Chapter 13, Problem 1SPPA

To determine

Total income of Amy is $12 a week. The price of coffee is $2 a cup and price of soda is $1 a cup. Create the graph of Amy's budget line. Can Amy consume the combination of 7 cans of soda and 2 cups of coffee a week or 7 cups of coffee and 2 cans of soda a week? Also, determine the relative price of a cup of coffee

Explanation of Solution

The budget line linear equation is:

  $\begin{array}{l}\text{\$2C + \$1S = \$12}\\ \text{Where, C = Cups of Coffee, and}\\ \text{S = Cans of Soda}\end{array}$

The x-axis coordinate of budget line is: Income divided by price of Coffee: 6

The y-axis coordinate of budget line is: Income divided by price of Soda: 12

Amy's budget line is given below:

Now, with the different consumption bundles:

With 7 cans of soda and 2 cups of coffee, the total expenditure would be $11 which is less than total income of $12:

  $\begin{array}{l}\text{(\$2×2) + (\$1×7) < \$12}\\ \text{\$4 + \$7 < \$12}\\ \text{\$11 < \$12}\end{array}$

The consumer, Amy can afford this consumption bundle because the expenditure is less than income but some income is still saved. So, Amy can consume more of Soda cans or use it in other combination of consumption bundle so that her total expenditure is equal to total income.

Whereas, with 2 cans of Soda and 7 cups of coffee, the total expenditure would be $16 which is more than total income of $12:

  $\begin{array}{l}\text{(\$2×7) + (\$1×2) > \$12}\\ \text{\$14 + \$2 > \$12}\\ \text{\$16 > \$12}\end{array}$

So, Amy cannot afford this consumption bundle because its expenditure is more than her income level.

The first and second consumption bundles are shown in the diagram below as point A and point B, respectively.

The relative price of a cup of coffee is the price of coffee divided by price of a can of soda.

Therefore, $\frac{\$2}{\$1}=2$, it means in order to consume one cup of coffee, Amy should give up 2 cans of Soda.

Economics Concept Introduction

Budget Line: It is a graphical representation of a budget constraint of a consumer. The budget constraint is a linear equation which is the function of price of goods, income of the consumer and quantities consumed by the consumer. It is given below:

For two goods, the equation of budget line is: ${\text{(P}}_{\text{x}}{\text{×x) + (P}}_{\text{y}}\text{×y) = M}$

Where, ${\text{P}}_{\text{x}}$ is price of good X,

  ${\text{P}}_{\text{y}}$ Is price of good Y,

  $\text{M}$ is the income of the consumer, and

'X' and 'Y' are the quantities of two goods.