Chapter 1, Problem 3P

Sub part (a):

To determine

The possible combination of consumption of two goods.

Explanation of Solution

The consumption bundle of two goods can be calculated by using the following formula.

$\left({\text{Price}}_{\text{Candy}}\times {\text{Quantity}}_{\text{Candy}}\right)+\left({\text{Price}}_{\text{Peanut}}\times {\text{Quantity}}_{\text{Peanut}}\right)=\text{Income}$ (1)

Substitute the respective values in equation (1) to calculate the number of peanut bags purchased while consuming 0 units of candy bars.

$\begin{array}{c}\left(\text{0}\text{.75}\times \text{0}\right)+\left(\text{1}\text{.5}\times {\text{Qunantity}}_{\text{Peanut}}\right)=\text{15}\\ 0+\left(\text{1}\text{.5}\times {\text{Qunantity}}_{\text{Peanut}}\right)=15\\ {\text{Qunantity}}_{\text{Peanut}}=\frac{15}{1.5}\\ =10\end{array}$

When the person consumes 0 quantities of candy bars, then he can purchase 10 units of peanut bags.

Table -1 shows the possible quantity of candy bars and peanut bags with the given level of income that is obtained by using equation (1).

Table -1

Goods/Combination	1	2	3	4	5	6
Candy bars	0	4	8	12	16	20
Bags of peanuts	10	8	6	4	2	0

Economics Concept Introduction

Concept introduction:

Budget constraint: Budget constraints define the possible bundles of services and commodities that are purchased at a given price level with the entire income.

Opportunity cost: Opportunity cost refers to the benefits given up in the process of obtaining some other benefit.

Sub part b:

To determine

The possible combination of consumption of two goods.

Explanation of Solution

The diagram below shows the possible combination of two goods that can be purchased with the limited income. It is drawn based on the values given in the Table -1.

In Figure 1, the horizontal axis measures the quantity of candy bars and the vertical axis measures the quantity of peanut bags. The downward slope indicates the budget line.

The slope can be calculated as follows.

$\begin{array}{c}\text{Slope}=\frac{{\text{Quantity of peanut}}_{\text{Present}}-{\text{Quantity of peanut}}_{\text{Previous}}}{{\text{Quantity of candy bar}}_{\text{Present}}-{\text{Quantity of candy bar}}_{\text{Previous}}}\\ =\frac{8-10}{4-0}\\ =\frac{-2}{4}\\ =-0.5\end{array}$

Thus, the slope of this budget line is -0.5.

Opportunity cost (OP) of obtaining one more candy bar can be calculated as follows.

$\begin{array}{c}{\text{OP}}_{{}_{\text{Candy bar}}}=\frac{{\text{Quantity of peanut}}_{\text{Present}}-{\text{Quantity of peanut}}_{\text{Previous}}}{{\text{Quantity of candy bar}}_{\text{Present}}-{\text{Quantity of candy bar}}_{\text{Previous}}}\\ =\frac{8-10}{4-0}\\ =\frac{-2}{4}\\ =-0.5\end{array}$

In the calculation of opportunity cost, the sign can be ignored. Thus, the opportunity cost of getting one more candy bar is 0.5.

The opportunity cost (OP) of obtaining one more peanut bag can be calculated as follows.

$\begin{array}{c}{\text{OP}}_{{}_{\text{Peanut}}}=\frac{{\text{Quantity of candy bar}}_{\text{Present}}-{\text{Quantity of candy bar}}_{\text{Previous}}}{{\text{Quantity of peanut}}_{\text{Present}}-{\text{Quantity of peanut}}_{\text{Previous}}}\\ =\frac{4-0}{8-10}\\ =\frac{4}{-2}\\ =-2\end{array}$

In the calculation of opportunity cost, the sign can be ignored. The opportunity cost of getting one more candy bar is 2. The opportunity costs are constant over the possible combination of bundles since the slope of the budget line remains the same over different points in the budget line.

Economics Concept Introduction

Concept introduction:

Budget constraint: Budget constraints define the possible bundles of services and commodities that are purchased at a given price level with the entire income.

Opportunity cost: Opportunity cost refers to the benefits given up in the process of obtaining some other benefit.

Sub part (c):

To determine

The possible combination of consumption of two goods.

Explanation of Solution

The budget line shows only the possible combination of goods and services that can be purchased simultaneously within the given income level. Thus, it does not determine the optimum quantity of two goods.

Economics Concept Introduction

Concept introduction:

Budget constraint: Budget constraints define the possible bundles of services and commodities that are purchased at a given price level with the entire income.

Opportunity cost: Opportunity cost refers to the benefits given up in the process of obtaining some other benefit.

Sub part (d):

To determine

The possible combination of consumption of two goods.

Explanation of Solution

Table -2 shows the possible quantity of candy bars and peanut bags with the increased level of income that is obtained by using equation (1).

Table -2

Goods/ Combination	1	2
Candy bars	0	40
Bags of peanuts	20	0

The diagram below shows the possible combination of two goods that can be purchased with a limited income. It is drawn based on the values given in Table -2.

In Figure 2, the horizontal axis measures the quantity of the candy bar and the vertical axis measures the peanut bags. The downward slope (a) indicates the budget line with a $15 income, and the downward slope (b) indicates the budget line with a $30 income. Increasing the level of the income shifts the budget line to the right side.

Economics Concept Introduction

Concept introduction:

Budget constraint: Budget constraints define the possible bundles of services and commodities that are purchased at a given price level with the entire income.

Opportunity cost: Opportunity cost refers to the benefits given up in the process of obtaining some other benefit.