An economist estimated that the cost function of a single-product firm is: C( Q

Question

An economist estimated that the cost function of a single-product firm is:

C(Q) = 110 + 20Q + 30Q2 + 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

C(Q) = 110 + 20Q + 30Q2 + 10Q3

(a)

FC = 110, irrespective of level of Q.

(b)

VC = 20Q + 30Q2 + 10Q3

VC when Q = 10 is

= (20 x 10) + (30 x 100) + (10 x 1,000)

= 13,200

(c)

TC = VC + FC

= 13,200 + 110 = 13,310

(d)

AFC = FC / Q

When Q = 10, AFC = 110 / 10 = 11

(e)

AVC = VC / Q

When Q = 10, AVC = 13,200 / 10 = 1,320

(f)

ATC = TC / Q

When Q = 10, ATC = 13,310 / 10 = 1,331

(g)

When Q = 9, TC = 110 + 20Q + 30Q2 + 10Q3

= 110 + (20 x 9) + (30 x 81) + (10 x 729)

= 10,010

When Q = 10, TC = 13,310 [Part (c)]

So, MC when Q = 10

= TC (Q = 10) - TC (Q = 9)

= 13,310 - 10,010

= 3,300

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