Chapter 6, Problem 1.1P

To determine

Sketch the budget constraint.

Explanation of Solution

Maximum unit of good Y (0 unit of good X is purchased) that a person can purchase with the given income and price can be calculated by using the following formula:

${\text{Quantity}}_{\text{Y}}=\frac{\text{Income}}{\text{Price of Y}}$ (1)

Substitute the respective values in Equation (1) to calculate the maximum unit of Y that can be purchased.

$\begin{array}{c}{\text{Quantity}}_{\text{Y}}=\frac{5,000}{25}\\ =200\end{array}$

The maximum unit of Y is 200 units.

Maximum unit of good X (0 unit of good Y is purchased) that a person can purchase with the given income and price can be calculated by using the following formula:

${\text{Quantity}}_{\text{X}}=\frac{\text{Income}}{\text{Price of X}}$ (2)

Substitute the respective values in Equation (2) to calculate the maximum unit of X that can be purchased.

$\begin{array}{c}{\text{Quantity}}_{\text{Y}}=\frac{5,000}{100}\\ =50\end{array}$

The maximum unit of X is 50 units.

Option (a):

Figure 1 shows the budget constraint of case “a”.

In Figure 1, the vertical axis measures the price of good Y and horizontal axis measures the price of good X. The downward sloping cure is the budget constrain of the household.

Option (b):

The maximum quantity of good X and Y is 25 and 40 respectively that is obtained by using Equation (1) and (2).

Figure 2 shows the budget constraint of case “b”.

In Figure 2, the vertical axis measure price of good Y and horizontal axis measures price of good X. The downward sloping cure is the budget constrain of the household.

Option (c):

The maximum quantity of good X and Y is 40 and 5, respectively that is obtained by using Equation (1) and (2).

Figure 3 shows the budget constraint of case “c”.

In Figure 3, the vertical axis measures the price of good Y and horizontal axis measures the price of good X. The downward sloping cure is the budget constrain of the household.

Option (d):

The maximum quantity of good X and Y is 20 and 50, respectively that is obtained by using Equation (1) and (2).

Figure 4 shows the budget constraint of case “d”.

In Figure 4, the vertical axis measures the price of good Y and horizontal axis measures the price of good X. The downward sloping cure is the budget constrain of the household.

Option (e):

The maximum quantity of good X and Y is 4 and 6, respectively that is obtained by using Equation (1) and (2).

Figure 5 shows the budget constraint of case “e”.

In Figure 5, the vertical axis measures the price of good Y and horizontal axis measures the price of good X. The downward sloping cure is the budget constrain of the household.

Option (f):

The maximum quantity of good X and Y is 24 and 4, respectively that is obtained by using Equation (1) and (2).

Figure 6 shows the budget constraint of case “f”.

In Figure 6, the vertical axis measures the price of good Y and horizontal axis measures the price of good X. The downward sloping cure is the budget constrain of the household.

Option (g)

The maximum quantity of good X and Y is 4 and 24, respectively that is obtained by using Equation (1) and (2).

Figure 7 shows the budget constraint of case “g”.

In Figure 7, the vertical axis measures the price of good Y and horizontal axis measures the price of good X. The downward sloping cure is the budget constrain of the household.

Economics Concept Introduction

Budget constraints: Restrictions imposed on household’s choices by the factors like wealth, income and price of product are termed as the budget constraint.