Chapter 25, Problem 2FT

To determine

Draw a budget line.

Explanation of Solution

Budget constraint equation:

General budget constraint equation can be written as follows:

${\text{Price}}_{\text{X}}\times {\text{Quantity}}_{\text{X}}+{\text{Price}}_{\text{Y}}\times {\text{Quantity}}_{\text{Y}}=\text{Income}$ (1)

Substitute the respective values in Equation (1) to calculate the maximum quantity of Lat can buy (when the consumer buys 0 units of Sco) with initial price.

$\begin{array}{c}\left({\text{Price}}_{\text{Sco}}\times {\text{Quantity}}_{\text{Sco}}\right)+\left({\text{Price}}_{\text{Lat}}\times {\text{Quantity}}_{\text{Lat}}\right)=\text{Income}\\ \left(\text{1}\text{.5}\times \text{0}\right)+\left(\text{2}\times {\text{Quantity}}_{\text{Lat}}\right)=240\\ 0+\left(\text{2}\times {\text{Quantity}}_{\text{Lat}}\right)=240\\ {\text{Quantity}}_{\text{Lat}}=\frac{240}{2}\\ =120\end{array}$

The maximum quantity of Lat is 120 units.

Substitute the respective values in equation (1) to calculate the maximum quantity of Sco can buy (when the consumer buys 0 units of Lat) with initial price.

$\begin{array}{c}\left({\text{Price}}_{\text{Sco}}\times {\text{Quantity}}_{\text{Sco}}\right)+\left({\text{Price}}_{\text{Lat}}\times {\text{Quantity}}_{\text{Lat}}\right)=\text{Income}\\ \left(\text{1}\text{.5}\times {\text{Quantity}}_{\text{Sco}}\right)+\left(\text{2}\times \text{0}\right)=240\\ \left(\text{1}\text{.5}\times {\text{Quantity}}_{\text{Sco}}\right)+0=240\\ {\text{Quantity}}_{\text{Sco}}=\frac{240}{1.5}\\ =160\end{array}$

The maximum quantity of Sco is 160 units.

Substitute the respective values in Equation (1) to calculate the maximum quantity of Lat can buy (when the consumer buys 0 units of Sco) with new price.

$\begin{array}{c}\left({\text{Price}}_{\text{Sco}}\times {\text{Quantity}}_{\text{Sco}}\right)+\left({\text{Price}}_{\text{Lat}}\times {\text{Quantity}}_{\text{Lat}}\right)=\text{Income}\\ \left(\text{2}\text{.25}\times \text{0}\right)+\left(\text{3}\times {\text{Quantity}}_{\text{Lat}}\right)=240\\ 0+\left(\text{3}\times {\text{Quantity}}_{\text{Lat}}\right)=240\\ {\text{Quantity}}_{\text{Lat}}=\frac{240}{3}\\ =80\end{array}$

The maximum quantity of Lat is 80 units.

Substitute the respective values in Equation (1) to calculate the maximum quantity of Sco can buy (when the consumer buys 0 units of Lat) with new price.

$\begin{array}{c}\left({\text{Price}}_{\text{Sco}}\times {\text{Quantity}}_{\text{Sco}}\right)+\left({\text{Price}}_{\text{Lat}}\times {\text{Quantity}}_{\text{Lat}}\right)=\text{Income}\\ \left(\text{2}\text{.25}\times {\text{Quantity}}_{\text{Sco}}\right)+\left(\text{3}\times \text{0}\right)=240\\ \left(\text{2}\text{.25}\times {\text{Quantity}}_{\text{Sco}}\right)+0=240\\ {\text{Quantity}}_{\text{Sco}}=\frac{240}{2.25}\\ =106.67\end{array}$

The maximum quantity of Sco is 106.67units.

Figure 1 illustrates the budget line for the different price levels.

Figure 1

In Figure 1, the horizontal axis measures the quantity of Sco and the vertical axis measures the quantity of Lat. When the income is fixed, increasing price reduces the quantity of goods that can be purchased. This would shift the budget line inward.

Substitute the respective values in Equation (1) to calculate the maximum quantity of Lat can buy (when the consumer buys 0 units of Sco) with new price and new income.

$\begin{array}{c}\left({\text{Price}}_{\text{Sco}}\times {\text{Quantity}}_{\text{Sco}}\right)+\left({\text{Price}}_{\text{Lat}}\times {\text{Quantity}}_{\text{Lat}}\right)=\text{Income}\\ \left(\text{2}\text{.25}\times \text{0}\right)+\left(\text{3}\times {\text{Quantity}}_{\text{Lat}}\right)=360\\ 0+\left(\text{3}\times {\text{Quantity}}_{\text{Lat}}\right)=360\\ {\text{Quantity}}_{\text{Lat}}=\frac{360}{3}\\ =120\end{array}$

The maximum quantity of Lat is 120 units.

Substitute the respective values in Equation (1) to calculate the maximum quantity of Sco can buy (when the consumer buys 0 units of Lat) with new price.

$\begin{array}{c}\left({\text{Price}}_{\text{Sco}}\times {\text{Quantity}}_{\text{Sco}}\right)+\left({\text{Price}}_{\text{Lat}}\times {\text{Quantity}}_{\text{Lat}}\right)=\text{Income}\\ \left(\text{2}\text{.25}\times {\text{Quantity}}_{\text{Sco}}\right)+\left(\text{3}\times \text{0}\right)=360\\ \left(\text{2}\text{.25}\times {\text{Quantity}}_{\text{Sco}}\right)+0=360\\ {\text{Quantity}}_{\text{Sco}}=\frac{360}{2.25}\\ =160\end{array}$

The maximum quantity of Sco is 160units.

Figure 2 illustrates the budget line for the different price levels.

In Figure 2, the horizontal axis measures the quantity of Sco and the vertical axis measures the quantity of Lat. When the income increases, the quantity of goods that can be purchased would increase. This shifts the budget line outward to the initial level. The impact of increasing price of 50% for both the goods offset by increasing the income by 50% .

Economics Concept Introduction

Concept Introduction:

Budget line: Budget line (Budget constraint) refers to all the possible combinations of goods and services that can be purchased with the entire income, at a given price level.