Question

Consider the following cost function.

A. Find the average cost and marginal cost functions.
B. Determine the average and marginal cost when x = a.
C. Interpret the values obtained in part​ (b).
C(x) = 1000 + 0.1x, 0 ≤ x ≤ 50000 ≤ x ≤ 5000, a = 2000

Answer 1

a)Average cost function =
`\bar{C(x)}=(1000+0.1x)/(x)`

Marginal cost function =
`C'x=0.1`

b)
`\bar{C(2000)}=0.6`

`C'(2000)=0.1`

c)
`\bar{C(2000)}=0.6` is the average cost to produce first 2000 items

C'(2000)=0.1 is the marginal cost to produce 2001 th item

Explanation:

Cost function:
`C(x) = 1000 + 0.1x`

a)Find the average cost and marginal cost functions.

Average cost function =
`\bar{C(x)}=(C(x))/(x)`

Average cost function =
`\bar{C(x)}=(1000+0.1x)/(x)`

Marginal cost function =
`C'x=0.1`

b) Determine the average and marginal cost when x = a.

a = 2000

Average cost function =
`\bar{C(x)}=(1000+0.1x)/(x)=(1000+0.1a)/(a)=(1000+0.1(2000))/(2000)=0.6`

So,
`\bar{C(2000)}=0.6`

Marginal cost function =
`C'(2000)=0.1`

c)Interpret the values obtained in part​ (b).

`\bar{C(2000)}=0.6` is the average cost to produce first 2000 items

C'(2000)=0.1 is the marginal cost to produce 2001 th item