(a) Gwyneth is conducting research into consumer behaviour. She has decided touse the utility function u(x1, x2) = Inx₁ + x2, where x₁ is her consumption ofsalad and x2 is her consumption of candles. Let prices of x₁ and x2 bedenoted by p₁ and p2. Gwyneth earns an income of m.i.Set up the utility maximisation problem.ii.Use a Lagrangian to derive the demands for salad and candles.iii.Illustrate the income offer curve and engel curves for salad.(') Do you think the utility function in (a) is sensible? Explain.

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Answered: (a) Gwyneth is conducting research into…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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There two goods, candy and soda, available in arbitrary non-negative quantities (so the consumption set is R2+). A consumer has preferences over consumption bundles that are represented by the following utility function:u(x, y) = −|4 − x| − |4 − y|where x is the quantity of candy (in grams), y is the quantity of soda (inliters), and |.| denotes the absolute value: for any real number r ∈ R, |r| = r if r ≥ 0 −r if r < 0. The consumer has wealth of w > 0 Dirhams. The price of candy is p > 0 Dirhams/gram, and the price of soda is q > 0 Dirhams/liter. (a) Calculate the utility of the following consumption bundles: (4, 4), (4, 5), (5, 4), (4, 3), (3, 4), and α(4, 5) + (1 − α)(3, 4) for α ∈ [0, 1]. (b) In an appropriate diagram, illustrate the consumer’s map of indifference curves.
Amy consumes x and y and her preferences can be represented by the following utility function U(x,y) = 4x + y. 1. Are Amy's preferences transitive? 2. Does the marginal utility of x diminish, remain constant, or increase as the consumer buys more x? Explain. 6- 3. Can you use (2) to answer whether Amy's preferences are strictly monotonic? 4. What is MRS.y ? Is MRSx.y diminishing, constant, or increasing as the consumer substitutes x for y along an indifference curve? 5. On a graph with x on the horizontal axis and y on the vertical axis, draw a typical indifference curve. Also indicate on your graph whether the indifference curve will intersect either or both axes. Label the curve U1. 6. Are Amy's preferences convex? Are they strictly convex? Explain
Q2. Suppose a consumer seeks to maximize the utility function U (x, y) = (x + 2) (y + 1), where and y represent the quantities of the two goods consumed. The prices of the two goods and the consumer's income are pa, py, and I. Write out the consumer's budget constraint and the Lagrangian function for the problem.
Huang is determining how much Coke and Pepsi he will buy. Use the information in italics to answer the bolded question below. • Huang's preferences for Coke (C) and Pepsi (P) are represented by the following utility function: U = 2C + 3P • Huang has $12 to spend on soft drinks. • The price of Coke (P) is $0.50/can. • The price of Pepsi (Pp) is $1.00/can. Which of the following statements referring to Huang's preferences is incorrect. O Huang does NOT experience diminishing MRS. If Huang gives up two cans of Pepsi, he needs to purchase 3 cans of Coke to remain equally satisfied. Pepsi and Coke are perfect substitutes for Huang O None of the above statements are incorrect.
Focus on parts e-h
Consider a person who consumes two goods, x and y, and has a utility function given by U(x, y) = In(x)+y. This person has an income of $100 and faces a price of $0.50 for good x and $1 for good y. Price of x then rises to $0.60. Solve for the compensating variation (CV) and equivalent variation (EV) of this price change. Show your work.
Consider a consumer with M = $120 to spend (income) and faces prices PX = $15 and PY =$5 for goods X and Y. Her utility function is U(X, Y) = X1/2 + Y1/2.a Carefully. express the consumer’s choice problem, using the given information (this is whereyou write out the max operator, the choice variables, the objective function, and the budget constraint). b. Compute the absolute value of the consumer’s marginal rate of substitution, and inspect it todetermine the shape of the consumer’s indifference curves: C-shaped, linear, )-shaped, or some other shape.To show your work, neatly use the arrow argument, increasing X (↑) and decreasing Y (↓) to see whether|MRS(X, Y)| is diminishing along an indifference curve. c. If the indifference curves are C-shaped write out the budget line and the equal slopes conditionthat characterize an interior solution to the consumer’s choice problem. Use the particulars for the givenconsumer. Solve these conditions to find the interior solution. On the other…
Gino derives utility from only two goods, carrots (Qc) and donuts (Qd). His utility function is as follows:U(Qc,Qd) = (Qc)(Qd)The marginal utility that Donald receives from carrots (MUc) and donuts (MUd) are given as follows:MUc = Qd MUd = QcGino has an income (I) of £120 and the price of carrots (Pc) and donuts (Pd) are both £1. - what is Gino's budget line and what quantities of Qc and Qd will maximise Gino's utitlity? - holding income and Pd constant, what is Gino's demand curve for carrots? - suppose a tax of 1 pound per unit is levied on donuts. how will this alter Gino's utility maximisinzing market basket of goods?

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