Question

Suppose that the marginal rate of substitution is 2, the price of X is sh 3,and the price of Y is sh.1 a. If the consumer obtains 1 more unit of X, how many units of Y must be given up in order to keep utility constant? b. If the consumer obtains 1 more unit of Y, how units many of X must be given up in order to keep utility constant? c. What is the rate at which the consumer is willing to substitute X for Y? d. What is the rate at which the consumer is able to substitute X for Y ?

Answer 1

$MRS=\frac{Mu_x}{Mu_y}=2$

a) $\frac{-\delta Y}{\delta X}=2$

$-\delta Y= 1 \times 2=2$

$\therefore= \Delta Y= -2$

b) $\frac{-\delta Y}{\delta X}=2$

$\delta X= \frac{2}{-1}=-2$

$\therefore= \Delta X= -2$

c) The consumer is willing to substitute 2 units of X for good Y

d) The consumer is willing to substitute 2 units of Y for X