1.Consider the following utility functions:(a)u(x1, x2)=x1x2,I(b)u(x1, x2)=xx,(c)u(x1, x2) = ln x1 + ln x2, and(d)u(x1, x2)=√√x1x2,where x is the amount of good 1 and x2 is the amount of good 2.(1)(2)(3)(4)For each of the utility functions, find the marginal utility (MU₁) with respect togood 1. (5 points)For each of the utility functions, find the marginal utility (MU2) with respect togood 2. (5 points)For each of the utility functions, consider the following indifference curve:k = u(x1, x2) for some constant k. Find the marginal rate of substitution (MRS)of good 1 for good 2 at a point (x1, x2) on the indifference curve. (5 points)Show that each of the utility functions has a diminishing MRS. (5 points)

Answered: 1. Consider the following utility…

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
3) Oğuz has the utility function U(x1,X2) = x:*x2². (X: nuts, X2: berries). %3D a) If Oğuz has 25 units of nuts and 17 units of berries, the price of nuts is 2 and the price of berries is 1 liras, what would be the optimal consumption of Oğuz? b) Assume the prices change, so that nuts cost 1 and berries cost 3 liras. What is the new demand? In this change, What is the pure substitution effect? What is the income effect? c) In the change calculated in part (b), what is the pure substitution effect? d) In the change calculated in part (b), what is the income effect? In the change calculated in part (b), what is the endowment effect?
1
For each of the following utility functions get the marginal utility of consumption of each of the goods. 1/2 1/2 (a) u(a,b) = a b (b) u(x, y) = x³/4y1/4 (c) u(a, b) = n(a) + In(x) (d) u(x, y) = ln(x) + ln(y) (e) u(a, b) = 2xa +Xb
Kate’s utility function includes coffee (c) and sugar (s). She only consumes coffee and sugar together, and she only consumes in the ratio of one unit (cup) of coffee with two units (spoons) of sugar. Her utility function is What is her marginal utility of sugar if she has 4 cups of coffee and 6 spoons of sugar? Remember that unit are infinitely divisible (you can have parts of units). (a) 0 (b) 1 (c) ½ (d) 2
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1. Suppose you are considering to make a decent holiday dinner. In this year, to be creative, you are thinking to put Copper River Salmon from Alaska (fillet) and fresh Atlantic Lobsters from Maine as entrée on the table. Use the information given, to finish the questions below. (1) The table following provides you total utility (U) and marginal (MU) from consuming Salmon and Lobster. Suppose your total utility of Salmon consumption (U1) is a function of the units (Q as pound or lbs.) of salmon consumed, as U1 =. =/400Q. Similarly, your total utility of Lobster (U2) has the form as units (Q as lbs.) of lobster consumed, which is U2 = /36Q + 40. Now fill the empty spots in the table using the information given. Total utility and marginal utility of Salmon and Lobster. Copper River Salmon Atlantic Lobster Q (Ibs.) U1 MU1 U2 MU2 1 20.00 20.00 8.72 8.72 2 3 4. 6. 7 8 10 (2) With a certain amount of budget, you are going to purchase both Salmon and Lobsters. To maximize your total…
Suppose Ed's utility from the consumption of martinis (m) is proportional to the number he drinks: U(m) = m. Further, Ed is particular about his martinis: He enjoys them in exactly three parts of gin (g) to one part vermouth (v). So we can write the utility as: U(m) = U (g, v) = min (g, 3v). (a) Provide a sketch of Ed's indifference curve in the (g, v)-space for various level of utility. (a) Let the prices be p, and p, and Ed's income be I. Find the demand functions for 9 and v [Hint: Use the proportional rule and budget constraint. No need for differential calculus] (b) Using the results in (b), what is Ed's indirect utility function? (c) Find the expenditure function; given a level of utility U, and prices pg and Pv.
You are choosing between two goods, X and Y, and your marginal utility from each is as shown in the table below. If your income is $9 and the prices of X and Y are $2 and $1, respectively, what quantities of each will you purchase to maximize utility? What total utility will you realize? Assume that, other things remaining unchanged, the price of X falls to $1. What quantities of X and Y will you now purchase? Using the two prices and quantities for X, derive a demand schedule (price–quantity-demanded table) for X.
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A consumer finds only three products, X, Y, and Z, are for sale. The amount of utility yielded by their consumption is shown in the table below. Assume that the prices of X, Y, and Z are $10, $2, and $8, respectively, and that the consumer has an income of $74 to spend. (a) Complete the following table by computing the marginal utility per dollar for successive units of X, Y, and Z to one or two decimal places. (b) How many units of X, Y, and Z will the consumer buy when maximizing utility and spending all income? Show this result using the utility maximization formula. (c) Why would the consumer not be maximizing utility by purchasing 2 units of X, 4 units of Y, and 1 unit of Z? Product X Product Y Quantity Utility Marginal Quantity Utility Marginal Utility Utility per$ per$ 1 23 4567 42 82 118 148 170 182 182 1 23 4 5 6 7 14 26 36 44 50 54 56.4 Product Z Quantity Utility Marginal Utility per$ 1 23456 7 32 60 84 100 110 116 120 3..
1 Consider a consumer who consumes only two goods, 21 and z2. His utility function is u (21, 22) = In z1 + 2. where In represents the natural logarithm. 1.a Derive the consumer's MRS of good 1 for good 2 using calculus to calculate his marginal utility from z and his marginal utility from z2. 1.b If the price of z1 is $2 per unit and the price of z2 is $4 per unit, and the consumer's income is $100, What is the equation of this consumer's budget line? 1.c What are the optimal consumption choices, z and z5, for this consumer? Show your work.

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