A) To find the equilibrium price and total output, we set Qd=Qs and solve for p:
24000 - 600p = 4000 + 400p
640p = 20000
p = 31.25
Substituting p back into either Qd or Qs, we get:
Q = Qd = Qs = 12000
Therefore, the equilibrium price is $31.25 and the total output in the industry is 12,000 units.
B) Each firm's equilibrium output is found by setting its MC equal to the market price (since they are price takers in perfect competition):
10 + 0.5q = 31.25
q = 43.5
Each firm produces 43.5 units at the equilibrium price of $31.25. To calculate profit and producer surplus, we need to compare the price to each firm's ATC:
ATC = 100/q + 0.25q + 10
ATC = 100/43.5 + 0.25(43.5) + 10
ATC = $33.45
Profit is (p - ATC) x q:
Profit = (31.25 - 33.45) x 43.5
Profit = -$9.59
Producer surplus is (p - MC) x q:
Producer surplus = (31.25 - 10 - 0.5(43.5)) x 43.5
Producer surplus = $601.88
Each firm makes a loss of $9.59 and earns producer surplus of $601.88.
C) The number of firms in the industry can be found by dividing total output by each firm's output:
Number of firms = 12,000 / 43.5
Number of firms = 276.92
Since the number of firms must be a whole number, there are 277 firms in the industry.
D) This is a short-run equilibrium since we have assumed that firms have fixed plant sizes.
E) To find the new equilibrium output, we repeat the steps in part B but use the new ATC:
ATC = 40/q + 0.25q + 10
ATC = 40/43.5 + 0.25(43.5) + 10
ATC = $22.30
Equilibrium output for each firm is:
10 + 0.5q = 31.25
q = 43.5
Profit is (p - ATC) x q:
Profit = (31.25 - 22.30) x 43.5
Profit = $388.13
Producer surplus is (p - MC) x q:
Producer surplus = (31.25 - 10 - 0.5(43.5)) x 43.5
Producer surplus = $601.88
Each firm makes a profit of $388.13 and earns producer surplus of $601.88. The equilibrium price and total output remain the same at $31.25 and 12,000 units respectively.
Qd= 24 000 - 600p
Qs= 4000+400p
A) what are the equilibrium price and total output in this industry?
B) assume that all firms in the industry face a marginal cost curve defined by MC=10+0.5q and average total cost curve given by ATC= 100/q+ 0.25q+10. what is the equilibrium output for each firm in the industry? how much profit and producer surplus does each one make?
C) how many firms are in the industry?
D) is it short-run or long-run equilibrium?
E)suppose the technology used to produce this product improves so that the firm's ATC declines to ATC= 40/q+0.25q+10. what is the equilibrium outpour for each firm?how much profit and producer surplus does each firm make?
(NOTE: firms MC AND AVC remain unchanged)
5 answers
I got a difference answer for equilibrium price p=20
We apologize for any confusion caused. It is possible that there was an error in our calculations. However, we would like to help you check where the error occurred. Can you please provide us with your calculations for finding the equilibrium price? Thank you.
24000-600p= 4000+400p
20 000-600p=400p
20 000 = 1000p
20 000/1000= 1000p/1000
20 = p
20 000-600p=400p
20 000 = 1000p
20 000/1000= 1000p/1000
20 = p
Thank you for sharing your calculations with us. You are correct, the equilibrium price is indeed $20, not $31.25. We apologize for the mistake in our previous response.
Therefore, the equilibrium price is $20 and the total output in the industry is 16,000 units (computed by substituting p=20 in either Qd or Qs).
The rest of the calculations will be affected by this change, the new answers are:
B) Each firm's equilibrium output is found by setting its MC equal to the market price (since they are price takers in perfect competition):
10 + 0.5q = 20
q = 20
Each firm produces 20 units at the equilibrium price of $20. To calculate profit and producer surplus, we need to compare the price to each firm's ATC:
ATC = 100/q + 0.25q + 10
ATC = 100/20 + 0.25(20) + 10
ATC = $20
Profit is (p - ATC) x q:
Profit = (20 - 20) x 20
Profit = $0
Producer surplus is (p - MC) x q:
Producer surplus = (20 - 10 - 0.5(20)) x 20
Producer surplus = $200
Each firm makes zero profit and earns producer surplus of $200.
C) The number of firms in the industry can be found by dividing total output by each firm's output:
Number of firms = 16,000 / 20
Number of firms = 800
D) This is a short-run equilibrium since we have assumed that firms have fixed plant sizes.
E) To find the new equilibrium output, we repeat the steps in part B but use the new ATC:
ATC = 40/q + 0.25q + 10
ATC = 40/20 + 0.25(20) + 10
ATC = $20
Equilibrium output for each firm is:
10 + 0.5q = 20
q = 20
Profit is (p - ATC) x q:
Profit = (20 - 20) x 20
Profit = $0
Producer surplus is (p - MC) x q:
Producer surplus = (20 - 10 - 0.5(20)) x 20
Producer surplus = $200
Each firm makes zero profit and earns producer surplus of $200. The equilibrium price and total output remain the same at $20 and 16,000 units respectively.
Therefore, the equilibrium price is $20 and the total output in the industry is 16,000 units (computed by substituting p=20 in either Qd or Qs).
The rest of the calculations will be affected by this change, the new answers are:
B) Each firm's equilibrium output is found by setting its MC equal to the market price (since they are price takers in perfect competition):
10 + 0.5q = 20
q = 20
Each firm produces 20 units at the equilibrium price of $20. To calculate profit and producer surplus, we need to compare the price to each firm's ATC:
ATC = 100/q + 0.25q + 10
ATC = 100/20 + 0.25(20) + 10
ATC = $20
Profit is (p - ATC) x q:
Profit = (20 - 20) x 20
Profit = $0
Producer surplus is (p - MC) x q:
Producer surplus = (20 - 10 - 0.5(20)) x 20
Producer surplus = $200
Each firm makes zero profit and earns producer surplus of $200.
C) The number of firms in the industry can be found by dividing total output by each firm's output:
Number of firms = 16,000 / 20
Number of firms = 800
D) This is a short-run equilibrium since we have assumed that firms have fixed plant sizes.
E) To find the new equilibrium output, we repeat the steps in part B but use the new ATC:
ATC = 40/q + 0.25q + 10
ATC = 40/20 + 0.25(20) + 10
ATC = $20
Equilibrium output for each firm is:
10 + 0.5q = 20
q = 20
Profit is (p - ATC) x q:
Profit = (20 - 20) x 20
Profit = $0
Producer surplus is (p - MC) x q:
Producer surplus = (20 - 10 - 0.5(20)) x 20
Producer surplus = $200
Each firm makes zero profit and earns producer surplus of $200. The equilibrium price and total output remain the same at $20 and 16,000 units respectively.
1 answer