Question

1. The total cost, C(x) associated with producing and marketing x units of an item is given by

C (x) = 0.005x3 -0.02x2 -30x +3000

Find (i) Total cost when output is 4 units.

(ii) Average cost of output of 10 units.

(iii) Marginal cost when output is 3 units.

Answer 1

C=0.005X³-0.02X²-30X+3000

i) Total Cost when the output is 4 units

$TC=0.005(4)$³$-0.02(4)$²$-30X+3000$

$TC=0.005(64)-0.02(16)-120+3000$

$TC=0.32-0.32-120+3000$

$TC=2,880$

ii) Average cost is equal to total cost (TC) divided by the number of units of a good produced.

Average Cost (AC) = TC/Q

AC = (0.005X³-0.02X²-30X+3000)/X

$AC=0.005X$²$-0.02X-30+3000/X$

$AC=0.005(10)$²$-0.02(10)$$-30+3000/10$

$AC=0.5-0.2-30+300$

$AC$ $=270.30$

iii) Marginal Cost represents the incremental costs incurred when producing additional units of a good or service. It is calculated by taking the total change in the cost of producing more goods and dividing that by the change in the number of goods produced.

$MC=dTC/dX=0.015X$²$-0.04X-30$

$MC=0.015(3)$²$-0.04(3)-30$

$MC=0.135-0.12-30$

$MC=$$-29.985$