Question

PART 2 - Short Answer, 8 points overall, point values are indicated for each part of the question. 1. Suppose Henry has $8 of income to spend on his two passions: Mountain Dew and Red Bull. At the local convenience store, Henry can buy cans of Dew for $1 each and cans of Red Bull for $2 each. Assume he will spend all of his $8 on these two goods. The table below displays Henry's preferences. Quantity of Total utility Quantity of Total utility Mountain Mountain Red Bull Red Bull Dew Dew (Dewtility) 46 24 56 26 27 6 6 60 a. (2 points) Determine the optimal bundle of the two goods that will maximize Henry's utility level. Show (in the table) how you determined this bundle. Explain briefly how you determined what he would buy. b. (2 points) Create a graph that displays Henry's consumer choice decision as described above. Please put Mountain Dew on the vertical (y) axis. You should draw several indifference curves including one that shows his optimal choice. Label the optimal bundle. (3 points) Suppose that a tragic accident by a Red Bull drinker reveals that the beverage does not, in fact, "give you wings". As a result, the popularity of Red Bull drops and the price fails to $1 a can. Show on a new graph how this has affected Henry's consumer choice decision and his utility. (NOTE: assume this change only affects Henry's decision by changing the price, his love for Red Bull is not affected by the accident). You do not need to re-solve for the new optimal bundle, just show the change graphically (show before and after on the same graph). Explain briefly what the graph depicts in real world terms. d. (1 point) Suppose that we are back in the original situation where Henry has the preferences given in the table and has $8 to spend. The price of Mountain Dew is $1 and the price of Red Bull is $2. Now suppose a promotion is going on, and Henry is handed two free cans of Mountain Dew. Assuming he will still spend his $8 on some combination of Mountain Dew and Red Bull, how many cans of each will he end up with now? Explain briefly.

Answer 1

a. We can make the following table to determine the quantity of red bull he buys if he buys x units of mountain dew, by using (8-x)/2 as the formula since the price of mountain dew is 1 and of red bull is 2. This is also called the budget line. We can also show the utility from the respective quantities of the two drinks (for fractional quantity of red bull, I show the utility from the integer below that quantity). Since 63 is the highest utility bundle (total of utility from mountain dew and red bull), he should buy 2 units of mountain dew and 3 units of red bull

Total budget = 8
Budget line
Quantity of mountain dew	Quantity of red bull	total utility of mountain dew	total utility of red bull	Total utility
0	4	0	56	56
1	3.5	10	46	56
2	3	17	46	63
3	2.5	21	34	55
4	2	24	34	58
5	1.5	26	18	44
6	1	27	18	45

b. We can show it as below. The indifference curve that meets the budget line at point A represents 63 units of utility and maximizes utility. The other indifference curves are either too high (won't fit into the budget line) or too low (not maximizing utility by spending the available amount of money).

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c. As shown below, as a result of the drop in red bull's price the budget line pivots rightwards (represented by the solid downward sloping line). This implies that he can buy more of red bull (for the same quantity of mountain dew as earlier). This enables him to settle on a much higher indifference curve getting a much higher quantity of utility.

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d. Let's modify the table to show the 2 free cans by modifying the formula (in a. above) we used to get the quantity of red bull for a given (x) quantity of mountain dew as follows: 2+(8-x)/2. Now he will buy 4 units of mountain dew (and consume 4 of red bull, 2 of which he bought and 2 which he got free).

Total budget = 8
Budget line
Quantity of mountain dew	Quantity of red bull	total utility of mountain dew	total utility of red bull	Total utility
0	6	0	60	60
1	5.5	10	60	70
2	5	17	60	77
3	4.5	21	56	77
4	4	24	56	80
5	3.5	26	46	72
6	3	27	46	73