Chapter 51, Problem 2CYU

a)

To determine

The consumption bundles that lie on the consumer budget line.

Explanation of Solution

  

Income is 20

Quantity of movie tickets ($10 each)	Quantity of popcorn buckets ($5 per each)
2	0
1	2
0	4

On the vertical axis of the graph and the horizontal axis, respectively, are the budget line symbols for movie tickets and buckets of popcorn. Two movie tickets and four buckets of popcorn are included in the budget line, which displays an income of $20.

Therefore, the equation of the budget line would be:

  $\begin{array}{c}{\text{M = P}}_{\text{x}}{\text{Q}}_{\text{x}}{\text{+P}}_{\text{y}}{\text{Q}}_{\text{y}}\hfill \\ \begin{array}{l}\text{20 = }\left(\text{10}\right)\left(\text{2}\right)\text{+ (5)(0)}\\ \begin{array}{l}\text{20 = }\left(\text{10}\right)\left(\text{1}\right)\text{+ }\left(\text{5}\right)\left(\text{2}\right)\hfill \\ \text{20 = }\left(\text{10}\right)\left(\text{0}\right)\text{+ }\left(\text{5}\right)\left(\text{4}\right)\hfill \end{array}\end{array}\hfill \end{array}$

Here, M is the income of the consumer; P_x is the price of each movie ticket; P_y is the price of each popcorn bucket; Q_x is the quantity of each movie ticket, and Q_y is the quantity of each popcorn bucket.

Economics Concept Introduction

Introduction: Budget line is the graphical presentation of all combinations of goods that can be bought at certain income or prices.

b)

To determine

The consumption bundles that lie on the consumer budget line.

Explanation of Solution

  

Income is 12

Quantity of underwear ($4 each)	Quantity of socks ($2 per pair)
0	6
1	4
2	2
3	0

On the vertical axis of the graph and the horizontal axis, respectively, are the budget line symbols for the pair of socks and the quantity of underwear. Combining 6 pairs of socks and 3 sets of underwear yields a $12 income.

Therefore, the equation of the budget line would be:

  $\begin{array}{l}{\text{M = P}}_{\text{x}}{\text{Q}}_{\text{x}}{\text{+P}}_{\text{y}}{\text{Q}}_{\text{y}}\hfill \\ \text{12 = }\left(\text{2}\right)\left(\text{6}\right)\text{+ }\left(\text{4}\right)\left(\text{0}\right)\hfill \\ \text{12 = }\left(\text{2}\right)\left(\text{4}\right)\text{+ }\left(\text{4}\right)\left(\text{1}\right)\hfill \\ \text{12 = }\left(\text{2}\right)\left(\text{2}\right)\text{+ }\left(\text{4}\right)\left(\text{2}\right)\hfill \\ \text{12 = (2)(0)+}\left(\text{4}\right){\left(\text{3}\right)}_{}\hfill \end{array}$

Here, M is the income of the consumer; P_x is the price of each pair of socks; P_y is the price of each pair of underwear; Q_x is the quantity of each pair of socks, and Q_y is the quantity of each pair of underwear.

Economics Concept Introduction

Introduction: Budget line is the graphical presentation of all combinations of goods that can be bought at certain income or prices.