Chapter 4, Problem 10P

(a)

To determine

The budget constraint.  

Explanation of Solution

Budget equation can be written as follows:

$\left(\begin{array}{l}{\text{Quantity}}_1\\ \times {\text{Price}}_1\end{array}\right)+\left(\begin{array}{l}{\text{Quantity}}_2\\ \times {\text{Price}}_2\end{array}\right)+\mathrm{...}+\left(\begin{array}{l}{\text{Quantity}}_{\text{n}}\\ \times {\text{Price}}_{\text{n}}\end{array}\right)=\text{Income}$ (1)

Figure 1 illustrates the budget constraint with commodities, music, and fireworks.

In Figure 1, the horizontal axis shows the fireworks and the vertical axis shows the music. The income of the consumer is $240. The price of music is $12 per CD. Therefore, the consumer can purchase maximum $20 (240/12) music CDs. The price of the fireworks is $8 per bag. Therefore, the consumer can purchase maximum $30(240/8) bags. Hence, Figure 1 represents the budget constraint with music and fireworks.

Economics Concept Introduction

Budget constraint: The budget constraint is a curve that describes the entire set of consumption bundles a consumer can purchase when spending all income.

(b)

To determine

The total amount spend on music.

Explanation of Solution

In Figure 1, the x-axis shows the fireworks and the y-axis shows the music. The income of the consumer is $240. The price of music is $12. If the consumer spends entire income on the music, then the number of music CDs that can be afforded is calculated as follows:

$\begin{array}{c}\text{Music}=\frac{\text{Income}}{\text{Price}}\\ =\frac{240}{12}\\ =20\end{array}$

The consumer can afford 20 music CDs, if he spends the entire income on music. This is shown as point b in Figure 2.

(c)

To determine

The total amount spend on fireworks.

Explanation of Solution

The income of the consumer is $240. The price of the fireworks is $8. If the consumer spends entire income on fireworks, then the amount of fire bags that can be calculated as follows:

$\begin{array}{c}\text{Fireworks}=\frac{\text{Income}}{\text{Price}}\\ =\frac{240}{8}\\ =30\end{array}$

The consumer can afford 30 bags for fireworks, if he spends the entire income on it. This is shown as point d in Figure 2.

(d)

To determine

The half of the total income was spend on the fireworks and half of the income on the music.

Explanation of Solution

If the consumer spends half of the income on fireworks, then the amount of bags for fireworks can be calculated as follows:

$\begin{array}{c}\text{Fireworks}=\frac{\frac{1}{2}\text{I}}{{\text{P}}_{\text{F}}}\\ =\frac{0.5\times 240}{8}\\ =15\end{array}$

Therefore, the consumer spends half of the income on fireworks 15 bags of fireworks, he can afford. This is shown by the point d in Figure 2.

If the consumer spends half of the income on music, then the number of music CDs can be calculated as follows:

$\begin{array}{c}\text{Fireworks}=\frac{\frac{1}{2}\text{I}}{{\text{P}}_{\text{F}}}\\ =\frac{0.5\times 240}{12}\\ =10\end{array}$

Therefore, if consumer spends half of the income on music, he can afford 10 CDs. This is shown by the point d in Figure 2.

(e)

To determine

The slope of the budget constraints.

Explanation of Solution

Figure 2 illustrates the budget constraint with commodities, music, and fireworks.

The slope of the budget constraint is determined by the relative price of the two goods. Therefore, it can be calculated as follows:

$\begin{array}{c}\frac{\Delta \text{M}}{\Delta \text{F}}=\frac{20}{30}\\ =\frac{2}{3}\end{array}$

Hence, the budget constraint is $\frac{2}{3}$.

Economics Concept Introduction

Budget constraint: The budget constraint is a curve that describes the entire set of consumption bundles a consumer can purchase when spending all income.

(f)

To determine

The price of fireworks and the price of music.

Explanation of Solution

The price of fireworks is divided with the price of music.

$\begin{array}{c}\frac{{\text{P}}_{\text{F}}}{{\text{P}}_{\text{M}}}=\frac{8}{12}\\ =\frac{2}{3}\end{array}$

Hence, the value of price divided with the price of music is $\frac{2}{3}$. This is the slope of the budget constraint.

Economics Concept Introduction

Budget constraint: The budget constraint is a curve that describes the entire set of consumption bundles a consumer can purchase when spending all income.

(g)

To determine

The new budget constraint.  

Explanation of Solution

Figure 3 illustrates the new budget constraint with commodities, music, and fireworks.

In Figure 3, the horizontal axis shows the fireworks and the vertical axis shows the music. The new income of the consumer is $360. The price of music is $12. Therefore, the consumer can purchase maximum 30 (360/12) music CDs. The price of the fireworks is $8. Therefore, the consumer can purchase maximum 45 fire bags (360/8) with the new income. Hence, Figure 3 represents the budget constraint of music and fireworks at the new income level.

Economics Concept Introduction

Budget constraint: The budget constraint is a curve that describes the entire set of consumption bundles a consumer can purchase when spending all income.

(h)

To determine

The number of fire bags and music CDs that can earned at new income level.

Explanation of Solution

The new income of the consumer is $360. Then, the new bundles of fireworks and music can be calculated as follows:

$\begin{array}{c}\text{Fireworks}=\frac{\text{Income}}{\text{Price}}\\ =\frac{360}{8}\\ =45\end{array}$

The consumer can afford 45 bags of fireworks, if he spends the entire income.

$\begin{array}{c}\text{Music}=\frac{\text{Income}}{\text{Price}}\\ =\frac{360}{12}\\ =30\end{array}$

The consumer can afford 30 music CDs, if he spends the entire new income.

Economics Concept Introduction

Consumption bundle: The consumption bundle is set of goods and services a consumer considers purchasing.