Question

1. A company is considering entering industry A which is perfectly competitive. Here are further details on the industry: 100 firms currently operating each with a fixed cost of $1,000 and TVC of 5Q+100 Industry demand is given by P 400-20/19 a) (40 points) Given that the industry is in the short run, that is, there is no entry and exit, how much profit would be made by each company b) (60 points) How many firms would enter into this industry in the long run?

Answer 1

a) Each firm will produce where its profit is maximize and as they are operating in perfectly competitive market so the profit maximizing condition is P = MC

MC = d(TVC) /dQ

MC = 10Q + 10

In perfectly competitive firm, supply = MC

So supply of 1 firm will be,

P = 10Q +10

Q = (P - 10 )/10

supply of 100 firms

100*Q = 10P - 100

Q = 10P - 100 (here we take 100*Q = industry supply (Q))

now equilibrium or market price is where industry supply = industry demand)

industry demand:

P = 400 - 2Q/19

19*P = 7600 - 2Q

Q =( 7600 -19P)/ 2

10P - 100 = (7600 - 19P)/2

20P - 200 = 7600 - 19P

39*P = 7800

P= 200

Each firm at P= 200 will produce

P=MC

200 =10Q + 10

Q = 19

so, profit by each company:

Profit = P*Q - 1000 - 5Q² - 10Q

Profit = 200*19 - 1000 - 5*19² - 10*19 = 805

each company will made a profit of $805

b) In long run no. of firms will increase so profit of each firm will reduce to 0 (or the price = min ATC)

ATC = 1000/Q + 5Q +10

d(ATC)/dQ = -1000/Q² + 5 =0

Q² = 200

Q = 14 (approx) (each firm will produce)

ATC at Q = 14

ATC = 1000/14 + 5*14 + 10 = 151.43 =P

At this price quantity demanded,

151.43 = 400 - 2Q/19

2877 = 7600 - 2Q

2Q = 4723

Q = 2361.5

no. of firms in the long run = 2361.5 / 14 = 168.67 = 169 ( approximately)

so 169 - 100 = 69 firms would enter into this industry.