Chapter 2, Problem 8PA

(a)

To determine

Consumer price index.

Explanation of Solution

Given information:

Price of a red apple in the first year is $1.

Price of a green apple in the first year is $2.

Quantity of red apples consumed in the first year is 10.

Price of a red apple in the second year is $2.

Price of a green apple in the second year is $1.

Quantity of green apples consumed in the second year is 10.

Calculation:

To calculate the consumer price index, fix the basket of goods in the first year. Thus, the first year price is considered as base year price; therefore, the consumer price index in the first year is equal to 1. The calculation of CPI (Consumer Price Index) in the second year is shown below:

$\begin{array}{c}{\text{CPI}}_2=\left(\frac{\left({\text{Price}}_{\text{Red apple}}^2\times {\text{Quantity}}_{\text{Red apple}}^1\right)+\left({\text{Price}}_{\text{Green apple}}^2\times {\text{Quantity}}_{\text{Green apple}}^1\right)}{\left({\text{Price}}_{\text{Red apple}}^1\times {\text{Quantity}}_{\text{Red apple}}^1\right)+\left({\text{Price}}_{\text{Green apple}}^1\times {\text{Quantity}}_{\text{Green apple}}^1\right)}\right)\\ =\left(\frac{\left(2\times 10\right)+\left(1\times 0\right)}{\left(1\times 10\right)+\left(2\times 0\right)}\right)\\ =\left(\frac{20}{10}\right)\\ =2\end{array}$

CPI (Consumer Price Index) in  the second year is 2.

Economics Concept Introduction

Consumer Price index (CPI): Consumer price index is a measure that examines the changes in price levels of a basket of consumer goods and services for the present time from the base year.

(b)

To determine

Nominal spending on apples in two years.

Explanation of Solution

Mr. A purchases 10 red apples in the first year at $1 for each and purchases 10 green apples in the second year at $1. Thus, Mr. A’s nominal spending is $10.

(c)

To determine

Real spending on apples in two years.

Explanation of Solution

Calculation of real spending in both years is shown below:

$\begin{array}{c}{\text{Real spending}}_1=\left({\text{Price}}_{\text{Red apple}}^1\times {\text{Quantity}}_{\text{Red apple}}^1\right)+\left({\text{Price}}_{\text{Green apple}}^1\times {\text{Quantity}}_{\text{Green apple}}^1\right)\\ =\left(1\times 10\right)+\left(1\times 0\right)\\ =10\end{array}$

Real spending of the consumer in the first year is $10.

$\begin{array}{c}{\text{Real spending}}_2=\left({\text{Price}}_{\text{Red apple}}^1\times {\text{Quantity}}_{\text{Res apple}}^2\right)+\left({\text{Price}}_{\text{Green apple}}^1\times {\text{Quantity}}_{\text{Green apple}}^2\right)\\ =\left(1\times 0\right)+\left(2\times 10\right)\\ =20\end{array}$

Real spending of the consumer in the second year is $20. The real spending is doubled.

(d)

To determine

Implicit price deflator.

Explanation of Solution

The general formula for calculating the implicit price deflator is given below:

$\text{Implicit price deflator}=\left(\frac{\text{Nominal spending}}{\text{Real spending}}\right)$

Substitute the respective values in the above equation to calculate the implicit price deflator in the first year.

$\begin{array}{c}{\text{Implicit price deflator}}_1=\left(\frac{10}{10}\right)\\ =1\end{array}$

Implicit price deflator in the first year is 1.

By using the same equation, the calculation of the implicit price deflator in the second year is shown below:

$\begin{array}{c}{\text{Implicit price deflator}}_1=\left(\frac{10}{20}\right)\\ =0.5\end{array}$

Implicit price deflator in the second year is 0.5. The implicit price deflator is decreased by half in the second year.

(e)

To determine

Cost of living and example of Laspeyres price index and Paasche price index.

Explanation of Solution

If the consumer assume that, the red apple and green apple are given the same level of utility or both are perfect substitute, the cost of living does not changed. He spends $10 for 10 apples. The consumer price index is a Laspeyres price index and it indicates that the cost of living index is doubled. On the other hand, the implicit price deflator is a Paasche price index. It indicates that the cost of living was fallen half. The reason is it does not consider the changes in the relative price.