Question

Given the indifference curve shown to the right:

a. What is the marginal rate of substitution are you move from point F to point G?

b. Would you expect the absolute value of the MRS to be higher lower or the same as you continue to substitute audio CDs for books?

Answer 1

Marginal rate of substitution is the rate of exchange between two goods which determine how many units of good \(\mathrm{X}\) should given up in order to get an extra unit of good \(\mathrm{Y}\).

a)

The marginal rate of substitution from point \(\mathrm{F}\) to point G will be:

From moving point \(\mathrm{F}(36,5)\) to \(\mathrm{G}(47,4)\)

$$ \begin{aligned} M R S &=\frac{\Delta y}{\Delta x} \\ &=\frac{5-4}{36-47} \\ &=-\frac{1}{11} \end{aligned} $$

Thus, MRS is - 1/11

b)

The absolute value of MRS to be lower as consumer continue to substitute audio CDs for book.

For instance:

The marginal rate of substitution from point \(\mathrm{G}\) to point \(\mathrm{B}\) will be:

From moving point G \((47,4)\) to \(\mathrm{B}(60,3)\)

$$ \begin{aligned} M R S &=\frac{\Delta y}{\Delta x} \\ &=\frac{4-3}{47-60} \\ &=-\frac{1}{13} \end{aligned} $$

This happens because the absolute value \((-1 / 13)\) is lower than the absolute value \((-1 / 11)\).