please help the question 4 (a) ~ (c) 4. Suppose that given your extensive knowle
ID: 1105992 • Letter: P
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please help the question 4 (a) ~ (c)
4. Suppose that given your extensive knowledge of Microeconomics, Amy recommends you to mini or mini pies - 70p. There are 50 bakeries that are currently selling min pies, and her friend Rachel Ray to study the market of mini pies. She wants to open a shop to sell pies (because mini pies are the new cupcakes). The aggregate demand function f is given by Q(p) = 3750 each of them has a cost function C(q) = 5q2 + 125. ve for the price, quantity, and profits for each individual firm and then also for ag- gregate quantity demanded, when the number of firms is fixed. Show your work. Q (a) Sol points) (b) Define a free entry competitive equilibrium. (4 points)Explanation / Answer
Marginal cost (MC) = dC(q) / dq = 10q
(a) Each firm's supply function is its MC function. So, firm's supply curve:
P = 10q
Since there are 50 firms, Market (Aggregate) supply(Q) = 50 x q
q = Q / 50
P = 10 x (Q / 50)
P = Q / 5
Q = 5P [Aggregate supply]
In equilibrium, Aggregate demand equals Aggregate supply:
3750 - 70P = 5P
75P = 3750
P = 50
Q = 5 x 50 = 250
q = Q / 50 = 250 / 50 = 5
Firm profit = Revenue - Cost = (P x q) - (5q2 + 125) = (50 x 5) - [(5 x 5 x 5) + 125] = 250 - (125 + 125) = 250 - 250
= 0
(b)
Free entry competitive equilibrium is the level of equilibrium when there is long run equilibrium in the market caused by free entry (if firms were earning short run economic profit) or free exit (if firms were earning short run economic loss). In this equilibrium, no firm has any incentive to enter to exit the market.
(c)
In long run equilibrium, P = MC= AC where
AC = TC(q) / q = 5q + (125 / q)
Equating AC with MC,
5q + (125 / q) = 10q
5q = 125 / q
q2 = 25
q = 5
MC = P = 5 x 10 = 50
QD = 3750 - (70 x 50) = 3750 - 3500 = 250
Number of firms = Q / q = 250 / 5 = 50
In long run equilibrium profit equals Zero since Price equals Average cost.
Note that results in part (a) are the same as in part (c), which means that the data given pertains to a market in long run equilibrium itself.
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