Rui's utility function is U=X+4XZ+Z. Let the price of good X be px, the price of good Z be normalized to $1.00, and U be her level of well-being. What is her expenditure function? Rui's expenditure function (E) is E = (2√/Px (1 +4u) - (Px + 1)). (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a subscript can be created with the character.) Derive her uncompensated demand curve for X. Let Y be her income. Rui's uncompensated demand curve for good X is X = 0.5Ypx +0.125px -0.125 (Properly format your expression using the tools in the palette.) Derive her compensated demand curve for X. Rui's compensated demand curve for good X is X= (Properly format your expression using the tools in the palette.)

Rui's utility function is U=X+4XZ+Z. Let the price of good X be px, the price of good Z be normalized to $1.00, and U be her level of well-being. What is her expenditure function? Rui's expenditure function (E) is E = (2√/Px (1 +4u) - (Px + 1)). (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a subscript can be created with the character.) Derive her uncompensated demand curve for X. Let Y be her income. Rui's uncompensated demand curve for good X is X = 0.5Ypx +0.125px -0.125 (Properly format your expression using the tools in the palette.) Derive her compensated demand curve for X. Rui's compensated demand curve for good X is X= (Properly format your expression using the tools in the palette.)

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Student question Time Left : 00:09:39 5) Quasimodo consumes earplugs and other things. His utility function for earplugs x and money to spend on other goods y is given by ux,y=100x-x22+y What kind of utility function does Quasimodo have? What is his inverse demand curve for earplugs? (Implicitly, the price of money left over for other goods is 1) If the price of earplugs is $50, how many earplugs will he consume? If the price of earplugs is $80, how many earplugs will he consume? Suppose that Quasimodo has $4,000 in total to spend a month. What is his total utility for earplugs and money to spend on other things if the price of earplugs is $50? What is his total utility for earplugs and other things if the price of earplugs is $80? How much does the utility decrease when the price changes from $50 to $80?
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Suppose the utility function for goods x and y is given Utility = U(x,y) = xy +y Suppose price of both x and y is $1. You have total $10 to spend. Suppose price of x changed to $0.5. Price of y and your disposable income remain the same: a. calculates the change in the amount of good x, that is caused by the substitution effect (the effect on consumption due to a change in price holding real income or utility constant). b. calculate the change in the amount of good x, that is caused by the income effect (the effect on consumption due to a change in real income caused by a change in price).
Columns 1 through 4 of the accompanying table show the marginal utility, measured in utils, that Ricardo would get by purchasing various amounts of products A, B, C, and D. Column 5 shows the marginal utility Ricardo gets from saving. Assume that the prices of A, B, C, and D are $18, $6, $4, and $24, respectively, and that Ricardo has an income of $105. What quantities of A, B, C, and D will Ricardo purchase in maximizing his utility? How many dollars will Ricardo choose to save? Check your answers by substituting them into the algebraic statement of the utility‑maximizing rule. In other words, show it works when using this rule.
Suppose Carlos has to choose between purchasing jewelry and water. Which of the following is the utility-maximizing rule that Carlos should follow while choosing the optimal quantities of these two goods? (Note: In the answer options that follow, MU stands for "marginal utility.") O (MU of Water) x (Price of Water) = (MU of Jewelry) x (Price of Jewelry) O MU of Water = MU of Jewelry MU of Jewelry %3D Price of Water MU of Water Price of Jewelry MU of Jewelry Price of Jewelry MU of Water %3D Price of Water Since water costs little and jewelry is expensive, it must follow that when people choose their optimal quantities of water and jewelry to purchase, the marginal utility they receive from the last piece of jewelry they buy is than the marginal utility they receive from the last gallon of water they buy.
Find the expenditure function corresponding to utility function u(x₁,x₂) = ln(x₁ +a)+ln(x₂+b). a.e(p₁u) = 2√P₁P₂)eu/2 b.e(p,u)=e¹(√P₁P₂)+ap₁ + bp₂ Ⓒc. e(p₁u) = 2(√P₁P₂)eu/2-ap₁-bp₂ d.elpu)=e"√√P₁P₂
QUESTION 1 For the utility function U = Qx0.50Qy(1-0.50) and the budget 122 = 8Qx + 14Qy find the CHANGE in optimal consumption of Y if the price of Xincreases by a factor of 1.7. Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 1.2, 1.14 = 1.1).
A consumer has an annual budget constraint for two goods: “housing sq. ft." and "$ for everything else". Draw the budget constraint for this consumer if income (v) = $50,000 and price per sq. ft. of housing, ph, is S200. Please be sure to fully label your graph (i.e., slope, intercept, etc.). Note: plot "housing sq. ft." on the x-axis. How would this consumer's budget line change if she received a $5,000 raise and the price of housing increased to $250? Include a graph with your answer. How did the economic rate of substitution (ERS) between housing and $ for everything else change when pa changed? Please interpret the ERS both before and after the price change.
3. Let there be two goods x and y with prices px and py respectively, and let M be the consumer's income. Let the consumer's preferences be represented by the utility function min(2x, y). Find the consumer's expenditure function. Note: you cannot use the Lagrange method as the utility function is not differentiable - but you have used the min U = utility function before. (4)
Q.7 A consumer's utility function is given by the expression: U = (0.6A"' + 0.47'"s} Determine the marginal utility functions for each commodity. Does marginal utility decrease when consumption increases? Assuming that the price of good X is Rs 15 and the price of Y is Rs 6, write the equation of the budget line and plot it when income is Rs 450. What is its slope? What does it indicate? Calculate the marginal rate of substitution of Y for X and interpret its economic meaning. Write the equation showing consumer's equilibrium condition. Obtain the equilibrium values of X and Y. Find the expressions for change in MUx due to increase in Y and change in MUy due to increase in X.
3. Consider the following utility function, a (1.2) = min , br), 00 (a) in details.) Does the Marshallian demand increase with price? Are the two consumption goods normal goods? Derive the Marshadian demand functions. (Explain your derivation