Chapter 15, Problem 1FRQ

a)

To determine

The question requires us to determine the value of the price index in 2010.

Answer to Problem 1FRQ

The price index in the year 2010 is 100.

Explanation of Solution

Given,

Year 2010 is the base year.

Price of goods in the year 2010 = $P

Price of goods in the year 2030 = $2P

  $\begin{array}{c}\text{Price}\text{index}\text{for}\text{year}\text{2010=}\frac{\text{Price}\text{of}\text{good}\text{in}\text{current}\text{year}}{\text{Price}\text{of}\text{good}\text{in}\text{base}\text{year}}\text{×100}\\ \text{=}\frac{\text{\$P}}{\text{\$P}}\text{×100}\\ \text{=100}\end{array}$

The price index for the year 2010 is 100.

Economics Concept Introduction

The formula for the price index is:

  $\text{Price}\text{index=}\frac{\text{Price}\text{of}\text{good}\text{in}\text{current}\text{year}}{\text{Price}\text{of}\text{good}\text{in}\text{base}\text{year}}\text{×100}$

b)

To determine

The question requires us to determine the value of the price index in 2030.

Answer to Problem 1FRQ

The value of the price index in the year 2030 is 200.

Explanation of Solution

Given,

Year 2010 is the base year.

Price of goods in the year 2010 = $P

Price of goods in the year 2030 = $2P

  $\begin{array}{c}Priceindexforyear2030=\frac{Priceofgoodincurrentyear}{Priceofgoodinbaseyear}\times 100\\ =\frac{\$2P}{\$P}\times 100\\ =200\end{array}$

The value of the price index in the year 2030 is 200.

Economics Concept Introduction

The formula for the price index is:

  $\text{Price}\text{index=}\frac{\text{Price}\text{of}\text{good}\text{in}\text{current}\text{year}}{\text{Price}\text{of}\text{good}\text{in}\text{base}\text{year}}\text{×100}$

c)

To determine

The question requires us to determine the percentage change in nominal income between 2010 and 2030.

Answer to Problem 1FRQ

Nominal income rises by 100 percent from 2010 to 2030.

Explanation of Solution

Given,

Nominal income in the year 2010 = $40,000

Nominal income in the year 2030 = $80,000

  $\begin{array}{c}\text{Percent increase in nominal income =}\frac{\text{Nominal income in}2030-\text{Nominal income in}2010}{\text{Nominal income in}2010}\text{×100}\\ =\frac{80,000-40,000}{40,000}\times 100\\ =100\end{array}$

Nominal income rises by 100 percent from 2010 to 2030.

d)

To determine

The question requires us to determine the real income between 2010 and 2030.

Answer to Problem 1FRQ

Real income remains the same between 2010 and 2030.

Explanation of Solution

Real income remains the same between 2010 and 2030 because the price and nominal income both doubled during the given period.

An increase in price causes the purchasing power of money to fall, but the simultaneous increase in income level compensates for the higher price and the individual remains unaffected.

  $\text{Real income = }\frac{\text{Nominal}\text{income}}{\text{Change}\text{in}\text{price}}$

Suppose, the price index in 2010 = 100,

Price index in 2030 = 200 (double of 2010 price)

  $\begin{array}{c}\text{Real income in 2010 = }\frac{\text{\$40,000}}{\text{100}}\\ \text{=\$400}\\ \text{Real income in 2030 = }\frac{\text{\$80,000}}{\text{200}}\\ \text{=\$400}\end{array}$

So, real income remains the same.