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![Suppose the consumer's utility is given by u(c,l) = c + 2*l0.5, and the consumer chooses I = 3
as the optimal choice.
Now consider another consumer, whose utility is given by u(c,l) = c + 2*]1.5, and the rest of
the parameters are exactly the same as for the first consumer. Would you expect that the
second consumer chooses more, less, or the same amount of leisure, compared to the first
consumer?
more
less
same
not enough info to answer](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3bae1eec-35a7-4ea6-b315-a96389a51fed%2F90cce402-c506-4f52-bbf8-a865eedfd0d8%2F9qr30e_processed.png&w=3840&q=75)
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- Adrienne consumes three goods, x, y, and z. Her consumption preference is given by the utility function: u(x, y, z) = x*y} z#, (Pz-Py, Pz) where x, y, and z are the quantities she consumes (respectively). Let p = be the prices of the goods. Answer the following questions, and justify your answers carefully and mathematically. (a) Last year p = sumption bundle last year. (1, 10, 10) and Adrienne's income was 35. Find her optimal con- (b) This year, the prices of x and z have both risen 3.5% while the price of y has risen 7%, and Adrienne got an income raise of 3%. Find the (approximate) percentage changes of her consumption in the three goods due to these changes in prices and income. Does her raise adequately compensate her for the changed prices? What additional percentage change of her income would be needed if we were to restore Adrienne to last year's exact utility level?EXERCISE 7 Aisha is considering how to allocate the next 6 hours of her free time. She could choose between leisure (L) and helping her neighbour with the house chores. If she decides to help her neighbour, she is going to get paid at £25 per hour, which she can then spend on her favourite pizza (P). Suppose the price of pizza is £12.50. Aisha's preferences for leisure and pizza are given by the following utility function: U(L, P) = 3L + P. (MU₁ = 3, MUp = 1). a) Write down Aisha's budget equation and draw the corresponding budget line. Clearly label the axes and calculate the coordinates of the points of intersection of the budget line with each axis. b) Calculate Aisha's marginal rate of substitution between leisure and pizza. Explain the concept of MRS and interpret the figure obtained. c) Find Aisha's optimal consumption bundle, both algebraically and graphically. Explain your reasoning. d) Would Aisha's optimal choice change if she could get a discount on her pizza purchases so…John likes Coca-Cola. After consuming one Coke, John has a total utility of 10 utils. After two Cokes, he has a total utility of 25 utils. After three Cokes, he has a total utility of 50 utils. Does John show diminishing marginal utility for Coke, or does he show increasing marginal utility for Coke? Supposethat John has $3 in his pocket. If Cokes cost $1 each and John is willing to spend one of his dollars on purchasing a first can of Coke, would he spend his second dollar on a Coke, too? What about the third dollar? If John’s marginal utility for Coke keeps on increasing no matter how many Cokes he drinks, would it be fair to say that he is addicted to Coke?
- Only typed answer Oscar makes purchases of an existing product (X) such that the marginal utility of the last unit he consumes is 10 utils and the price is $5. He also tries a new product (Y) and the marginal utility of the last unit he consumes is 8 utils and the price is $1. The equal marginal principle suggests that Oscar should Multiple Choice increase his consumption of product X and decrease his consumption of product Y. increasePaolo enjoys consuming both soda and coffee. Each can of soda costs Ps = $1, and each cup of coffee costs Pc = $2. Suppose that Paolo buys 75 cans of soda and 50 cups of coffee per month. The following graphs show his marginal utility curves for soda and coffee. At his current consumption level, Paolo's marginal utility from consuming the last can of soda he bought is MUS = 12 utils per can, and his marginal utility from consuming the last cup of coffee he bought is MUC = 12 utils per cup. 24 20 20 16 25 50 75 100 125 150 25 50 75 100 125 150 SODA (Cans) COFFEE (Cups) Is Paolo currently maximizing his utility? O No; he likes coffee and soda more than other goods, so he should buy more of both. O No; he could buy less soda and more coffee, not spend any more money, and be better off. O Yes; the marginal utility he receives from his last can of soda equals that of his last cup of coffee. O No; he could buy more soda and less coffee, not spend any more money, and be better off. MU OF SODA…True or false Law of diminishing margnal utility law states that utility derived from each successive consumption will keep falling.
- What is meant by form utility?Sam's extended family spends $3,200 per month on wine and beer. Their utility function is given by U = 200WB, where W represents the number of bottles of wine that they buy, and B represents the number of cases of beer that they buy. Wine costs $25 per bottle and beer costs $32 per case. Sam's family wants to maximize their utility. Calculate how many bottles of wine and how many cases of beer they should buy. Show your calculation(s).A 2015 report by the music industry estimated the revenue lost to the industry every yearfrom illegal downloading. In this problem we will derive some of the estimates that may havegone into their calculation (approximately).First, start with the individual consumer’s problem. Suppose a typical consumer has a yearlyentertainment budget of I that they can allocate between music downloads (D) and otherforms of entertainment (E). Consumer preferences are characterized by a utility functionU(D, E). a.) Write an expression for the consumer’s budget constraint as a function of their entertainment budget and the prices of music downloads (Pd ) and other entertainment (Pe). (b) Write the consumer’s constrained optimization problem in Lagrangian form. (Note: Youdo not need to solve it or derive first order conditions.)
- Carol needs to decide how to spend her wealth on sh and chicken.For Carol, 1 lb of sh is equivalent to 2 lb of chicken. Her preferencecan be represented by the utility functionu(x; y) = 2x + ywhere x is the quantity of sh (in lbs) and y is the quantity of chicken(in lbs). The consumption set is R2+. (a) Draw two typical indi erence curves for Carol, one correspondingto a utility level of u1 and one corresponding to a utility level u2,where 0 < u1 < u2. Make sure you label the slope of the indif-ference curves and the intercepts with the horizontal and verticalaxes.(b) Suppose the price of sh is $1:5 per lb and and the price of chickenis $1 per lb. Carol has $20 to spend on sh and chicken.(i) Draw Carol's budget set, labeling the slope and the interceptpoints clearly.(ii) How much sh and chicken will Carol choose to purchase? I am looking for an answer to the points (c) and (d) below (c) Suppose now that the price of sh increases to $2 per pound.(i) Draw Carol's budget set,…A consumer is making purchases of products Alpha and Beta such that the marginal utility of product Alpha is 63 and the marginal utility of product Beta is 40. The price of product Alpha is $9, and the price of product Beta is $5. The utility-maximizing rule suggests that, to stay within a given budget constraint, this consumer should Multiple Choice O O O increase consumption of product Beta and increase consumption of product Alpha. make no change in the consumption of Alpha or Beta. increase consumption of product Beta and decrease consumption of product Alpha. increase consumption of product Alpha and decrease consumption of product Beta.Gina is at a toy store and is buying toy T-Rex's (x), which cost på, and toy yaks (y), which cost py. Her income is I. She likes 3 T-Rex's as much as she likes 4 yaks. These toys are perfect substitutes for her.
