is the first derivative of the total cost function given in the question.
c). Solution :- Equating price (P) and marginal cost (MC) in the given question :-
P = MC
5 = 0.005q
q = 5 / 0.005
q = 1000 units.
Total revenue (TR) = price (P) * quantity (q)
= 5 * 1000
= $ 5000.
Total cost (TC) = 784 + (1000)2 / 400 (Put the value of Q = 1000 in total cost function given in the question)
= 784 + 1000000 / 400
= 784 + 2500
= $ 3284.
Profit earned by firm = Total revenue - Total cost
= 5000 - 3284
= $ 1716.
Conclusion :-
Short-run equilibrium price $ 5. Short-run equilibrium quantity 6000 units.Related Questions
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