Chapter 78, Problem 1FRQ

a)

To determine

The median and mean income of the economy

Explanation of Solution

  $\begin{array}{l}\text{The total income of the Equalor economy would be:}\hfill \\ \text{= 99×10,000+1}\left(\text{\$1,010,000}\right)\hfill \\ \text{= \$2,000,000}\hfill \\ \text{Therefore, the mean income would be:}\hfill \\ \text{= }\frac{\text{Total income}}{\text{Population}}\hfill \\ \text{= }\frac{\text{\$2,000,000}}{100}\hfill \\ \text{= \$20,000}\hfill \\ \hfill \\ \text{Then, Median income would be:}\hfill \\ \begin{array}{l}\text{The total number of households is 100 and the central points are 50 and 51}\\ \text{where the income is 10,000 for both households therefore,}\end{array}\hfill \\ \text{Median = }\frac{\left({\text{Income of 50th household + 51}}^{\text{st}}\text{household}\right)}{2}\hfill \\ \text{= }\frac{\left(\text{\$10,000+\$10,000}\right)}{2}\hfill \\ \text{ = \$10,000}\hfill \end{array}$

Economics Concept Introduction

Introduction: Total income is the gross income of a country from all sources of revenue that subtract some deductions such as expenses and allowances. The amount of income, where one group of the population earns income below that amount and one group earns above that amount refers to the median income. Whereas, mean income is the average income of the population.

b)

To determine

The median and mean income of the economy, whether mean income changed, and the indicator (mean or median household income) which is better for the typical Ecuadorian household's income when the government redistributes the income.

Explanation of Solution

  $\begin{array}{l}\begin{array}{l}\text{As the government collects \$990,000 from the richest household and this income is}\\ \text{distributed among the remaining 99 households equally, then each household will get}\end{array}\hfill \\ \text{= 1,010,000-990,000}\hfill \\ \text{= \$20,000}\hfill \\ \text{The total income of the Equalor economy would be:}\hfill \\ \text{= 99×20,000+1}\left(\text{\$20,000}\right)\hfill \\ \text{= \$2,000,000}\hfill \\ \text{Therefore, the new mean income would be:}\hfill \\ \text{= Total income/Population}\hfill \\ \text{= \$2,000,000/100}\hfill \\ \text{= \$20,000}\hfill \end{array}$

  $\begin{array}{l}\text{Then, new Median income would be:}\hfill \\ \begin{array}{l}\text{The total number of households is 100 and the central points are 50 and 51 }\\ \text{where the new income is 20,000 for both households therefore,}\end{array}\hfill \\ \text{Median = }\left(\text{income of 50th household + 51st household}\right)\text{/2}\hfill \\ \text{ = }\left(\text{\$20,000+\$20,000}\right)\text{/2}\hfill \\ \text{ = \$20,000}\hfill \end{array}$

The median income is changed from $10,000 to $20,000 but the mean income is the same.

Here, the better indicator is median income because it better provides the difference or disparity in income of households.

Economics Concept Introduction

Introduction: Total income is the gross income of a country from all sources of revenue that subtract some deductions such as expenses and allowances. The amount of income, where one group of the population earns income below that amount and one group earns above that amount refers to the median income. Whereas, mean income is the average income of the population.