Given the market demand and supply schedules in a perfectly competitive market:

ID: 1186232 • Letter: G

Question

Q(d) = 50 - 4P and Q(s) = -6 + 3P and given the total cost function for the firm:

C= 20 + 12Q - 4Q^2 + .5Q^3

a) Determine the profit maximizing output and amount of profits for the firm.

b) Check second order conditions.

c) If the market demand increases to Q(d) = 57 - 4P, determine the new profit maximizing output and profits.

d) Check second order conditions.

e) Explain whether this model represent a short run or long run time horizon.

MC = dC/dQ

= 12-8q - 1.5q^2

P= 12.5 - 0.25 q

R(Q) = 12.5 q -0.25q^2

MR = 12.5 -0.5 q

to maximize profit MR = MC

12-8q - 1.5q^2 = 12.5 -0.5 q

=> 1.5q^2 +7.5 q +0.5 =0

=> 3q^2+ 15q +1 =0

solve the equation to get q.

sub stitue in the equation P= 12.5 -0.25 q to get the maximum profit

c) again change the demand function and follow the above procedure

e) the model represents short-term

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