I need fast typing clear urjent no chatgpt used i will give 5 upvotes pls full explain 4) What kind of preferences do the following utility functions represent? Draw the indifference curves ineach case (at least two curves). (a. U(x, y) = 2x+5yb. U(x, y)=√xyc. U(x, y) = min{8x, 3y}

Here are the indifference curves for the given utility functions:1. Case a: U(x,y)=2x+5y (Perfect…

Answered: 4) What kind of preferences do the…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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2) Which of the following utility functions represent the same preferences? Explain. a) U (x₁, x₂) = X₁ X₂ b) W (x₁, x₂) = 5lnx₁ +5lnx₂ c) V (x₁, x₂) = x₁¹/3x₂ ¹/3 - 0.8 d) Z(x₁, x₂) = 0.5x₁ + 0.5x₂
Lionel eats ham (x) and cheese (y). The utility function U(x,y)=0.25x + 2y^0.5 represents his preferences.a) What is Lionel’s MRS? Holding y constant, how does his MRS change as ham (x) is increased?b) What does your answer in (a) imply about his indifference curves as you hold y constant and increase x? In (c) and (d) you are asked about the Marshallian and Hicksian Demands for cheese (y). Do NOT calculate the demand functions to answer these questions. Use your answers to (a) and (b) to explain your answer. c) Holding prices constant, what is the effect of an increase in income on his Marshallian demand for cheese (y)? Briefly explain your answer.d) Holding prices constant, what is the effect of an increase in utility on his Hicksian demand for cheese (y)? Briefly explain your answer.
What kind of preferences are represented by a utility function of theform u(x1, x2) = √x1 + x2? What about the utility function v(x1, x2) =13x1 + 13x2?
4.4 (0) Phil Rupp's utility function is U(x, y) = max{x, 2y}. (a) On the graph below, use blue ink to draw and label the line whose equation is x = 10. Also use blue ink to draw and label the line whose equation is 2y = 10. (b) If x = 10 and 2y < 10, then U(x, y) If x < 10 and 2y = 10, %3| then U(x, y) (c) Now use red ink to sketch in the indifference curve along which U (x, y) = 10. Does Phil have convex preferences?. 15 10 5 10 15 20 20
Donald likes fishing (X1) and hanging out in his hammock (X2). His utility function for these two activities is u(x1, x2) = 3X12X24. (A) Calculate MU1, the marginal utility of fishing. (B) Calculate MU2, the marginal utility of hanging out in his hammock. (C) Calculate MRS, the rate at which he is willing to substitute hanging out in his hammock for fishing. (D)Last week, Donald fished 2 hours a day, and hung out in his hammock 4 hours a day. Using your formula for MRS from (c) find his MRS last week. (E) This week, Donald is fishing eight hours a day, and hanging out in his ham mock two hours a day. Calculate his MRS this week. Has his MRS increased or decreased? Explain why? (F) Is Donald happier or sadder this week compared to last week? Explain.
Consider the following utility function for goods x1 and x2: u(x1,x2)=(x1+x2)2 What type of preferences does this utility function represent and why?
(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?
2. Utility function: U(X,Y)= 2XY* Budget Constraint: 2X +4Y = 80 a. Calculate the utility maximizing amount of X and Y.
2. Maria likes to have one cup of coffee (x) and two slices of bread (y) each morning. Which of the following utility functions represents Maria's preference for (x, y)? (a) U(x, y) = min(8x, 2y) (b) U(x, y) = min (4x, 2y) - RIGHT ANSWER (c) U(x, y) = min(x, 2y) (d) U(x, y) = min(x, 2y)
U(x, y) = xayb A consumer maximises utility subject to a budget constraint M = Pxx+Pyy Where px is the price of good x, py is the price of good y and M is the budget available. a. Derive an expression for the marginal utility of x. Under what condition is the marginal utility diminishing. b. Derive an expression for the marginal utility of y. Under what condition is the marginal utility diminishing.
Suppose that you go to a restaurant with your friends. a) One of your friends always eat exactly one chicken wrap (C) and drinks two cups of ayran (A). He never changes this combination of food choice. (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) Determine the demand function of your friend for each product as a function of prices and income. Denote prices as Pc, Pa; income as M. b) Suppose that one of your friends does not care if she consumes spaghetti(S or noodle(N).She wants to consume either two-dish spaghetti or two-dish noodle or any combination of both which adds up to two dishes. (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…

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4) What kind of preferences do the following utility functions represent? Draw the indifference curves in each case (at least two curves). ( a. U(x, y) = 2x+5y b. U(x, y)=√xy c. U(x, y) = min{8x, 3y}