4. Suppose that given your extensive knowledge of Microeconomics, Amy recommends
ID: 1105812 • Letter: 4
Question
4. Suppose that given your extensive knowledge of Microeconomics, Amy recommends you to her friend Rachel Ray to study the market of mini pies. She wants to open a shop to sell mini pies (because mini pies are the new cupcakes). The aggregate demand function for mini pies is given by Q(p) = 3750-70p. There are 50 bakeries that are currently selling min pies, and each of them has a cost function C(a) 5q2 125. (a) Solve 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. (7 points)Explanation / Answer
Marginal cost (MC) = dC(q) / dq = 10q
(a) Individual firm's supply function is its Marginal Cost. Therefore, firm's supply curve:
P = 10q
Since there are 50 firms, Market (Aggregate) supply (Q) = 50q
q = Q / 50
P = 10 x (Q / 50)
P = Q / 5
Q = 5P [Aggregate supply function]
In equilibrium, Aggregate demand is equal to Aggregate supply.
3750 - 70P = 5P
75P = 3750
P = 50
Q = 5 x 50 = 250
q = Q / 50 = 250 / 50 = 5
Each Firm's profit = Total Revenue - Total 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 equilibrium state of the market, when long run equilibrium price and quantity in the market are a result of free entry (if firms were earning short run positive economic profit) or free exit (if firms were earning short run negative economic profit, i.e. economic loss). In this equilibrium, no firm has any incentive to enter to exit the market, ceteris paribus.
(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 is always Zero because Price is equal to AC.
Price and quantity results in part (a) are the same as in part (c), which means that the data is given for a market that already is in long run equilibrium.
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