Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
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Question
Chapter 4, Problem 4.10P
(a)
To determine
To calculate:The indirect utility function.
(b)
To determine
To calculate:The expenditure function for this case.
(c)
To determine
To show:The compensation required to offset the effect of an increase in the price of
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Consider the two questions about utility. The table refers to the first question only.
Tod loves to travel, and he takes several river cruises per year. The table contains information about the utility Tod gets from the river cruises.
Number of river cruises
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0
0
1
12
12
2
20
8
3
25
5
From this information, it can be concluded
that the number of river cruises Tod takes is indeterminable without knowing Tod’s income or the price of the cruises.
that total utility is maximized when Tod takes one river cruise.
that Tod will take two river cruises.
that Tod will take three river cruises.
Suppose that Jim has $4 to spend on a snack and that the only thing available is tea and scones. Jim’s marginal utility of the first cup of tea is 30 and his marginal utility of the second cup of tea is 20. Each cup of tea costs $1. Jim’s marginal utility of the first scone is 80 and his marginal utility of the second scone is 60. Each scone costs…
K
Tiffany's constant elasticity of substitution (CES) utility function is
U(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 +92
There is a positive monotonic transformation such that there is an equilivalent utility function because
OA
B.
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OE
1
(ai +92) * =q+ + 2
(af + a) (a² + a) ³ only wa+h+a+2> (a +² +a+g) ²
af + a²>q* f+q* £ ony # (af +ah) ³ > (a •{• a•h) ²
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2)
(a +42 ) ² >9² +92.
Currently, Paula is maximizing utility by purchasing five TV dinners (T) and four LeanCuisine Meals (L) each week. Suppose both T and L cost $5 each.a. Graph Paula’s initial utility-maximizing choice.b. Suppose the price of T falls by $1 and the price of L rises by $1.25. Can Paula stillafford to buy her initial consumption choices? What do you know about her new budgetconstraint?c. Make a new graph to show why Paula will choose to consume more T and less Lgiven her new budget constraint to maximize utility. Is her utility increased, decreased,or unchanged given the price change? [Hint: try to make the graph as big as possible tosee how the utility is tangent/intersects with the lines more easily]
d. In part (b), suppose another scenario where the price of T rises by $1 and the priceof L falls by $1.25. Is Paula’s utility increased, decreased, or unchanged given the pricechange?
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.Similar questions
- Recent research confirms that the demand for cigarettes is not only inelastic, but it also indicates that smokers with incomes in the lower half of all incomes respond to a given price increase by reducing their purchases by amounts that are more than four times as large as the purchase reductions made by smokers in the upper half of all incomes. How can the income and substitution effects of a price change help explain this finding?arrow_forwardAnswer the following short questions:a. Suppose that a consumer’s preferences between goods x andy are represented by the utility function u(x, y) = x^2 + 16xy + 64y^2. If these two goods have the same price, describe the optimal consumptionchoice of this consumer.b. Suppose that when the price of a good change, the incomeand substitution effects change the consumer’s demand for that goodin opposite directions.i. Is this good a normal or an inferior good? Explain.ii. Is this good a Giffen or an ordinary good? Explain.c. Is the following statement true or false? The differencebetween a monopolist’s marginal cost and its profit-maximizing price issmaller when the demand is more elastic.arrow_forwarda. Is the “more is better” assumption satisfied for both goods? Explain.b. What type of function is this? Explain.c. Provide expressions for the marginal utilities of x and y and does the marginal utility of x increase, remain constant, or diminish as the consumer buysmore units of x? Explain. Does the marginal utility of y increase, remain constant, or diminish as the consumer buysmore units of y? Explain.d. Provide an expression for the marginal rate of substitution of x for y.e. Is MRSx,y diminishing, constant, or increasing as the consumer substitutes more x for y alongan indifference curve? Explain.f. On a graph with x on the horizontal axis and y on the vertical axis, draw the indifferencecurves for U1 and U2 where U2 has a higher value than U1 instructions: answer d,e, and f onlyarrow_forward
