Question

A competitive firm has the following short run cost function T C = Q 3 − 8Q 2 + 30Q + 5 .

(a) Find marginal cost, average cost, and average variable cost and sketch them on a graph.

(b) At what range of prices will the firm supply zero output, i.e. shutdown?

(c) Identify the firms supply curve

(d) At what price would the firm supply exactly 6 units of output?

(e) Compute the price elasticity of supply at the pair of price quantity computed in part d

Answer 1

Q	MC	AC	AVC
0	30		30
1	17	28.00	23
2	10	20.50	18
3	9	16.67	15
4	14	15.25	14
5	25	16.00	15
6	42	18.83	18
7	65	23.71	23
8	94	30.63	30
9	129	39.56	39
10	170	50.50	50

a)

MC = 3Q^2-16Q+30

AC = Q^2-8Q+30+5/Q

AVC = Q^2-8Q+30

b) Any price less than AVC, a firm would consider to shut down and here it is below $14

c). MC curve above the AVC represents the supply curve

d). At P = $42

e) % change in Q/%change in P = ((6-5)/5)/((42-25)/25) = 0.29