If the marginal cost function is given by MC=2(2x+9)-1/2 and the fixed cost is Rs. 4 , find the average cost for 8 units of output.
given, The marginal cost function, M.C = 2(2x + 9)-½
we know, C = ∫(M.C) dx
= ∫2(2x + 9)-½ dx
= 2√(2x + 9) + k , where k is constant.
here given fixed cost is Rs. 4
means if C= 4 then x = 0 and hence, 4 = 2√(2 × 0 + 9) + k
⇒4 = 2 × 3 + k ⇒k = -2
Thus total cost function is C = 2√(2x + 9) - 2
now average cost function A.C = total cost function/x
= C/x
= [2√(2x + 9) - 2]/x
for x = 8, A.C = [2√(2 × 8 + 9) - 2]/8 = 1