Exam 5: Demand-Part A

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Murphy's utility function is U(x, y)= min{4x + y, 2x + 2y, x + 4y}.Murphy is consuming 12 units of x and 6 units of y. a.Draw the indifference curve through this point.At what points does this indifference curve have kinks? b.The price of good x is $1.What is the highest possible price for y? What is the lowest possible price for y?

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For m > p2, the demand functions for goods 1 and 2 are given by the equations, x1 = m/p2 - 1 and x2 = p1/p2, where m is income and p1 and p2 are prices.Let the horizontal axis represent the quantity of good 1.Let p1 = 1 and p2 = 2.Then for m > 2, the income offer curve is

(Multiple Choice)
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Miss Muffet insists on consuming 2 units of whey per 1 unit of curds.If the price of curds is $3 and the price of whey is $3, then if Miss Muffett's income is m, her demand for curds will be

(Multiple Choice)
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Harry has $10 to spend on cans of Coke and Pepsi, which he regards as perfect substitutes, one for one.Pepsi costs $.50 a can and Coke costs $.60 a can.Harry has 20 coupons, each of which can be used to buy 1 can of Coke for $.40.Which of the following bundles will Harry buy?

(Multiple Choice)
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Carlos consumes only two goods, apples and bananas.His utility function is U(a, b)= a3b2.Before he trades, his initial endowment is wa apples and wb bananas.After he trades to his optimal consumption point at these prices, the relative prices change.Carlos is allowed to make further trades if he wishes.

(Multiple Choice)
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Robert's utility function is U(x, y)= min{4x, 2x + y}.The price of x is $3 and the price of y is $1.Robert's income offer curve is

(Multiple Choice)
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In economic theory, the demand for a good must depend only on income and its own price and not on the prices of other goods.

(True/False)
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A good is a luxury good if the income elasticity of demand for it is greater than 1.

(True/False)
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Fred has a Cobb-Douglas utility function with exponents that sum to 1.Sally consumes the same two goods, but the two goods are perfect substitutes for her.Despite these differences, Fred and Sally have the same price offer curves.

(True/False)
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Which of the following utility functions represent preferences of a consumer who does not have homothetic preferences?

(Multiple Choice)
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A rational consumer spends her entire income.If her income doubles and prices do not change, then she will necessarily choose to consume twice as much of every good as she did before.

(True/False)
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If preferences are homothetic and all prices double while income remains constant, then demand for all goods is halved.

(True/False)
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A consumer has a utility function given by U = min{x1, 2x2}.If good 2 has a price of zero, the consumer will always prefer more of good 2 to less.

(True/False)
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Ambrose's brother Sebastian has a utility function U(x1, x2)= 60x1/21 + x2.His income is $165, the price of good 1 (nuts)is $6, and the price of good 2 (berries)is $1.How many units of nuts will Sebastian demand?

(Multiple Choice)
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Daisy received a tape recorder as a birthday gift and is not able to return it.Her utility function is U(x, y, z)= x + z1/2 f(y), where z is the number of tapes she buys, y is the number of tape recorders she has, and x is the amount of money she has left to spend.f(y)= 0 if y < 1 and f(y)= 8 if y is 1 or greater.The price of tapes is $1 and she can easily afford to buy dozens of tapes.How many tapes will she buy?

(Multiple Choice)
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Darlene's utility function is U(x, y, z)= x 4y 8z.If her income doubles and prices remain unchanged, her demand for good y will more than double.

(True/False)
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Wilma Q.has a utility function U(x1, x2)=x21 +1.5x1x2 + 30x2.The prices are p1 = $1 and p2 = $1.For incomes between $20 and $60, the Engel curve for good 2 is

(Multiple Choice)
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Katie Kwasi's utility function is U(x1, x2)= 2(ln x1)+ x2.Given her current income and the current relative prices, she consumes 10 units of x1 and 15 units of x2.If her income doubles, while prices stay constant, how many units of x1 will she consume after the change in income?

(Multiple Choice)
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Is the following statement true or false? "If consumers spend their entire incomes, it is impossible for the income elasticity of demand for every good to be bigger than 1." Write a brief but convincing explanation of your answer.

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If Charlie's utility function were X 4A XB and if apples cost 30 cents each and bananas cost 10 cents each, Charlie's budget line would be tangent to one of his indifference curves whenever

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