Question 10 Healthy Hank consumes only nuts (xl) and berries (xa). HIs P x)j2xX2
ID: 1137628 • Letter: Q
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Question 10 Healthy Hank consumes only nuts (xl) and berries (xa). HIs P x)j2xX2 commodities can be represented by the utility fun preferences over these two ction: Part (): Suppose that the price of nuts is pi-$2, an as $42 to spend on nuts and berries, what is his optima nuts is pi-$2, and that the price of berries is p2 $2. If Hank Part (ii): Suppose that the price of nuts is p1-$3, and that the price of berries is p2 $2. If Hank has $42 to spend on nuts and berries, what is his optimal bundle, (x1*x2*)? Part (iil); Suppose that the price of nuts is pi-$5, and that the price of berries is p2-$2. If has $42 to spend on nuts and berries, what is his optimal bundle, (xi*x2*)?Explanation / Answer
U = 2x1 + x2
For a linear utility function, indifference curves are straight lines touching both axes and optimal bundle lies on one of the corner points. The goods are substitutes and so, only one is consumed.
(Part i) Budget line: 42 = 2x1 + 2x2, or x1 + x2 = 21
When x1 = 0, x2 = 21 and U = 2 x 0 + 21 = 21
When x2 = 0, x1 = 21 and U = 2 x 21 + 0 = 42
Since utility is higher when x1 = 21 and x2 = 0, this is the optimal bundle.
(Part ii) Budget line: 42 = 3x1 + 2x2
When x1 = 0, x2 = 42/2 = 21 and U = 2 x 0 + 21 = 21
When x2 = 0, x1 = 42/3 = 14 and U = 2 x 14 + 0 = 28
Since utility is higher when x1 = 14 and x2 = 0, this is the optimal bundle.
(Part iii) Budget line: 42 = 5x1 + 2x2
When x1 = 0, x2 = 42/2 = 21 and U = 2 x 0 + 21 = 21
When x2 = 0, x1 = 42/5 = 8.4 and U = 2 x 8.4 + 0 = 16.8
Since utility is higher when x1 = 0 and x2 = 21, this is the optimal bundle.
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