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

$TC(q)=1500+15*q-6q^2+q^3$

a)

Fixed cost is not changed when the quantity of goods manifactured (denoted by q) is changed. Hence, this part of total cost is not equal to zero when the q is equal to zero:

$FC=TC(0)=1500+15*0-6*0^2+0^3=1500$

FC does not depend on q.

ANSWER

The total fixed cost for producing 1000 units ia equal to 1500. The total fixed cost for producing 500 units of output is also 1500.

b)

The average fixed cost can be calculated by means of the following formula:

$AFC(q)=FC/q=1500/q$ .

Hence, AFC depends on q.

When q is equal to 1000 then AFC is 1.5, bacause $AFC(1000)=1500/1000=1.5$

When q is equal to 500 then AFC is 3, bacause $AFC(500)=1500/500=3$

c) The variable cost formula can be easy inferred from the following formula:

$TC(q)=FC+TVC(q)$

hence, $TVC(q)=TC(q)-FC$

$TVC(q)=1500+15*q-6q^2+q^3-FC=1500+15*q-6q^2+q^3-1500$

$TVC(q)=15*q-6q^2+q^3$

When q=50 the TVC is equal to 110,750, because $TVC(50)=50*(15-6*50+50*50)=50*2765=110,750$ .

Avarege variable cost (denoted by AVC) can be calculated by means of the following formula:

$AVC(q)=TVC(q)/q=15-6*q+q^2$

When q=50 the AVC is equal to 2,215, because $AVC(50)=15-6*50+50^2=2,215$

Marginal cost (denoted by MC) can be calculated as the first-order derivative of the TC with respect to q.

Hence, $MC(q)=dTC(q)/dq=d(1500)/dq+d(15*q)/dq-d(6*q^2)/dq+d(q^3)/dq$

Then, $MC(q) =0+15-12q+3q^2=15-12q+3q^2$

When q=50 the MC is equal to 6,915, because $MC(50)=15-12*50+3*50^2=6,915$

Average cost (denoted by AC) can by calculated by means of the following formula:

$AC(q)=TC(q)/q=FC/q+VC(q)/q=AFC(q)+TVC(q)$

$AFC(50)=1500/50=30$

$TVC(50)=2,215$

$AC(50)=2,215+30=2,245$

ANSWER

TVC at 50 units of output is equal to 110,750

AVC at 50 units of output is equal to 2,215

MC at 50 units of output is equal to 6,915

AC at 50 units of output is equal to 2,245