Question

5 Android Phones - 2 points Suppose the market for Android smart phones is perfectly competitive. All firms are identical with the same cost functions: TC = 9° +800+100, MC = 2q + 80, (q is the quantity produced by a representative firm). The market demand is P = 150 - Q. (Q is market quantity). (a) Given the above information: find the equation for FC, VC, TC, ATC, and AVC. (1/2 point) (b) Determine q, P and the number of firms in the long run. (1/2 point) (c) Calculate the value of profits for a representative firm in the long run? (1/2 point) (d) Derive the market supply curve. (Hint: use your MC curve to find another point on the firm supply curve: when q = 0, then MC = 80. So, when price is 80, the quantity produced by a representative firm is 0 units and therefore the market quantity is also 0 units.) (1/2 point)

Answer 1

TC = q² + 80q + 100

FC = 100

VC =   q² + 80q

AVC = VC/q  

=   (q² + 80q )/q

= q + 80

ATC = TC/q  

=   (q² + 80q + 100)/q

= q + 80 + 100/q  

b) In long run equilibrium P = MC = ATC

MC = ATC

2q + 80 = q + 80 + 100/q

2q - q = 80 - 80 + 100/q

q = 100/q

q² = 100  

q = 10

thus, in long run a representative firm produces 10 units of output

P = MC

= 2q + 80

= 2(10) + 80

= 20 + 80

= 100

Thus, long run equilibrium price is 100

Market Demand Q = 150 - P

Q = 150 - 100

Q = 50

Number of firms n = Q/q

= 50/10

= 5

c) Profit of a representative firm  $\pi$ = Pq - TC

= Pq - q² - 80q - 100

= 100(10) - 10² - 80(10) - 100

= 1000 - 100 - 800 - 100

= 1000 - 1000

= 0

d)

Supply curve of a firm is given by

P = MC

P = 2q + 80

P - 80 = 2q

q = P/2 - 80/2

= P/2 - 40

Since there are 5 firms in the long run

Market supply Qs = nq  

= 5(P/2 - 40)

= 2.5P - 200