Answer to Question #259412 in Microeconomics for farouk

Question

C(Q) = 100 + 20Q + 15Q² + 10Q³

Based on the cost function, determine:

       i.           The fixed cost of producing 10 units of outputs

     ii.           The variable cost of producing 10 unit of outputs

   iii.           The total cost of producing 10 unit of outputs

    iv.           The average fixed cost of producing 10 unit of outputs

      v.           The average variable cost of producing 10 unit of outputs

    vi.           The marginal cost when Q= 10 

Answer 1

$C(Q) = 100 + 20Q + 15Q^2 + 10Q^3$

(i) Fixed cost (FC) = $100 (which is fixed irrespective of output level)

(ii) Variable cost $(VC) = 20Q + 15Q^2 + 10Q^3$

When $Q = 10, VC = (20 \times 10) + (15 \times 10 \times 10) + (10 \times 10^3) = 200 + 1,500 + 10,000 = \$11,700$

(iii) Total cost $(TC) = FC + VC = \$(100 + 11,700) = \$11,800$

(vi) Average fixed cost $(AFC) = \frac{FC}{Q} = \frac{100}{10} = \$10$

(v) Average variable cost $(AVC) =\frac{VC}{Q} = \frac{11,700 }{ 10} = \$1,170$

(vi) Marginal cost$(MC) = \frac{dC(Q)}{dQ} = 20 + 30Q + 30Q^2$

When $Q = 10, MC = 20 + (30 \times 10) + (30 \times 10 \times 10) = 20 + 300 + 3,000 = \$3,320$