not use ai please 4. Sam's preferences are represented by the following utility function: U (x, y) =min (x2,2y).(a) Are any of the two goods in his utility function "essential?(b) Draw Sam's indifference curve for utility of 2 and utility of 3/2.(c) Calculate the marginal rate of substitution at the following three points:[4, 1], [9, 1], and [4,2].

Part (b): Draw Sam's indifference curve for utility of 2 and utility of 3/2.Explanation: To find the…

Answered: 4. Sam's preferences are represented by…

Economics (MindTap Course List)

13th Edition

ISBN:9781337617383

Author:Roger A. Arnold

Publisher:Roger A. Arnold

Chapter20: Consumer Choice: Maximizing Utility And Behavioral Economics

Section: Chapter Questions

Problem 3WNG

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Take Jeremys total utility information in Exercise 6.1, and use the marginal utility approach to confirm the choice of phone minutes and round trips that maximize Jeremys utility.
Would you expect marginal utility to rise or fall with additional consumption of a good? Why?
1 Marginal utility and marginal rate of substitution Suppose an individual who derives utility u(x, y) from consuming a units of good X and y units of good Y. For each of the following utility functions, derive the marginal utility of good X, the marginal utility of good Y, and the marginal rate of substitution between X and Y. (A) u(x, y) = x+by¹/3 (B) u(x, y) = (xy) (C) u(x, y) = ax + xy + by² (D) u(x, y) = n(ax + y) 1 (E) u(x, y) = (x² + √y²) = 2
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?
4. Consider the utility function U(r,g) r + Iny. (a) Find the marginal rate of substitution. MRS of this function. Interpret the result (b) Find the equation of the indifference curve for this function (c) Compare the marginal utility of r and y. How do you interpret these functions? How might a consumer choose between e and y as she tries to increase utility by, for example, consuming more when their income increases?
2)Ben is choosing between cookies and soda. Denote the marginal utility of cookies is MUc, and the marginal utility of soda is MUs. Which of the following relationship is true regarding the marginal utility of substitution (MŘS) of cookie in terms of soda? A) MRS= MUc B) MRS = MUS C) MRS = MUS / MUC D) MRS = MUc / MUs
(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? < (d) What do we mean by a composite good? What does this composite good look like with these preferences? 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.<
1. Calculate the marginal rate of substitution for the following utility functions: (a) u(x1, x2) = ax₁ + bx2 (b) u(x1, x2) = 2√√x₁ + x₂ (c) u(x1, x2) = ln(x₁) + x2 (d) u(x1, x2) = x1x2 (e) u(x1, x2) = xx h (f) u(x₁, x₂) = x + x² 2. Marie Curie has a utility function U(x, y) = max{x, 2y}. Note that the max{} function es- sentially says that the value of the function takes the highest of the values in the set (the set is denoted as the things inside the curly braces). (a) Draw a graph, plotting the indifference curve along which U(x, y) = 10. (b) Are Marie's preferences convex?
6.
16. Utility functions are simply mathematical representations of preferences.(a) True(b) False
2. Suppose that you are perfectly indifferent between a cup of coffee (c) and a cup of tea (t). (a) Graph three indifference curves for your preferences. Coffee (b) Write a utility function for your preferences.
5) Consider indifference curves for the consumption of milk and chocolates (you may assume that both are 'goods'). The indifference curves are drawn with the number of chocolate bars on the horizontal axis and pints of milk on the vertical axis. Suppose that at every point, consumer A's indifference curve is flatter than consumer B's. What can you conclude about consumers A and B tastes and preferences?

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