(a) Suppose we have preferences U(X, Y) = min [X, 3Y]. Graph/sketch the indifference curvethrough the bundle (X = 30, Y = 30). What is the utility of (30, 30) and explain why theindifference curves look the way they do.(b) What does the Marginal Rate of Substitution tell us about preferences? <(c) Why is the Marginal Rate of Substitution not applicable in this example? <(d) What do we mean by a composite good? What does this composite good look like with thesepreferences? Show and explain.<(e) State the consumer's maximization problem and express this in words.<(f) Now let Px = 10, Px= 20 and income M = 2000. Find optimal X*, Y*, and the resulting Utility(U*). Show your work. <(g) Now let Py = 15. How does optimal consumption (X*.Y*) and utility (U*) change relative to(e)? Explain in simple terms and show in a diagram.<

Here we are given the utility function which is a function of 2 goods X & Y. And we are also…

(a) Suppose we have preferences U(X, Y) = min [X, 3Y]. Graph/sketch the indifference curve through the bundle (X=30, Y = 30). What is the utility of (30, 30) and explain why the indifference curves look the way they do. (b) What does the Marginal Rate of Substitution tell us about preferences? < (c) Why is the Marginal Rate of Substitution not applicable in this example? <

(a) Suppose we have preferences U(X, Y) = min [X, 3Y]. Graph/sketch the indifference curve through the bundle (X=30, Y = 30). What is the utility of (30, 30) and explain why the indifference curves look the way they do. (b) What does the Marginal Rate of Substitution tell us about preferences? < (c) Why is the Marginal Rate of Substitution not applicable in this example? <

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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4. Let u(z) be a utility function that represents the preferences of a household. We say that the function v(r) is a monotonic transformation of u if f(-) is a strictly increasing function and v(z) = f(u(z)). (a) Show that if v(z) is a monotonic transformation of u, it represents the same preforences. (b) Can you explain why taking a monotonic transformation of a utility function does not change the marginal rate of substitution? (c) What kind of preferences are reprosented by a utility function of the form u(a1, 12) = VEi +#2? What about the function v(z1, r2) = 13z + 13r2? (d) Consider the function u(r1, 2) = VE1#2. What kind of preferences does it represent? Is the function (11, r2) jz a monotonic transformation of 1 u(r1, 12)? Is the function w(r1, 12) u(r1, 12)? = zfr a monotonic transformation of
Please show your answer step by step with reasons. (i) A consumer has income of £3,000. Apple juice is priced at £3 a bottle and cheese is priced at £6 a kilo. Draw the budget constraint for a consumer with standard preferences. What is the slope of this budget constraint?(ii) Show a consumer’s budget constraint and indifference curves for apple juice and cheese. Show the optimal consumption choice. If the price of juice is £3 a bottle and the price of cheese is £6 a kilo, what is the marginal rate of substitution at this optimum? (iii) The price of cheese rises from £6 to £10 a kilo, while the price of juice remains at £3 a bottle. For a consumer with a constant income of £3,000, show what happens to consumption of juice and cheese. Decompose the change into income and substitution effects.
(a). What kind of preferences are represented by a utility function of the form u(x₁, x₂) = √√x₁ + x₂? What about the utility function v(x₁, x₂) = 13x₁ + 13x₂? Compute the slope of the two indifference curves. Do their slopes depend on the bundle? (b). What kind of preferences are represented by a utility function of the form u(x1, x₂) = x₁ + √√x₂ ? Compute the slope of the indifference curve. Does it depend on the bundle? In which way? (c). Consider the utility function u(x₁, x₂) = √x₁x2. What kind of preferences does it represent? Is the function v(X₁, X2) = X₁X2 a monotonic transformation of u(x₁, x₂)? Compute the slope of the indifference curve. Does it depend on the bundle? In which way?
Abby likes tangerines and oranges. For every 4 tangerines, Abby is equally happy to consume 2 oranges instead. Let x be the number of tangerines, and y be the number of oranges. (a) Graph Abby's indifference curves. Make sure to mark the direction of the preferred bundles. (b) Write down an utility function that represents Abby's preferences. (c) Write down another utility function different from your previous answer but also represents Abby's preferences. (d) Does v(x, y) = x + y represent Abby's preferences? (e) What is Abby's marginal rate of substitution? (f) Suppose that px = 1, py = 1, and Abby has Y = 20. Compute Abby's optimal consumption bundle.
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3. We claimed in the text that if preferences were monotonic, then a diag- onal line through the origin would intersect each indifference curve exactly once. Can you prove this rigorously? (Hint: what would happen if it intersected some indifference curve twice?)
5. Suppose a preference relation is represented by a utility function u(x₁, x₂) = x₁ + x₂. Explain why the function -u(x₁, x₂) = −x₁ - x₂ does not represent the same preference relation. It is enough to explain using two appropriate bundles.
1. For each of the three utility functions below, find the substitution effect, the income effect, and the total effect that result when prices change from p = (2,1) to p' = (2,4). Assume the consumer has income I = 20. (a) Before doing any calculation, make an educated guess about the relative magnitude of the three substitution effects and the three income effects to be found below. (b) u(x1, x2) = x1 + x2. (c) u(x1, x2) = x1x2. (d) u(x1,x2) = min {x1,x2). (e) Rank the substitution effects and the income effects found above by their magnitude. To what extent do they conform to your guess?
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Suppose that one of your friends does not care if she consumes spaghetti (S) or noodle (N). She wants toconsume either two-dish spaghetti or two-dish noodle or any combination of both which adds up to twodishes.(i) Write the utility function of your friend to represent his preferences.(ii) Draw couple of indifference curves of your friend on graph with appropriate labels.(iii) Denote prices as Pn, Ps; income as M. If Pn < Ps, then determine the demand function of your friend foreach product as a function of prices and income.
Draw the indifference curves fort he preference indicated below. (Do not forget to represent the name of the axis) 1) Marry lives by the motto "eat, drink and be merry today, for tomorrow doesn't matter." (Hint: Today's consumption is measured on the horizontal axis and tomorrow's consumption is measured on the vertical axis) 2) Boris likes homework (H) but hates exercise (E). 3) Bianca's marginal utility of pizza equals 2 and her marginal utility of salad equals 4 always. ww www www 4)Adam is very picky about his tahin-pekmez. He always mixes one spoon of tahin with two spoons of pekmez. 5)Marty likes rap and rock music. Marty's preferences exhibit a diminishing marginal rate of subsitution between the two types of music. wwwwww 6) Beatrix hates studying both economics and history. The more time she spends studying either subject, the less happy she is.