This question will let you examine/explore a more interesting utility func-tion than the simple example discussed in class as there will be both cross-price elas-ticity and an inferior good. Suppose you are told a consumer has the following utilityfunction:U (9x9₂) = 9x + √√9₂ +9₂You should assume income is Y, the price of good z is Pr, and the price of good z isP₂. This question will ask about several concepts discussed in lecture.(a)What is the Marshallian demand for goods x and z? I.e. find (9)for both interior solutions and corner solutions. Note: the outcome is "ugly"for the interior section and both corner should include constraints, i.e. limitsusing Y relative to f(P2, P₂). Hint: if solving using MRS = MRT, can use thisinformation again in part (d).

The objective of this question is to find the Marshallian demand for goods x and y given the utility…

Answered: This question will let you…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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A consumer’s preferences over two goods x and y are given bythe utility function U(x, y) = xαyβ with α, β > 0. The prices of the goods are px = 2 and py = 4.The consumer has an income of I > 0.(a) For what values of α and β are these utility functions strictly monotone?(b) For what values of α and β will the consumer demand (i.e., Walrasian demand) be more x than y?(c) For what values of α and β are these goods gross substitutes? For what values of α and β are these goods gross complements? Provide a justification for your answer.
Tony is throwing a party at his Fraternity and is trying to choose what booze to buy. A bottle of vodka has three times the alcohol as a six-pack of beer. Assume that Tony only cares about the total amount of alcohol in his basket. (use vodka on the X-axis and beer measured in six-pack on the Y-axis) a) Devise a utility function to represent these preferences. b) Suppose a bottle of vodka costs $40, a six-pack of beer costs $10, and the budget is $200. Write the budget constraint. c) Solve Tony’s utility maximization problem and find the optimal combination. d) Suppose that a bottle of vodka cost has increased to $50. What will be his new optimal combination.
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…
1. Suppose a consumer's utility function is: U (x1, x₂) xx. Furthermore, suppose the con- sumer's disposable income is $80, and the prices of the two goods are: x₁ = 4 and 2 2. Obtain the optimal amounts of î₁ and î that the utility maximizing consumer would buy. =
While visiting family in Mexico, your professor has a budget of $ 255 ($ = pesos) that he spends on tacos and tequila. The price of tacos is $ 6 and a shot of tequila is priced at $ 16. During his visit the price of tacos changes to $ 5. Assume your professor has a Cobb-Douglas utility function with (tacos) parameter a = ( 27 / 100). How many shots of tequila does your professor purchase ? (Assume both goods are commodities.) (Answer is : 11.63)
Refer to the graph below Quantity of Y 160 0 Multiple Choice The consumer's income is $1,000 Why doesn't the consumer choose the combination at point B O Quantity of X 200 O The marginal utility of Y exceeds the marginal uplity of X O The consumer is willing to give up more X for an additional unit of Y than must be given up given the relative prices of X and Y. The marginal utility per dollar spent on X exceeds the marginal utility per dollar spent on Y The consumer is willing to give up more Y for an additional unt of X than must be given up given the relative prices of X and Y
A utility function is given as U = √MB where B represents the quantity of books consumed and M represents magazines. This uülity is shown via indifference curves in the diagram to the right. Holding the number of magazines constant at 20 units, as we increase our consumption of books from 5 units to 10 to 15 and to 20 units, marginal utility with respect to books. is CIES Magazines (Y) 50- 45 40 35 30 25- 20- 15- 10- 5 0- 10 15 RSTV a quie 10 15 20 25 30 35 40 Books (X) 45 5 eboo SCOR scor scor score score
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There are two goods, X and Y, available in arbitrary non-negative quan- tities (so the consumption set is R²). Beenish has preferences over consumption bundles that can be represented by a differentiable, strictly increasing and strictly quasi-concave utility function u R² → R+, given by u(x, y) = xªy¹-a where x is the quantity of good X, y is the quantity of good Y, and a € (0, 1) is a preference parameter. = 1. Suppose Beenish has 80 AED. In a nearby store (called "Store A"), the price of good X is p = 2 AED per unit of good X, and the price of good Y is q 8 AED per unit of good Y. However, Beenish also has a time constraint. At Store A, it takes tx 4 minutes per unit to purchase good X and ty 1 minutes per unit to purchase good Y. That means, purchasing a consumption bundle (x, y) = R² at Store A would take 4x + y minutes. Beenish has only 80 minutes to do her shopping. = (a) In an appropriate diagram, illustrate Beenish's constraint set, given that she has both a monetary…
12) A consumer’s preferences are given by U(X,Y) = X0.6Y0.4. The price of X is 4, and the price of Y is 5. The consumer has an income of $2000.a) What is the utility maximizing choice of X and Y?b) How would the utility maximizing choice change if price of X falls to 3 because of a pricesubsidy?c) Given the answers to the previous parts plot a linear demand function for X.d) Show that the consumer would prefer the cash equivalent of the price subsidy in part b.
Suppose Rosie's marginal utility from attending her 5th Atlanta Braves game was 40 and the marginal utility from attending her 1st Taylor Swift concert was 200. Assume that the price of a Braves ticket is $20 and the price of a Taylor Swift ticket is $120. Which of the following would be TRUE? 1) Rosie would attend more Taylor Swift concerts and fewer Braves games. 2) Rosie would attend more Braves games and fewer Taylor Swift concerts. 3) Rosie would not alter her behavior. 4) Rosie would attend less of both Braves games and Taylor Swift concerts.
You consume music (M) and concert tickets (C). Your utility function is U(M, C) = M1/4C3/4. The marginal utility for concert tickets, MUC is MUC =3/4C-1/2M1/4 and the marginal utility for music, MUM is MUm = 1/4C3/4M-3/4 (a) Calculate MRSMC using only the given marginal utilities. (b) Solve for the utility of bundle A where M = 16 and C = 16. Solve for your utility at bundle B where M = 128 and C = 8. Are the utilities the same? (c) Calculate MRSMC at bundle A and at bundle B. Are they the same? (d) Are your indifference curves convex? Draw the ICs. Make sure to label the quantities of the consumption bundles, the axis, and the MRS at those bundles.

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