Paul\'s Picture Frames Inc. has total costs of production given by the equation
ID: 1103968 • Letter: P
Question
Paul's Picture Frames Inc. has total costs of production given by the equation TC=500+30Q+5Q^2. This implies that the firm's marginal cost is given by the equation MC=30+10Q.
Write the equations showing Paul's
average total cost (as a function of Q)
average variable cost (as a function of Q)
In short run, what is the lowest aceptable price for Paul?
Assuming the picture frame market is perfectly competitive, what output would be produced by the firm in long-run equilibrium? What would be the long-run equilibrium price?
If the picture frame market is perfectly competitive and consists of N identical picture frame factories, each with cost functions as above, give an equation for the industry supply curve.
If the market demand for picture frames is given by the equation p=230-Qd, how many firms will be in the industry in long-run equilibrium?
Explanation / Answer
TC = 500 + 30Q + 5Q2
(a) Average total cost = TC / Q = (500 / Q) + 30 + 5Q
(b) Total variable cost (TVC) = 30Q + 5Q2
Average variable cost (AVC) = TVC / Q = 30 + 5Q
(c) In the short run, minimum acceptable price is equal to the output level where Price = MC = AVC
30 + 10Q = 30 + 5Q
5Q = 0
Q = 0
Price = AVC = 30 + (5 x 0) = 30 + 0 = 30
(d) In long run equilibrium, Price = MC = ATC
30 + 10Q = (500 / Q) + 30 + 5Q
(500 / Q) = 5Q
5Q2 = 500
Q2 = 100
Q = 10
Long run equilibrium price = MC = 30 + (10 x 10) = 30 + 100 = 130
(e) Firm supply function is its MC, therefore firm supply function:
p = 30 + 10Q
When there are N firms, industry supply (QS) = N x Q
Q = QS / N
p = 30 + 10 x (QS / N) [Industry supply function]
NOTE: First 5 parts are answered.