1 Suppose all frms in a competitive market operating in the

1. Suppose all frms in a competitive market, operating in the log run, etheloing cost-functions C, (Vi)-y? +4, and market demand is given by D(p-42-p. (a) What is the long-run competitive equilibrium price (p)? b) What is the long run total output, i.e. (y\') (c) What is the long-run number of (n\')? (d) Now suppose each firms cost function is C(u)yB, where B is some constant. What is the long-run equilibrium price p with this cost function? (hint: p will be a function of B) (e) What value for B wil lead to only one firm being in the market at the long-run competitive equilibrium (i.e. find B such that n 1)?

Solution

a) From the cost function we find that AC = C/y or y + 4/y. MC = 2y. Since long run price P* is equal to MC and AC

we have

p* = AC = MC

y + 4/y = 2y

y = 4/y

y = 2 and so p* = 2*2 = $4.

b) At p* = 4, Qd = 42 - 4 = 38 units

c) n* = Qd/y = 38/2 = 19 firms

d) MC = 2y and AC = y + B/y. In this case price p* is

2y = y + B/y

y^2 = B and y = B^0.5

Then the price is 2B^0.5

e) At this price Qd = 42 - 2B^0.5

Then, n* = (42 - 2B^0.5)/B^0.5

Now n = 1 so we have

(42 - 2B^0.5)/B^0.5 = 1

(42 - 2B^0.5) = B^0.5

42/3 = B^0.5

B = 196.

For a monopoly B = 196.