Chapter 51, Problem 2FRQ

a)

To determine

Labeled budget line on the graph

Explanation of Solution

To draw budget line, we need:

In the equation form, the budget constraint can be written as:

5X+20Y=100

To find out the intercepts of the budget line and to find the x-intercept (0 for y) of the line:

  $\begin{array}{l}5X+20\times \left(0\right)=100\hfill \\ 5X+0=100\hfill \\ X=20\hfill \end{array}$

Now, to find the y-intercept (0 for x) of the line:

  $\begin{array}{l}5\times \left(0\right)+20Y=100\hfill \\ 0+20Y=100\hfill \\ Y=5\hfill \end{array}$

From these intercepts, the budget line by on the x- and y-intercepts would be shown on graph as:

  

Economics Concept Introduction

Introduction: A budget line is the graphical presentation of a price line that shows possible combination of goods that can be bought at various costs or different levels of income.

b)

To determine

Maximizing total utility if income is $100, good x is of $5, and good y is of $10. And, with current consumption one receives 100 utils from consuming last unit of good x and 400 utils from consuming last unit of good y.

Explanation of Solution

Yes, one can enjoy maximization of utility. Because from good x one can maximize by 100/5 and it can be 400/20 from good y, therefore, per dollar spent on good x, the marginal utility should be equal to marginal utility per dollar spent on good y.

Economics Concept Introduction

Introduction: Marginal utility refers to the benefit or satisfaction of person by consuming one additional unit of the good.

c)

To determine

The total and marginal utility by consuming one another unit of good

Explanation of Solution

By consuming another unit of good x, both the marginal utility of and the total utility of good x will decline because according to the law of diminishing marginal utility, an increase consumption of good (good x) at the time when keeping the same consumption of another good (good y), the marginal utility from additional consumption (good x) decreases.

This is the reason which is responsible to decrease the marginal utility per dollar spent on good x. And, from the marginal utility per dollar spent on good x, the additional benefit per dollar spent on good y will be higher but the total utility can be greater if one less unit would be spent on good x.

Economics Concept Introduction

Introduction: Marginal utility refers to the benefit or satisfaction of person by consuming one additional unit of the good.