2. Suppose TC 500+5q2 for each firm in a perfectly competitive industry a. Deriv

Question

2. Suppose TC 500+5q2 for each firm in a perfectly competitive industry a. Derive MC and ATC b. Derive the typical firm's supply function c. If there are currently 100 firms in the industry, derive the market supply function d. If Qd-1200-5P, solve for the equilibrium P e. Solve for the Eqilibrium market quantity and firm quantity f. Solve for the firm's profits In the long, run explain whether entry or exit will occur 8. h. Solve for the long run firm quantity i. Solve for the long run price j. Solve for the long run market quantity k. Solve for the number of firms that will exist in the market in the long run

Explanation / Answer

a)

TC = 500 + 5q2

MC = dTC/dq

MC = 10q

AC = TC/q

= (500 + 5q2)/q

= 500/q + 5q

b)

for supply function P = MC

P = 10q

q = P/10

C)

n = 100

Market supply function Qs = nq

= 100(P/10)

= 10P

Qs = 10P

d)

Qd = 1200 - 5P

equilibrium price is given by

Qd = Qs

1200 - 5P = 10P

1200 = 10P+5P

1200 = 15P

P = 1200/15

= 80

e) Qd = 1200 - 5P

= 1200 - 5(80)

= 1200 - 400

= 800

so Market quantity Q = 800

firm's quantity q = Q/n

= 800/100

= 8

f)

Firm's profit = Pq - TC

= Pq - 500 - 5q2

= 80(8) - 500 - 5(8)2

= 640 -500 - 320

= 640 - 820

= - 180

g)

we have profit = - 180

which is negative profit or loss so firms will exist in the long run

h)

We Have AC = 500/q + 5q

MC = 10q

so in LR AC = MC = P

AC = MC

500/q + 5q = 10q

500/q = 10q - 5q

500/q = 5q

100 = q2

so q = 10 is the long run firm quantity

i)

MC = 10q

= 10(10)

= 100

P = MC

P = 100 is the Long run price

j)

Qd = 1200 - 5P

= 1200 - 5(100)

= 1200 - 500

= 700

So long run market quntity Q = 700

k)

Number of firms n = Q/q

= 700/10

= 70

so 70 firms wil exist in long run

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