Question

Suppose you won \(15 on a lotto ticket at the local 7-Eleven and decided to spend all the winnings on candy bars and bags of peanuts. Candy bars cost \)0.75 each, while bags of peanuts cost \(1.50 each.

1. Construct a table showing the alternative combinations of the two products that are available.
2. Plot the data in your table as a budget line in a graph. What is the slope of the budget line? What is the opportunity cost of one more candy bar? What is the opportunity cost of one more bag of peanuts? Do these opportunity costs rise, fall, or remain constant as additional units are purchased?
3. Does the budget line tell you which of the available combinations of candy bars and bags of peanuts to buy?
4. Suppose thatyou had won \)30 on your ticketnot \(15. Show the \)30 budget line in your diagram. Has the number of available combinations increased or decreased?

Short answer

(a) The table showing the alternative combinations of the two products is as follows.

X	0	4	8	12	16	20
Y	10	8	6	4	2	0

(b) The budget line is as shown in the graph below.

The slope of the budget line is 0.5.

The opportunity cost for 1 more candy bar is a half unit of peanut.

The opportunity cost for 1 more bag of peanuts is 2 candy bars.

These opportunity costs remain constant.

(c) No, the budget line does not tell which of the available combinations to buy.

(d) The shift in the budget line is as shown below.

Yes, the number of available combinations has increased.

Step-by-step solution

Explanation for part 'a'

Let the units of the candy bar be x, and the units of a bag of peanuts be y. The budget line equation is

$15=0.75x+1.5y$

The table for the alternative combinations can be made as follows.

X	0	4	8	12	16	20
Y	10	8	6	4	2	0

For some arbitrary values of x commodity, the budget line equation can be solved for y commodity, such that the $15 budget is fully exhausted.

Explanation for part 'b'

By taking the values of alternative combinations from the above table, the budget line will be as follows.

The slope of the budget line can be estimated as below.

$Slope=\frac{∆y}{∆x}=\frac{2}{4}=0.5$

For consuming 4 candy bars, you will have to sacrifice 2 bags of peanuts.

$opportunity\cos t=\frac{2}{4}=0.5$

Therefore, the opportunity cost for 1 candy bar is 0.5 units of peanut.

For consuming 2 bags of peanuts, you will have to sacrifice 4 candy bars.

$opportunity\cos t=\frac{4}{2}=2$

Therefore, the opportunity cost for 1 bag of peanuts is 2 candy bars.

Explanation for part 'c'

No, the budget line does not tell which combination should be purchased because it does not specify which good or combination gives maximum utility. It does not clarify the number of bags of peanut and candy bars to purchase.

Explanation for part 'd'

As the budget has increased twice and the relative prices are constant, the number of possible combinations will also increase according to the new equation.

$30=0.75x+1.5y$

The table for the possible combinations is as follows.

X	0	4	8	12	16	20	24	28	32	36	40
Y	20	18	16	14	12	10	8	6	4	2	0