Question

Suppose that annual output in year 1 in a three-good economy is 3 quarts of ice cream, 1 bottle of shampoo, and 3 jars of peanut butter. In year 2, the output mix changes to 5 quarts of ice cream, 2 bottles of shampoo, and 2 jars of peanut butter. If the prices in both years are \(4 per quart for ice cream, \)3 per bottle of shampoo, and $2 per jar of peanut butter, what was the economy’s GDP in year 1? What was its GDP in year 2?

Short answer

The economy’s GDP in year 1 was $21.

The economy’s GDP in year 2 was $30.

Step-by-step solution

Economy’s GDP in year 1

Let the quantity of ice cream quarts, shampoo bottles, and peanut butter jars be x, y, and z, respectively.

Price of ice cream per quart = $4

Price of shampoo per bottle = $3

Price of peanut butter per jar = $2

Economy’s GDP = $4x + $3y + $2z

In year 1,

Economy's GDP = $4x3+$3x1+$2x3

=$12+$3+$6

=$21

Therefore, the economy’s GDP in year 1 is $21.

Economy’s GDP in year 2

In year 2, the prices remain the same while the quantity mixes change. Therefore, the economy’s income in year 2 is as follows:

Economy's GDP = $4x5+$3x2+$2x2

=$20+$6+$4

=$30

Therefore, the economy’s GDP in year 2 is $30.