KTiffany's constant elasticity of substitution (CES) utility function isU(91-92) = (a +92)Show that there is a positive monotonic transformation such that there is an equilivalent utility function (one with the same preferences ordering)U(91-92) =a +92There is a positive monotonic transformation such that there is an equilivalent utility function becauseOAB.O C.OD.OE1(ai +92) * =q+ + 2(af + a) (a² + a) ³ only wa+h+a+2> (a +² +a+g) ²af + a²>q* f+q* £ ony # (af +ah) ³ > (a •{• a•h) ²rif2)(a +42 ) ² >9² +92.

A positive monotonic transformation is a mathematical operation that is applied to a utility…

erasucity of SUD U(91-92) = (a +92) Show that there is a positive monotonic transformation such that there is an equilivalent utility function (one with the s U(91-92) =a +9 There is a positive monotonic transformation such that there is an equilivalent utility function because OA (a +92) =a² + a². +a)'

erasucity of SUD U(91-92) = (a +92) Show that there is a positive monotonic transformation such that there is an equilivalent utility function (one with the s U(91-92) =a +9 There is a positive monotonic transformation such that there is an equilivalent utility function because OA (a +92) =a² + a². +a)'

Micro Economics For Today

10th Edition

ISBN:9781337613064

Author:Tucker, Irvin B.

Publisher:Tucker, Irvin B.

