(show work please) An economist estimated that the cost function of a single-pro

Question

(show work please) An economist estimated that the cost function of a single-product firm is:

C(Q) = 120 + 20Q + 25Q2 + 10Q3.

Based on this information, determine the following:

a. The fixed cost of producing 10 units of output.

$

b. The variable cost of producing 10 units of output.

$

c. The total cost of producing 10 units of output.

$

d. The average fixed cost of producing 10 units of output.

$

e. The average variable cost of producing 10 units of output.

$

f. The average total cost of producing 10 units of output.

$

g. The marginal cost when Q = 10.

$

Explanation / Answer

Given cost function C(Q) = 120 + 20Q + 25Q2 + 10Q3

a) To determine fixed cost, C(0) = 120 + 20*0 + 25*0*0 + 10 * 0 * 0 = 120

b) Variable cost at Q = 10, C(10) - C(0) = 120 + 200 + 2500 + 10000 = 12820 - 120 = 12700

c) Total cost of producing 10 units = Fixed cost at 10 units + Variable cost at 10 units

= 120 + 12700 = 12820

d) Average Fixed cost of producing 10 units = C(0) / 10 = 120 / 10 = 12

e) Average variable cost of producing 10 units = C(0) / 10 = 12700 / 10 = 1270

f) Total Average cost of producing 10 units = Average Fixed cost at 10 units + Average variable cost at 10 units

= 12 + 1270 = 1282

g) Marginal Cost at Q = 10 is given by = (Q(11) - Q(9)) / (11 - 9) = ( (120 + 20 * 11 + 25 * 11*11 + 10 * 11*11*11)

- ( 120 + 20 * 9 + 25 * 9 * 9 + 10 * 9 * 9 * 9) ) /2

= ( 16675 - 9615 ) / 2 = 7060 / 2 = 3530

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