Chapter 8, Problem 1SPA

To determine

Consumer preferences and budget line.

Explanation of Solution

It is given that the total income of J is $12. The price of Yogurt is $2 and the price of Berries is $4. The equation of budget line is given using Equation (1) as follows.

$\text{Income}=\left({\text{Price}}_{\text{Yogurt}}\times {\text{Quantity}}_{\text{Yogurt}}\right)+\left({\text{Price}}_{\text{Berries}}\times {\text{Quantity}}_{\text{Berries}}\right)$ (1)

Assume J had spent his entire income to buy yogurt. The total quantity of yogurt consumed can be calculated by substituting the respective values in Equation (1).

$\begin{array}{c}\text{Total income}=\left(\text{2}\times {\text{Quantity}}_{\text{Yogurt}}\right)+\left(\text{4}\times {\text{Quantity}}_{\text{Berries}}\right)\\ \text{12}=\left(\text{2}\times {\text{Quantity}}_{\text{Yogurt}}\right)+\left(\text{4}\times \text{0}\right)\\ {\text{Quantity}}_{\text{Yogurt}}=\frac{12}{2}\\ =6\end{array}$

The quantity of yogurt consumed is 6 and the quantity of berries consumed is 0.

Similarly when the entire income is spent on the consumption of berries, the quantity can be calculated by substituting the respective values in Equation (1).

$\begin{array}{c}\text{Total income}=\left(\text{2}\times {\text{Quantity}}_{\text{Yogurt}}\right)+\left(4\times {\text{Quantity}}_{\text{berries}}\right)\\ \text{4}=\left(\text{2}\times \text{0}\right)+\left(4\times {\text{Quantity}}_{\text{berries}}\right)\\ {\text{Quantity}}_{\text{berries}}=\frac{12}{4}\\ =3\end{array}$

The quantity of berries consumed is 3 and the quantity of yogurt consumed is 0.

Table 1 shows the various combinations of yogurt and berries that can be bought with the given income that was obtained using Equation (1).

Table 1

Quantity of Yogurt	6	4	2	0
Quantity of Berries	0	1	2	3

Figure 1 shows the budget line of J.

The horizontal axis of Figure 1 measures the quantity of berries and the vertical axis measures the quantity of Yogurt. The budget line touches the vertical axis when the entire income is used to consume 6 units of yogurt and the horizontal axis when the entire income is spent on consuming berries. Each point on budget line shows various combination of consuming yogurt and berries by spending the whole income.

Economics Concept Introduction

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