- a. Is the “more is better” assumption satisfied for both goods? Explain.b. What type of function is this? Explain.c. Provide expressions for the marginal utilities of x and y and does the marginal utility of x increase, remain constant, or diminish as the consumer buysmore units of x? Explain. Does the marginal utility of y increase, remain constant, or diminish as the consumer buysmore units of y? Explain.d. Provide an expression for the marginal rate of substitution of x for y.e. Is MRSx,y diminishing, constant, or increasing as the consumer substitutes more x for y alongan indifference curve? Explain.f. On a graph with x on the horizontal axis and y on the vertical axis, draw the indifferencecurves for U1 and U2 where U2 has a higher value than U1arrow_forwardGiven the assumptions of the law of diminishing marginal utility (exactly the same product consumed within thesame time period), does this law apply to most people? Explain your answer briefly.arrow_forward27. Mike spends all his income on films (F) and concerts (C). Films cost $10 and concertscost $30. Mike’s preferences can be described by the utility function: U = F C and hence themarginal utility of films is C and the marginal utility of concerts is F. Which of the followingbundle will Mike purchase? (Hint: You do not need to know income in $ amount. Answerthe question using the tangency condition.)(a) Mike purchases 30 concerts and 10 films a month.(b) Mike purchases 10 concerts and 30 films a month.(c) Mike purchases 20 concerts and 20 films a month.(d) Mike purchases 5 concerts and 10 films a month.arrow_forward
- 4) Assume Linda only buys two goods, chicken and rice with her income of M, and prices, Pc & PR. a) Graph her consumer choice model (with chicken on thex axis. Nowlet price of chicken fall, causing Linda to consume more chicken and more rice. Indicate the income and substitution effects on the graph. b) Based on your graph from part a, draw Linda’s ordinaly demand (do) and compensated demand (dc) curves for chicken c) (True/False) this chicken must be a nomal good. Explain how you know. d) (True/False) this rice must be a nomal good. Explain how you know.arrow_forward5. Janice consumes two goods, X and Y. Janice has a utility function given by the expression: U=4X05Y05 and current prices of X and Y are $25 and $50, respectively. Janice currently has an income of 750 unit per time period. a. Write an expression for Janice's budget constraint. b. Calculate the marginal rate of substitution of X for Y. (horizontal line X, vertical line Y). c. Calculate the values of X and Y that will maximize utility. d. Graph your answers (budget line, indifference curve)arrow_forward2. 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?arrow_forward
- Ann consumes two goods, a and y. Her utility function is given by: u(x, y) = (x+1)G. The price of a is $4 per unit and the price of y is $ per unit. Ann's income is w. (a) * ) Nrite down an expression for Ann's budget line. (b) v- 'Determine the formula for Ann's marginal utility of a, and the formula for Ann's marginal utility of y. (c) ( » For each income level w > 0 calculate Ann's optimal consumption bundle. (d) For which income levels w is bang-for-buck equalization violated at Ann's optimal consumption bundle? Explain. , Assume that w = 2. Draw Ann's budget line in a figure with r on the hor- izontal axis. Add 2 indifference curves of Ann, including the indifference curve that contains Ann's optimal consumption bundle. Indicate Ann's optimal consumption (e) - bundle.arrow_forwardIn Example 4.1 we looked at the Cobb-Douglas utility function U(x,y)=xay1-a, where 0<=a<=1. This problem illustrates a few more attributes of that function. a. Calculate the indirect utility function for this Cobb-Douglas case. b. Calculate the expenditure function for this case. c. Shos explicitly how the compensation required to offset the effect of an increase in the price of x is related to the size of the exponent a.arrow_forwardhe Calculus of Utility Maximization and Expenditure Minimization -End of Appendix Problem uppose that there are two goods, X and Y. The price of X is $2 per unit, and the price of Y is $1 per unit. There are two onsumers, A and B. The utility functions for the consumers are UA(X,Y)= X05.05 UB(X,Y)= X0.8y0.2 Consumer A has an income of $100, and Consumer B has an income of $300. Using Lagrangians, solve for the optimal bundles of goods X and Y for both consumers A and B. a. The optimal bundle for consumer A is X = 25 and Y* = 50 - b. The optimal bundle for consumer B is X = 120 and Y* = 60arrow_forward
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