(a) In long run, individual firm produces where P = minimum of
AC
AC = C/q = (9/q) + (2q/q) + (q2/q) = (9/q) + 2 + q
So, d(AC)/dq = (-9/q2) + 1 = 0
So, 9/q2 = 1
So, q2 = 9/1 = 9
So, q = 3
(b) p = minimum of AC = (9/q) + 2 + q = (9/3) + 2 + 3 = 3 + 5 =
8
So, p = 8
Q = 26 - p = 26 - 8 = 18
So, Q = 18
(c) Number of firms = Q/q = 18/3 = 6
(d) If a lumpsum subsidy is provided then cost will decrease by the amount of lumpsum subsidy which will decrease AC. Thus, q will increase, P will decrease, and equilibrium quantity will also increase.
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