4) [10 points] A car wash enterprise faces a total costs of TC- 20+20+0.30 and a
ID: 1114498 • Letter: 4
Question
4) [10 points] A car wash enterprise faces a total costs of TC- 20+20+0.30 and a supply curve of P=2+ .60 If 10 such identical enterprises exist, what is the market supply curve? If market demand facing these firms is P- 10-.1Q, what is the equilibrium price and quantity for the market and for each individual car wash? a. b. c. What is the profit for each enterprise? d. If market demand increases to P 12- .1Q, what is the equilibrium price and quantity for the market and for each individual car wash? What is the profit for each enterprise with the increased demand? Does the direction of change for the profit make sense? Explain. e. f.Explanation / Answer
(a) Individual firm supply curve is its Marginal cost (MC) function.
MC = dTC / dQ = 2 + 0.6Q
Therefore, firm supply function: P = 2 + 0.6Q
When there are 10 firms, market supply, QS = 10 x Q
Q = QS / 10
P = 2 + (0.6 x QS / 10)
P = 2 + 0.06QS [Market supply curve]
(b) In equilibrium, Market quantity demanded equals market quantity supplied.
10 - 0.1Q = 2 + 0.06Q
0.16Q = 8
Q = 50 [Market quantity]
Firm quantity = 50 / 10 = 5
P = 10 - (0.1 x 50) = 10 - 5 = 5
(c) When firm output = 5,
Total revenue (TR) = P x Q = 5 x 5 = 25
Total cost (TC) = 20 + (2 x 5) + (0.3 x 5 x 5) = 20 + 10 + 7.5 = 37.5
Profit = TR - TC = 25 - 37.5 = - 12.5 (Loss)
(d) When market demand: P = 12 - 0.1Q, Equating with market supply,
12 - 0.1Q = 2 + 0.06Q
0.16Q = 10
Q = 62.5 [Market quantity]
Firm quantity = 62.5 / 10 = 6.25
P = 12 - (0.1 x 62.5) = 12 - 6.25 = 5.75
(e) With new values,
TR = 5.75 x 6.25 = 35.94
TC = 20 + (2 x 6.25) + (0.3 x 6.25 x 6.25) = 20 + 12.5 + 11.72 = 44.22
Profit = 35.94 - 44.22 = - 8.28 (loss)
(f) With increase in market demand, loss has decreased. This is expected because higher market demand will shift market demand curve rightward, increasing price and individual firm profit, cost structure remaining unchanged.
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