Chapter6: Consumer Choice Theory

Section: Chapter Questions

Problem 3SQP

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If consumers buy less of a commodity when their incomes rise, this commodity is ( an inferior good , or a normal good ) ? . When the price of this commodity rises, the substitution effect is ( negative or postive) and the income effect is ( negative or postive) ? . So the net result for consumption of this commodity ( depends on which effect dominates , is an increase , is a decrease) ? .
Rohan’s current marginal utility from consuming peanuts is 100 utils per ounce and his marginal utility from consuming cashews is 200 utils per ounce. If peanuts cost $0.10 per ounce and cashews cost $0.50 per ounce, is Rohan maximizing his total utility from the kinds of nuts? Instructions: Enter your responses as whole numbers. At the current level of peanut consumption, Rohan receives: utils per dollar.At the current level of cashew consumption, Rohan receives: utils per dollar.Therefore, Rohan maximizing his total utility because MUp/Pp is MUc/Pc.
Suppose that Dale consumes only coffee and cheese, both of which have diminishing marginal utility. For each of the following cases, determine whether Dale should 1Consume more coffee and less cheese, or2Consume less coffee and more cheese: 1.The marginal rate of substitution of cheese for coffee is 3 (i.e., the marginal utility of cheese is three times the marginal utility of coffee), while the price ratio is 2 (i.e., cheese costs twice as much as coffee). 2.The marginal rate of substitution of cheese for coffee is 1 (i.e., the marginal utility of cheese is equal to the marginal utility of coffee) while the price ratio is 2 (i.e., cheese costs twice as much as coffee). 3.The marginal rate of substitution is initially equal to the price ratio, but the price of coffee increases. 4.The marginal rate of substitution is initially equal to the price ratio, but the price of cheese decreases. 5.The marginal rate of substitution is initially equal to the price ratio, but Dale enters exam…
13. Shawn likes to consume pineapple smoothies and hotdogs. His preferences are represented by the utility function U(x,y) = 34x - x²/2 + y where x is his consumption of pineapple smoothies and y is his consumption of hotdogs. The price of pineapple smoothies is $2 and the price of hotdogs is $1. If the price of pineapple smoothies increases to $6, the change in Shawn's consumer surplus is: A) -144 B) -128 C) -120 D) -112 E) -90
A consumer has the following utility function: Ulx, y) = xy -y, *21 where x and y represents the quantities consumed of goods X and Y. y 20 What will be the substitution and income effects for X and Yassuming that the consumer attempts to maintain the same level of utility achieved before price of Y increased (that is, when price of Y was $1)? SEx= +0.5 IEx = -0.5 SE, = -0.25 IE- = -0.25 SEx= +0.293 IE = -0.293 SEy = -0.414 IE, = +0.414 SEr= +0.25 IE SE, = -0.75 IE, = -0.75 = -0.25 SEx= +0.414 IEx = -0.414 SEy = -0.293 IE, = -0.207 Income = $3 Px= $1, Py= $2
Jerry spends his entire budget on bread and gasoline. His preferences are complete, transitive, monotonic, and convex. For Jerry, bread is an inferior good that follows the law of demand. Moreover, his cross-price elasticity of demand for gasoline with respect to the price of bread is negative. Suppose the price of bread increases, all else constant. a. Create a chart to show the total, income, and substitution effects on bread and gasoline of the increase in the price of bread. b. Use budget lines and indifference curves to graphically illustrate the three effects. Be sure to label each effect on your graph (or through the chart from part a) and plot bread on the x-axis and gasoline on the y-axis
Carla has utility function U(x, y) = vx + 2y over goods x and y a) Do we have a name for this type of utility function? Are Carla's preferences well-behaved? b) Let Carla have budget I=$40, and let prices be Px=$2, Py=$8. What bundle will Carla consume? c) What if Carla's budget drops to $20? [Think about: could this utility function describe Carla's preferences over bread and ice cream?]
2. Suppose John's utility function is UX,Y) = 4/XY , where X is consumption of beer and Y is consumption of pizza. For this utility function, ( Calculus Kahuna say: MUx = 2Y/X and MUy = 2\X/Y ) a) Suppose Y=3. Calculate John's utility for X=4,9,16, and 25. For a given level of Y, does good X display diminishing marginal utility?
Farah has $100 to spend each month on bread and chicken. Suppose the price of bread is $4 a loaf and the price of chicken is $5 per pound. Draw her budget constraint and label it BC0. Put bread on the horizontal axis and chicken on the vertical axis. Be sure to identify the intercept values. Suppose Farah is a utility maximizer and she consumes 10 loaves of bread and 12 pounds of chicken. On the same graph you drew in part (a), draw an indifference curve to identify her optimal bundle. Label this bundle "E." Is her budget exhausted? Verify your answer. Now suppose Farah's income falls so that she can now devote only $80 to the two goods. Prices however remain unchanged. In the same diagram, graph her new budget constraint and label it BC1. Be sure to identify any new intercept values. Following the change in income, can Farah consume the same bundle "E"? Explain your answer. What must happen to her total utility following the decrease in her income?
Harry consumes 2 goods, X and Y and he spends N$60 per month. The price of good X is N$4 and the price of good Y is N$10. Harry's utility function is U(X, Y) = XY. (i) What is Harry's marginal rate of substitution? (5) (ii) What is the expression for Harry's budget constraint? (3) (iii) What is the slope of Harry's budget constraint? (2) (iv)Find the values of good X and Y maximizes Harry's utility. Show all your work. (6) (v) Illustrate Harry's utility maximizing combination on a clearly labelled graph. (4) (vi) Suppose the price of good X increased to N$6. Illustrate Harry's income and substitution effects on a well labelled graph. Show your work. (10) (vii) Suppose Genie is consuming two goods, coffee and beer. She spends all her income on a combination of coffee and beer where MUcoffee/Peoffee is 5 and MUbeer/Pbeer is 3. Explain why this combination is not maximizing her satisfaction. What should she do to maximize her utility? (5)
Rohan’s current marginal utility from consuming peanuts is 100 utils per ounce and his marginal utility from consuming cashews is 200 utils per ounce. If peanuts cost $0.10 per ounce and cashews cost $0.50 per ounce, is Rohan maximizing his total utility from the kinds of nuts? Enter your responses as whole numbers. At the current level of peanut consumption, Rohan receives: utils per dollar.At the current level of cashew consumption, Rohan receives: utils per dollar.Therefore, Rohan maximizing his total utility because MUp/Pp is MUc/Pc.
It is common for supermarkets to carry both generic (store-label) and brand-name (producer-label) varieties of sugar and other products. Many consumers view these products as perfect substitutes, meaning that consumers are always willing to substitute a constant proportion of the store brand for the producer brand. Consider a consumer who is always willing to substitute 4 pounds of a generic store brand for 2 pounds of a brand-name sugar. Do these preferences exhibit a diminishing marginal rate of substitution? Assume that this consumer has $24 of income to spend on sugar, and the price of store-brand sugar is $1 per pound and the price of producer-brand sugar is $3 per pound. How much of each type of sugar will be purchased? How would your answer change if the price of store-brand sugar was $2 per pound and the price of producer-brand sugar was $3 per pound?