Chapter 4, Problem 6CACQ

To determine

(a)

To find the prices of good X and Y.

Explanation of Solution

The equation of Initial budget line is as follows:

$\$400=\$100X+\$200Y$

The Standard Equation of budget line is as follows:

$\begin{array}{l}M=P_{X}X+P_{Y}Y\\ Where,Mistheincomeofconsumer\\ P_{X}isthepriceofgoodX\\ P_{Y}isthepriceofgoodY\end{array}$

On comparing with the standard equation of budget line price of good X is $100 and good Y is $200.

Economics Concept Introduction

Budget line: It is the graphical representation of all possible combination of two goods that consumer can afford within his limited income at given prices.

To determine

(b)

To find the number of units of good Y that can be purchased at point A.

Explanation of Solution

The number of units of good Y that can be purchased at point A is calculated as follows:

$\begin{array}{l}\$400=\$100X+\$200Y\\ PutX=0\\ \$400=\$100\times 0+\$200Y\\ \$400=0+\$200Y\\ \$200Y=\$400\\ Y=2units\end{array}$

Therefore, the number of units of good Y produced at point A is 2 units.

Economics Concept Introduction

Budget line: It is the graphical representation of all possible combination of two goods that consumer can afford within his limited income at given prices.

To determine

(c)

To find the number of units of good X that can be purchased at point E.

Explanation of Solution

The number of units of good X that can be purchased at point E is calculated as follows:

$\begin{array}{l}\$400=\$100X+\$200Y\\ PutY=0\\ \$400=\$100X+\$200\times 0\\ \$400=\$100X+0\\ X=4units\end{array}$

Economics Concept Introduction

Budget line: It is the graphical representation of all possible combination of two goods that consumer can afford within his limited income at given prices.

To determine

(d)

To find the number of units of good X that can be purchased at point B.

Explanation of Solution

The number of units of good X that can be purchased at point B is calculated as follows:

At point B consumer spent his entire nominal amount of money on good Y and buy 2 units of good Y and using $100 gift certificate consumer can consume 1 unit of good X.

Economics Concept Introduction

Budget line: It is the graphical representation of all possible combination of two goods that consumer can afford within his limited income at given prices.

To determine

(e)

To find the number of units of good X that can be purchased at point F.

Explanation of Solution

The number of units of good X that can be purchased at point F is calculated as follows:

At point consumer can consume 5 units of good X as buy spending his $400 income and additional $100 gift certificate, he is spending total of $500 on consumption of good X and consuming 5 units of good X.

Economics Concept Introduction

Budget line: It is the graphical representation of all possible combination of two goods that consumer can afford within his limited income at given prices.

To determine

(f)

To find the number of units of good X that can be purchased at point F.

Explanation of Solution

Based on preferences consumer can rank his preference A, B, C and D.

Consumer will rank his preference as follow:

$\begin{array}{l}D>B>C>A\\ D\left(liesonI{C}_2\right)>B\left(liesbetweenI{C}_{1}andI{C}_2\right)>C\left(liesonI{C}_2\right)>A\left(liesbelowI{C}_1\right)\end{array}$

IC₂ is the highest IC curve and gives more utility than IC₁.

Economics Concept Introduction

Budget line: It is the graphical representation of all possible combination of two goods that consumer can afford within his limited income at given prices.

To determine

(g)

To analyze whether good X is a normal good or inferior good.

Explanation of Solution

X is an inferior good because after getting gift card, he can spend gift card only on good X. Consumer is not splitting gift card on both the goods and using it to buy only X, which explains inferior nature of good X.

Economics Concept Introduction

Budget line: It is the graphical representation of all possible combination of two goods that consumer can afford within his limited income at given prices.