Question

2) Max lives on Snickers Bars and Doritos. The price of Snickers (S) is 2 dollars per bar and the price of Doritos (D) is 1 dollar per bag. Max allows himself to spend no more than 10 dollars a day on food. He also restricts his consumption to 5,000 calories per day. There are 500 calories in a Snickers Bar and 1000 calories in bag of Doritos. Assume that Max spends his entire money budget each day and consumes no more calories than his limit. a) Draw Max's Budget constraint and calculate the MRT. Put Snickers on the Y-Axis b) Draw Max's caloric constraint. c) Identify the set of possible bundles that satisfy Max's budget and caloric constraint? d) What is the highest number of Snickers bars Max could feasibly consume? Would he have income left if he did that? Does he meet his caloric constraint? What is the largest number of bags of Doritos he could feasibly consume? Would he have income left after that? Does he meet his caloric constraint? e) f) What combination of Snickers and Doritos would he consume if wanted to spend all his money and consume 5,000 calories? Lori is studying economics and political science. She can read 30 pages of political science per hour but only 5 pages of economics per hour. This week she has a 50-page assignment in economics and a 150-page assignment in political science. Because of her job, she cannot devote more than 10 hours to studying these subjects this week. She realizes she cannot complete all of her assignments but is determined to complete at least 30 pages of her economics reading. Draw a graph with pages of economics on the horizontal axis and pages of political science on the vertical axis. On this graph, show the possibilities that are consistent with the constraints that Lori has imposed on herself. (She is allowed to read ahead in either subject.) Label key points on your graph with their numerical values. 3)

Answer 1

2. (a) The graph is as below. The budget constraint would be $\dpi{80} D + 2S = 10$ .

The MRT would be as $\dpi{80} S = -0.5D + 5$ or $\dpi{80} \frac{\mathrm{d} S}{\mathrm{d} D} = -0.5$ .

(b) The graph is as below. The caloric constraint would be $\dpi{80} 1000D + 500S = 5000$ .

(c) The graph is as below.

The bundles in the region below ABC would be optimum ones. Bundles above AB in the below 5000 calorie region are not feasible, while bundles on right of BC below budget constraint are feasible, but have more calories than 5000.

We have $\dpi{80} S = -0.5D + 5$ , and putting it in the calorie constraint, we have $\dpi{80} 1000D + 500(-0.5D + 5) = 5000$ or $\dpi{80} D = 10/3$ and $\dpi{80} S = -0.5*10/3 + 5 = 10/3$ . This the point B. The feasible set of bundles would be hence $\dpi{80} S \leq \left\{\begin{matrix} -0.5D + 5 & for & D \leq 10/3\\ -2D+10 & for & 10/3 \leq D \leq 5 \end{matrix}\right.$ .

(d) At point A, Sam may have 5 snickers and zero doritos. Sam would have no income left, as point A is on the budget constraint. The calorie consumed will be less than 5000, which is the restriction.

(e) At point C, Sam may have 5 doritos. Same would have some income left ($5), as C is not on the budget constraint. But, Sam would be consuming 5000 calories, meeting the restriction.

(f) At point B, which is both on the budget and calorie constraint, Sam may consume 10/3 units of both, meeting his calorie restriction and exhausting his income.