QUES TION 1 A firm in a perfectly competitive industry has the following total c
ID: 2439841 • Letter: Q
Question
QUES TION 1 A firm in a perfectly competitive industry has the following total cost function TC 8,000+3000 -2502+ 03 The market demand and supply functions are respectively given by OD-600P+ 460,000 s 700P-60,000 a. Determine the market equilibrium price and quantity(4 points) b Determine the profit-maximizing output level for the firm. c. Suppose there was a decrease in demand and the demand function became QD-600P + 120,000 4 polnts) Should the fim produce at the new equilibrium price in the short run? Why or why not?(4points Please use the space below to state the answers for questions a, b, and c. Please provide a detailed explanation for your answers For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac) T T T DaranranhExplanation / Answer
a)
The market equilibrium price and quantity is found by equating demand and supply equations
Qd = Qs
-600P + 460,000 = 700P - 60,000
1300 P = 520,000
Equilibrium price P = $ 400
Q = - 600 * $ 400 + 460,000
Equilibrum quantity Q = 220,000 units
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b)
The profit maximizing level for this firm is found by equating marginal revenue and marginal cost
Qd = -600P + 460,000
600P = 460,000 - Qd
P = 766.67 - 0.00167Qd
Revenue = Price x Qd
Revenue = (766.67 - 0.00167Qd ) Qd
Marginal revenue = 766.67 - 0.0033Qd
Cost = 8000 + 300Q - 25Q2 + Q3
Marginal cost = 300- 50Qd + 3Qd2
766.67 - 0.0033Qd = 300- 50Qd + 3Qd2
3Q2 - 50Qd - 466.67 = 0
Q = 50+- 502 + 4 * 3 x 466.67 / 2*3
Q = 50 + 79 / 6
The profit maximizing output level Q = 22 units
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c)
-600P + 120,000 = Qd
200 - 0.00167Qd = P
At the new demand level, the equilibrium price will be
-600P + 120,000 = 700P - 60,000
P = $ 138.50
Equilibrium quantity = -600 * $ 138.50 + 120,000
Equilibrium quantity = 36,900
Profit = Revenue - cost
Profit = (200 - 0.00167Qd )Qd - [ 8000 + 300Q -25Q2 +Q3 ]
Profit = (200 - 0.00167*36900)*36900- [ 8000 + 300*36900 -25*369002+369003]
Profit = negative
The firm should not produce at the new equilibrium price level because the profit is negative.
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