Question

1.    Given the following cost function: TC = 1500 + 15Q – 6Q 2 + Q3            2 marks         

a.    Determine the total fixed cost for producing 1000 units of output and 500 units of output.

b.    What is AFC at:

                                                            i.     1000 units of output b)

                                                          ii.     500 units of output iii.

c.     Determine TVC, AVC, MC and AC at 50 units of output.

Answer 1

a). Total fixed cost

at Q=1000

FC = 1500

at Q=500

FC = 1500

b). AFC $= \frac{FC}{Q}$

i. at Q = 1000

$AFC = \frac{1500}{1000} = 1.5$

ii. at Q = 500

$AFC = \frac{1500}{500}=3$

c). TVC = TC – FC = 15Q – 6Q² + Q³

$AVC = \frac{TVC}{Q} = 15 - 6Q + Q^2 \\ AC = \frac{TC}{Q} = \frac{1500}{Q}+15-6Q+Q^2 \\ MC = \frac{dTC}{dQ}=15-12Q+3Q^2$

at Q = 50

$TVC = 15(50) -6(50)^2 + (50)^3 \\ = 750 -15000 + 125000 \\ = 110750 \\ AVC = \frac{TVC}{Q} \\ \frac{110750}{50}=2215 \\ AC = \frac{1500}{50}+15 - 6(50)+50^2 \\ = 2245 \\ MC = 15 -12(50) + 3(50)^2 \\ = 6915 \\ TVC = 110750 \\ AVC = 2215 \\ MC = 6915 \\ AC = 2245$