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Question 1) Charlie's utility is U(x1, x2) = 4x^1/2+x2. If the price of nuts (good 1)...

Question 1) Charlie's utility is U(x1, x2) = 4x^1/2+x2. If the price of nuts (good 1) is $1, the price of berries (good 2) is $4, and his income is $132, how many units of nuts will Charlie choose?

A. 128

B. 32

C. 67

D. 64

E. 17

Question 2) Kyle's utility function is U(A, B) = AB, where A and B are the numbers of apples and bananas, respectively, that he consumes. If Kyle is consuming 15 apples and 30 bananas, then if we put apples on the horizontal axis and bananas on the vertical axis, the slope of his indifference curve at his current consumption is

A. -2

B. -16

C. -1/2

D. -4

E. -1/4

Expert Solution

1. The correct option would be

d. 64

The utility function is given as . The budget constraint is given as or . The optimal solution is where slope of budget line is equal to slope of indifference curve.

The slope of indifference curve (in absolute terms) or MRS (marginal rate of substitution) would be as or or or . The slope of budget line (in absolute terms) would be as . The optimal combination of goods would be where or or or or or units.

The optimal amount of good 2 would be hence or or or units.

2. The correct option would be

a. -2

The utility function is . The slope of indifference curve would be as or . For B=30 and A=15, we have or .

For , we have the slope of indifference curve as or or , and for a constant utility level, we have or or .

Rahul Sunny answered 2 years ago

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