Exam 3: Utility-Part A

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Charlie's utility function is U(A, B)= AB, where A and B are the numbers of apples and bananas, respectively, that he consumes.When Charlie is consuming 20 apples and 80 bananas, 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

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D

Tim has preferences represented by the utility function U(x, y)= min{6x + y, x + 2y}.If x is on the horizontal axis and y is on the vertical axis, what is the slope of his indifference curve at the point (8,9)?

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C

Raymond's preferences are represented by the utility function U(x, y)= x/y if y > 0 and U(x, y)= 0 if y = 0.

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E

Jean-Pierre has preferences represented by the utility function U(x, y)=min{2x + y, x + 6y}.If x is on the horizontal axis and y is on the vertical axis, what is the slope of his indifference curve at the point (7,7)?

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Waldo's utility function is U(x, y)= xy.Waldo consumes 5 units of x and 25 units of y.

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Henrietta's utility function is U(x1, x2)= x1x2.She has diminishing marginal rate of substitution between goods 1 and 2.

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Harry Mazzola has the utility function U(x1, x2)= min{x1 + 2x2, 2x1 + x2}.He has $40 to spend on corn chips and french fries.If the price of corn chips is $1 per unit and the price of french fries is $4, then Harry will

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A person with the utility function U(x, y)= 10 + y2 + x has convex preferences.

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Charles's utility function is U(x, y)= xy.Anne's utility function is U(x, y)=1,000xy.Diana's utility function is -xy.Elizabeth's utility function is U(x, y)= -1/(xy + 1).Fergie's utility function is xy -010,000.Margaret's utility function is x/y.Philip's utility function is x(y + 1).(The goods x and y are two very expensive goods.We leave you to speculate about what they are.)Which of these persons have the same preferences as Charles?

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Doreen has preferences represented by the utility function U(x, y)= 10x + 5y.She consumes 10 units of good x and 9 units of good y.If her consumption of good x is lowered to 1, how many units of y must she have in order to be exactly as well off as before?

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Harmon's utility function is U(x1, x2)= x1x2.His income is $100.The price of good 2 is p2 = 4.Good 1 is priced as follows.The first 15 units cost $4 per unit and any additional units cost $2 per unit.What consumption bundle does Harmon choose?

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Henry's utility function is x2 + 16xw + 64w2, where x is his consumption of x and w is his consumption of w.

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Charlie has the utility function U(xA, xB)= xAxB.His indifference curve passing through 32 apples and 8 bananas will also pass through the point where he consumes 4 apples and

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Jim's utility function is U(x, y)= xy.Jerry's utility function is U(x, y)= 1,000xy + 0 2,000.Tammy's utility function is U(x, y)= xy(1 - xy).Oral's utility function is U(x, y)=-1/(10 + 2xy).Marjoe's utility function is U(x, y)= x(y + 1,000).Pat's utility function is U(x, y)= 0.5xy - 10,000.Billy's utility function is U(x, y)= x/y.Francis's utility function is U(x, y)= -xy. a.Who has the same preferences as Jim? b.Who has the same indifference curves as Jim? c.Explain why the answers to (a)and (b)differ.

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Maximilian consumes two goods, x and y.His utility function is U(x, y)= max{x, y}.Therefore x and y are perfect substitutes for Max.

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Josephine's utility function is U(x, y)= y + 5x.5.She has 1 unit of x and 2 units of y.If her consumption of x is reduced to zero, how much y must she have in order to be exactly as well off as before?

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Joe Bob's cousin Leonard consumes goods 1 and 2.Leonard thinks that 2 units of good 1 is always a perfect substitute for 3 units of good 2.Which of the following utility functions is the only one that would not represent Leonard's preferences?

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Angela has preferences represented by the utility function U(x, y)= 2x + 2y.She consumes 10 units of good x and 6 units of good y.If her consumption of good x is lowered to 4, how many units of y must she have in order to be exactly as well off as before?

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A person with the utility function U(x, y)= y + x2 has convex preferences.

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Ike's utility function is U(x, y)= xy.Ike consumes 2 units of x and 8 units of y.

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