Question

Suppose a firm with continuous production has short run cost function: C(Q) = 25Q2 + 200Q + 1000.

1) Give this firm’s fixed cost.

2) Give this firm’s variable cost function VC(Q).

3) Calculate the firm’s variable cost if it produces Q = 5 units; i.e., compute VC(5).

4) Calculate this firm’s marginal cost function MC(Q); i.e. differentiate the cost function.

5) Neatly graph this firm’s marginal cost function MC(Q) from 0 up to Q = 10 units. 6) Neatly shade the area under the curve from 0 up to Q = 5 units. Calculate this area (you may recognize the area as being made up of a rectangle and a triangle, whose areas are straightforward to calculate as base times height for the rectangle and ½ times base times height for the triangle).

Answer 1

2 delution 1) 2) 3) cost function : CCQ) = 25 é + 200 Q +1000 Firms fined cast is 1000 firm's vanable cout fumation: VCC@) - 250 + 2000 V(15) = 25.X25+ 200x5 = 1625 variable cost of producing 5 units 4) marginal Cort Function: McCQ)acce) - sol +200 all A МС Boo mclQ) = 50W+200 700 600 + Soo- + Yoo + 300 200 iz Šý s '7 Š ý 10 l Area Under mc lurue = (200 x 10) + 1 x 500 x 10 = 2000 + 2500 - 4500