Mariah consumes music downloads (M) and concert tickets (C). Her utility function is givehby U = 0.5M? + 2C².a. Using calculus, what is the marginal utility of music downloads?b. Using calculus, what is the marginal utility of concert tickets?Write the equation for the MRSMC (i.e., the MRS of C for M; M is increasing, C isС.decreasing).d. Would the bundles of (M = 4 and C = 1) and (M = 2 and C = 2) be on the same%3D%3D%3D%3Dindifference curve? How would you know?e. Calculate the MRSMC when M = 4 and C =1 and when M = 2 and C = 2. Explain why the%3D%3Dvalues of MRSMC differ across these two bundles.f. Based on your answers above, are Mariah's indifference curves convex? Explain usingthe values calculated.er this

The marginal utility is the additional satisfaction that a consumer gets by consuming an additional…

Answered: Mariah consumes music downloads (M) and…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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3. Consider the following utility function: U = 5 x1 + 2 x2 Also consider the following bundles: A=(6, 6) B=(8, 4) C=(4,11) D=(7, 9) E=(9, 3) If x1=20, how much of x2 does the consumer has to consume to obtain a utility level of 150? 50 300 170 25
2. Sally consumes two goods, X and Y. Her utility function is given by the expression U = 3XY². The current market price for X is £10, while the market price for Y is £5. Sally's current in come is £500. (a) Sketch a set of two indifference curves for Sally in her consumption of X and Y. (b) Write the expression for Sally's budget constraint. Graph the budget constraint and determine its slope. (c) Determine the X,Y combination which maximises Sally's utility, given her budget constraint. (d) Calculate the impact on Sally's optimum market basket of an increase in the price of X to $15. What will happen to her utility as a result of the price increase?
Q1. Jason has preferences defined over novels (good x) and DVDs (good y) described by the utility function U(x,y)= x2y2. He has income of $120; novels cost $5 each, while DVDs are priced at $15 each. a) Calculate Jason's optimal consumption bundle, AND his maximized utility level Suppose the price of novels increases to $7.5, while the price of DVDs and income are unchanged. b) In the same diagram, draw his old and new budget constraint; AND calculate his nep optimal bundle. c) Calculate the Total Effect (TE), Substitution Effect (SE) and Income Effect (E) of novels associated with the price increase of novels; AND SHOW them in your initial diagram. (Hint: keep 2 decimals if need)
U(x, y) = xayb A consumer maximises utility subject to a budget constraint M = Pxx+Pyy Where px is the price of good x, py is the price of good y and M is the budget available. a. Derive an expression for the marginal utility of x. Under what condition is the marginal utility diminishing. b. Derive an expression for the marginal utility of y. Under what condition is the marginal utility diminishing.
For each of the following situations, decide whether the bundle Lakshani is considering is optimal or not. If it is not optimal, how could Lakshani improve her overall level of utility? That is, determine which good she should spend more on and which good she should spend less on. Lakshani has $200 to spend on sneakers and sweaters. Sneakers cost $50 per pair, and sweaters cost $20 each. She is thinking about buying 2 pairs of sneakers and 5 sweaters. She tells her friend that the additional utility she would get from the second pair of sneakers is the same as the additional utility she would get from the fifth sweater. Lakshani has $5 to spend on pens and pencils. Each pen costs $0.50 and each pencil costs $0.10. She is thinking about buying 6 pens and 20 pencils. The last pen would add five times as much to her total utility as the last pencil. Lakshani has $50 per season to spend on tickets to football games and tickets to soccer games. Each football ticket costs $10 and each…
4. Tim wants to maximise his utility given his utility function of U (A, B) = A² B¹. He faces the following prices and income: PA = 25; PB = 20; M = 250. However, a change in the price of good A to PA 22 will change his optimal bundle. If he is only interested in being able to consume his original bundle of goods, how much income would he need after the price change? = (a) Tim would require £54 less income (b) Tim would require £18.33 more income (c) Tim would require £10 less income (d) Tim would require £16.66 more income (e) Tim would require £16.66 less income
What would happen to the utility maximising bundle due to income decreasing... (ceteris paribus) ?
Suppose Al is currently consuming five movies and two concerts per month. If his utility function is given by U = 15MC, where Mrepresents the number of movies seen and C represents the number of concerts attended, Al's total utility is equal to: 75 15 150 10 30
6. A consumer has an expenditure function given by E = Ū(P+). When the consumer has an income of 100, it can reach a maximum utility of 20. The price of x increases by 3 and the consumer's income increases by 25. Are they better off or worse off than before the changes? Explain how you know. Full solution please
Rick consumes 2 goods, Chicken McNuggets (M) with Szechuan sauce (S). His utility function is U(M, S) = M2/3S1/3 and his income is m. The price of Chicken McNuggets is p, and the price of Szechuan sauce is 1. d. Use the equation from part (c) and the budget constraint from part (a) to find Rick’s demand for each of the two goods. e. Suppose m=100 and p=1. How much of each good does Rick consume? Draw a graph showing Rick’s budget constraint and indifference curve passing through his chosen consumption bundle. f. Suppose m=100 and p=2. How much of each good does Rick consume? On the same graph from part (e), show Rick’s budget constraint and indifference curve passing through his new chosen consumption bundle.
Suppose that, by law, a person is required to consume a fixed amount of good X, say X0. Assuming X is a normal good, explain how this law reduces utility for both high and low income people.
Suppose that U(f,c) = f + 8c^(1/2)is a utility function that describes Amelia’s preferences over two goods: fish(f)and custard (c). For the following, think of fish as the good graphed on the horizontal axis.a. Derive an expression for her marginal utility (Uf)from a small increase in f holding c fixed. Also find themarginal utility for custard (Uc).b. What is Amelia’s marginal rate of substitution (MRS)? Give a brief (2 sentences maximum) intuitivedescription of what MRS represents. If Amelia has 4 units of custard, holding her utility constant, howmany units of custard would she be willing to give up in order to get one more unit of fish?c. Graph Amelia’s indifference curve for a utility level of 40. Be sure to specify at least 3 bundles of goodson the indifference curve.d. Does the fact that Amelia’s indifference curve intersects with the custard axis violate any of the 5properties of indifference curves? Briefly support your answer.e. Give another utility function that represents…

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