Suppose your firm\'s long-run total cost function (in a perfectly competitive ma

Question

Suppose your firm's long-run total cost function (in a perfectly competitive market) is given by: C(q) = 12 + 3q2-2q. 6. a. b. c. What is the firm's average cost function? What is the firm's marginal cost function? What is the firm's profit-maximizing equilibrium quantity in the long-run? Explain what you are doing to find it and why. d. What is the long-run equilibrium price? e. What is the firm's long-run supply curve, that is, quantity supplied as a function of price. (Remember there is no sunk fixed cost in the long-run. The constant term in the cost function is a quasi-fixed cost.)

Explanation / Answer

C = 12 + 3q2 - 2q

a)  

AC = C/q

= (12 + 3q2 - 2q )/q

= 12/q + 3q - 2

b) MC = dC/dq

= 6q - 2

MC = 6q - 2

c)

to find the quantity the firm will produce in LR we put

AC = MC

12/q + 3q - 2 = 6q - 2

12/q +3q = 6q

12/q + 3q - 6q = 0

12/q - 3q = 0

4/q - q = 0

4 = q2

q = 2  

so q = 2 is profit maximising quantity in LR

d)  

LR price can be found by putting P = MC

MC = 6q - 2

= 6(2) - 2

= 12 - 2

= 10

so P = 10

e)

supply function given by MC = P

p = 6q -2

p + 2 = 6q

q = (p+2)/6

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