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…

ECON MICRO

5th Edition

ISBN:9781337000536

Author:William A. McEachern

Publisher:William A. McEachern

Chapter6: Consumer Choice And Demand

Section: Chapter Questions

Problem 1.3P

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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?
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.
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?
4- An indifference curve connects points on a graph representing different quantities of two goods, points between which a consumer is indifferent. Food Clothing a) Danyal is obsessed with food and clothes. Assume you have no knowledge of the budget line, what point would Danyal prefer to be at. b) Why can't two indifference curves not intersect, explain and illustrate your answer. c) As we move from point c to f, who's marginal rate of substitution declines.
1. Marginal Utilities and the MRS: Find the marginal utility of x1, the marginal utility of x2, and the marginal rate of substitution for the following utility functions: 1. U(x,y) = 2x + 3y 2. U(x,y) = ax + by 3. U(x, y) = 2Vx + y 4. U(x,y) = xy 5. U(x,y) = xy 6. U(x,y) = (x + 2)(y+ 1) %3D
2. Suppose a consumer has a fixed budget of $200, and she spends it all on two goods, x1 and x2. The price of x, is $40 per unit and the price of x2 is $20 per unit; x, and x2 are normal goods. (a) Draw and label the consumer's budget constraint, with x1 on the horizontal axis and x2 on the vertical axis. (b) What is the value of the consumer's marginal rate of substitution at her optimal con- sumption bundle? Explain what you your answer means. (c) Suppose the price of x, increases to $25 per unit. Graphically show the effect of this price change on the consumer's budget constraint. (d) Explain the impact of the substitution effect and the income effect of the price change in part (c) on the individual's consumption of x, and x2. (Hint: For full credit, explain both the separate and combined impacts of substitution and income effects on x1. Do the same for x2).
2. Suppose a consumer has a fixed budget of $200, and she spends it all on two goods, x, and x2. The price of x, is $40 per unit and the price of x2 is $20 per unit; x1 and x2 are normal goods. (a) Draw and label the consumer's budget constraint, with x1 on the horizontal axis and x2 on the vertical axis. (b) What is the value of the consumer's marginal rate of substitution at her optimal con- sumption bundle? Explain what you your answer means. (e) Suppose the price of x, increases to $25 per unit. Graphically show the effect of this price change on the consumer's budget constraint.

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