Show whether or not the following utility functions are monotonic transformation of eachotheru = X,X2: u = lnX,lnX,%3!u = X, + X2: u = (X, + X,)u = X, + X2: u = (X1 + X2)?Show whether or not the following utility functions are convexU = x,°X,U = x, + X,2U = X, + X,X2X

Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Answered: Show whether or not the following…

Show whether or not the following utility functions are monotonic transformation of each other u = X,X2: u = lnX,lnX, %3D u = X, + X2: u = (X1 + X2) u = X1 + X,:u = (X + X2)? %3D

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

Q3: Are the following utility functions quasi-linear, quasi-concave, quasi-convex, homogenous of degree 0, homogenous of degree 1? Show your working: 1) U(x,y) = min(x,y) 2) U(x,y) = (x" + yaja
What is the optimum solution for this utility functions? • U= min (1/2x, 1/2y) • U= 1/2 x +1/2 y • -U= In x + y Explain why non-convex IC has a corner solution instead of an interior solution?
Help!
Question 4: Consider a general utility function U(x₁, x₂). Let's now solve for the optimal bundle generally using the Lagrangian Method. 1. Write down the objective function and constraint in math. 2. Set up the Lagrangian Equation. 3. Fnd the first derivatives. 4. Find the first order conditions. What's the interpretation for >? 5. Rearrange them to get the tangency condition.
Ginny likes to eat Bertie Bott’s Every Flavour Beans (b), and Chocolate Frogs (f). Herpreferences over these lollies are Cobb-Douglas, and can be presented by the utility functionu(b, f) = 1/5(b − 2)(f + 3). Each Every Flavour Bean costs 25 Knuts and each Chocolate Frogcosts 12 Knuts. Ginny has 314 Knuts to spend. Assume that beans and frogs are both perfectlydivisible goods.(a) Find Ginny’s optimal bundle.(b) Suppose that Ginny is mugged by Draco on her way to the lolly cart, so that by the timeshe is there, she is left only with 75 Knuts. What is her optimal bundle now?(c) Now, consider the general case, where Ginny’s income is m, the price of Every FlavourBeans is pb, and the price of Chocolate Frogs is given by pf . In other words, treat ChocolateFrogs as the numeraire. Find Ginny’s demand for each good in terms of m, pb and pf .(d) Find the good on which Ginny will always spend more than half of her income.(e) Find the own-price, cross-price, and income elasticities of good 2…
A consumer's utility function is given by (x₁+x₂); with MU and MU wherex, and x, denote the quantities of good 1 and good 2 consumed. 1 2 Calculate the utility maximizing quantity of good 1 if income is 397, price for good 1 is 6 and price for good 2 is 8. Please round your answer to the closest integer.
Please draw the income-consumption (or income-offer) curve for each of the following utility functions, indicating the slope of each: (a) U = (A)(x^a)(y^b) (b) U = min(ax, by) (c) U = ax + by
Part A . Consider an economy with the following features. • There are 100 identical consumers that derive utility from consuming three different goods: software, computers, and good m. • Each consumer decision utility function is given by U (c, 8) = 4c¹/48¹/4+m, where e denotes the amount of computers that she consumes, s denotes the amount of software that she consumes, and m denotes the amount of good m that she consumes. cand s must be non-negative, but m can take any real value. • Computers are produced by 20 identical competitive firms with a total cost function given by 10c². • Software is produced by 40 identical competitive firms with a total cost function given by 20s². . QUESTION 1: What are the equilibrium prices for software and comput- ers in equilibrium? Part B • Suppose that there is a positive technology shock in the software industry so that that the new cost function of the software firms becomes 10s². Let C and S denote, respectively, the aggregate level of…
Tim is buying pizza and salad for a company lunch. Suppose that a slice of pizza costs $4.00, and a bowl of salad costs $5.00. Let ♬ be the amount in dollars that Tim spends on pizza and salad. If Tim buys P slices of pizza and S bowls of salad, then the total amount of money he spends (B) can be represented by the equation Now rearrange the equation you wrote above so that S is written in terms of E and P. The quantity of salad he buys can be represented by the equation Suppose Tim has $40.00 to spend on pizza and salad; that is, E = $40.00. Complete the following table with the values of P or S that make the equation true. Hint: To complete the first row, determine the number of salad bowls Tim can purchase with $40.00, when the number of pizza slices he purchases is 0. Budget Pizza (Dollars) (Slices) 40.00 0 40.00 5 40.00 Use the black line (plus symbols) to plot the line illustrating the combinations of pizza and salad that Tim can purchase with a budget of $40.00. SALAD (Bowis) 14…