Question

Consider the following cost function.

Answer 1

Answer:

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

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

Step-by-step explanation:

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

a)Find the average cost and marginal cost functions.

Average cost function =$\bar{C(x)}=\frac{C(x)}{x}$

Average cost function =$\bar{C(x)}=\frac{1000+0.1x}{x}$

Marginal cost function =$C'x=0.1$

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

a = 2000

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

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