Chapter 4, Problem 1CACQ

To determine

(a)

To calculate:

The market rate of substitution between good X and Y.

Answer to Problem 1CACQ

The market rate of substitution between good X and Y is 3.

Explanation of Solution

At equilibrium, the marginal rate of substitution is equal to the ratio of prices of goods as shown below:

$\begin{array}{l}MRS=\frac{P_X}{P_Y}\\ MRS=\frac{15}{5}\\ MRS=3\end{array}$

Therefore, market rate of substitution between good X and Y is 3.

Economics Concept Introduction

Market Rate of Substitution: It is also known as marginal rate of substitution. It is the rate at which consumer is willing to give up of one good to get additional units of other good, maintaining constant utility.

To determine

(b)

To draw:

Consumers opportunity set diagram.

Explanation of Solution

The equation of budget line can be drawn as follows:

$\begin{array}{l}{\text{P}}_{\text{X}}{\text{Q}}_{\text{X}}{\text{+P}}_{\text{Y}}{\text{Q}}_{\text{Y}}\text{= M}\\ {\text{15Q}}_{\text{X}}{\text{+5Q}}_{\text{Y}}\text{= 300}\end{array}$

The opportunity set is shown below:

Quantity of good X	Quantity of good Y
0	60
10	30
15	15
20	0

 

Economics Concept Introduction

Opportunity Set: It refers to the all the possible combination of goods that consumer can afford within his limited income at given prices in the market.

To determine

(c)

To draw:

Consumers opportunity set diagram when consumer income increases.

Explanation of Solution

The new budget line when consumer income when increases by $300 is shown below:

$\begin{array}{l}{\text{P}}_{\text{X}}{\text{Q}}_{\text{X}}{\text{+P}}_{\text{Y}}{\text{Q}}_{\text{Y}}\text{= M}\\ {\text{15Q}}_{\text{X}}{\text{+5Q}}_{\text{Y}}\text{= 600}\end{array}$

The new opportunity set is shown below:

Quantity of good X	Quantity of good Y
0	120
10	90
15	75
40	0

 

The $ 300 increase in income does not alter the market rate of substitution as MRS is the ratio of prices and independent of change in income.

Economics Concept Introduction

Opportunity Set: It refers to the all the possible combination of goods that consumer can afford within his limited income at given prices in the market.