Chapter E, Problem 1QP

(a)

To determine

Draw the budget constraint when income = $4,000; PX = $50; PY = $100.

Explanation of Solution

Since the income is $4,000 and price of good X is $50, the quantity of good X can be calculated as follows:

$\begin{array}{c}\text{Quantity of good X}=\frac{\text{Income}}{\text{Price of good X}}\\ =\frac{\$4,000}{\$50}\\ =80\end{array}$

Thus, the consumer will consume 80X.

Since the income is $4,000 and price of good Y is $100, the quantity of good Y can be calculated as follows:

$\begin{array}{c}\text{Quantity of good Y}=\frac{\text{Income}}{\text{Price of good Y}}\\ =\frac{\$4,000}{\$100}\\ =40\end{array}$

Thus, the consumer will consume 40Y.

Now, the budget constraint can be represented as follows:

In Figure 1, the vertical axis measures the quantity of good Y and the horizontal axis measures the quantity of good X.

(b)

To determine

Draw the budget constraint when income = $3,000; PX = $25; PY = $200.

Explanation of Solution

Since the income is $3,000 and price of good X is $25, the quantity of good X can be calculated as follows:

$\begin{array}{c}\text{Quantity of good X}=\frac{\text{Income}}{\text{Price of good X}}\\ =\frac{\$3,000}{\$25}\\ =120\end{array}$

Thus, the consumer will consume 120X.

Since the income is $3,000 and price of good Y is $200, the quantity of good Y can be calculated as follows:

$\begin{array}{c}\text{Quantity of good Y}=\frac{\text{Income}}{\text{Price of good Y}}\\ =\frac{\$3,000}{\$200}\\ =15\end{array}$

Thus, the consumer will consume 15Y.

Now, the budget constraint can be represented as follows:

In Figure 2, the vertical axis measures the quantity of good Y and the horizontal axis measures the quantity of good X. 

(c)

To determine

Draw the budget constraint when income = $2,000; PX = $40; PY = $150.

Explanation of Solution

Since the income is $2,000 and price of good X is $40, the quantity of good X can be calculated as follows:

$\begin{array}{c}\text{Quantity of good X}=\frac{\text{Income}}{\text{Price of good X}}\\ =\frac{\$2,000}{\$40}\\ =50\end{array}$

Thus, the consumer will consume 50X.

Since the income is $2,000 and price of good Y is $150, the quantity of good Y can be calculated as follows:

$\begin{array}{c}\text{Quantity of good Y}=\frac{\text{Income}}{\text{Price of good Y}}\\ =\frac{\$2,000}{\$150}\\ =13.33\end{array}$

Thus, the consumer will consume 13.33Y.

Now, the budget constraint can be represented as follows:

In Figure 3, the vertical axis measures the quantity of good Y and the horizontal axis measures the quantity of good X.