Consider the following cost function:

$$

$($

$$

$1$

$,$

$$

$2$

$,$

$$

$)$

$=$

$$

$1$

$1$

$4$

$$

$2$

$3$

$4$

$$

$2$

$.$

$($

a

$)$

$$Find the marginal cost function, the average cost function, the supply function, and the

demand function for input

$1$

$.$

$($

b

$)$

$$Sketch the supply curve and the demand curve for input

$1$

$.$

$($

c

$)$

$$What is the effect of an increase in the price of input

$2$

$$on the supply curve and the

demand curve for input

$1$

$?$

$$Illustrate your answers.

Solution:

$($

excluding graphs

$)$

$$

$$

$=$

d

e

l

c

d

e

l

y

$=$

$2$

$$

$1$

$1$

$4$

$$

$2$

$3$

$4$

$$

$$

$$

$=$

$$

$$

$=$

$$

$1$

$1$

$4$

$$

$2$

$3$

$4$

$$

$2$

$$

$=$

$$

$1$

$1$

$4$

$$

$2$

$3$

$4$

$$

Supply:

$$

$=$

$$

$$

$=$

$>$

$$

$=$

$2$

$$

$1$

$1$

$4$

$$

$2$

$3$

$4$

$$

To get demand for input

$1$

$,$

$$use Shephard's lemma:

$$

$1$

$=$

$$

$$

$1$

$($

$$

$,$

$$

$)$

$=$

$1$

$4$

$$

$1$

$-$

$3$

$4$

$$

$2$