Suppose the market for Android smart phones is perfectly competitive. All rms ar
ID: 1152779 • Letter: S
Question
Suppose the market for Android smart phones is perfectly competitive. All rms are identical with the same cost functions: TC = q2 + 80q + 100, MC = 2q + 80, (q is the quantity produced by a representative rm). The market demand is P = 150 ?? Q. (Q is market quantity).
(a) Given the above information: nd the equation for FC, VC, TC, ATC, and AVC.
(b) Determine q, P and the number of rms in the long run.
(c) Calculate the value of prots for a representative rm in the long run?
(d) Derive the market supply curve. (Hint: use your MC curve to nd another point on the rm supply curve: when q = 0, then MC = 80. So, when price is 80, the quantity produced by a representative rm is 0 units and therefore the market quantity is also 0 units.)
Explanation / Answer
The market is perfectly competitive with each firm having a cost function TC = q2 + 80q + 100 and marginal cost MC = 2q + 80. The market demand is P = 150 - Q.
(a) FC = fixed part of total cost = 100
VC = q^2 + 80q
TC = q^2 + 80q + 100
ATC = TC/q = q + 80 + 100/q and
AVC = q + 80
(b) In the long run price = ATC = MC
q + 80 + 100/q = 2q + 80
q^2 = 100
q = 10 and so Long run price = 2*10 + 80 = 100. With P = 100, market quantity = 150 - 100 = 50 units. Each firm produces 10 units so there are 50/10 = 5 firms in the long run
(c) Since P = ATC there are no profits for any firm in the long run.
(d) The market supply curve is determined from marginal cost.
MC = 2q + 80. Minimum price is 80. This gives MC = P = 2q + 80 or q = (P - 80)/2
q = 0.5P - 40
For 5 firms, market supply curve is 5q = Qs = 2.5P - 200
Hence Market supply is Q = 2.5P - 200 or P = 0.4Q + 80
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