Question

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.

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