1Cobb-Douglas utility maximizationGiven the two-good Cobb-Douglas utility function:И(х, у) — хау1-а ,where 0 < a < 1, px and p, denote the prices of goods x and y, respectively, and M denotes theconsumer's income:Write down the general inequality condition representing the consumers' budgetconstraint.(a)(b)Derive the consumer's optimality condition MRSxy = Px/Py at which the consumer'sutility is maximized and solve the resulting expression for px.Substitute the expression derived in part (b) into the budget constraint derived in part (a)to derive the consumer’s (Marshallian) demand function for good y.(c)(d)Using the result from part (c), derive the consumers’ (Marshallian) demand function forgood x. Show that the demand functions for goods x and y are homogenous of degreezero.Assume p, = 1, py = 2, and M = 10. How much of goods x and y will the consumerdemand? Graph your answer on a well-labeled budget constraint/indifference curvediagram, and be sure to appropriately demark the vertical and horizontal intercepts of thebudget constraint.(e)

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ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

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Suppose that we can represent Joyce's preferences for cans of pop (the x-good) and pizza slices (y-good) with the utility function min[4x,5y]. a) Find her Marshallian Demand Functions. b) Find her Hicksian Demand Functions
Utility maximization under constraint, substitution and income effect, CV and EV Josh gets utility (satisfaction) from two goods, A and B, according to the utility function U(A, B) = 4[A-4 + B-4-4 + 40. While Josh would like to consume as much as possible he is limited by his income. a. Maximize Josh's utility subject to the budget constraint using the Lagrangean method b. Suppose PA increases. Show graphically the income, substitution effect and total effect and explain c. Suppose PA increases. Show the graphs for CV and EV and explain. One graph for CV and one graph for EV
A consumer has the following utility function: U(x, y) = y + x1/2. Let px and py bt the corresponding prices and m her income. a). Write down the corresponding Lagrangian function and find the first order conditions (FOCs). b). Use these FOCs to find the expression for the marginal rate of substitution (MRS). Bearing in mind that the MRS is the slope of the indifference curve, what can you tell about the indifference curves of a quasilinear utility function?
A consumer has a utility function given by lnU =5linx subscrip1 +3lnx subscript 2 if the budget constraint is given by 10x subscript 1 +14x subscript 2 =124 find the optimal quantity of the two commodities
Q.3 A utility function is given by the equation U = 120 x0.7 y0.3 where x is the number of hours spent playing golf and y is the hours spent playing cards per month. Calculate the values of x and y for which utility is maximised, subject to the constraint 21x + 3y = 180
Consider an individual with preferences represented by the following utility function: U (x1, 12) = x{x; The individual faces prices: P1 = 0.5; p2 = 1 And has income: M = 250 If the price of good one increases to p1 =1 For this change in price, mark all of the following answers that are correct. (EV = equivalent variation; CV = compensating variation) O In absolute value, EV is greater than Cv O In absolute values, change in Consumer surplus is smaller than CV. O In absolute value, CV is greater than EV In absolute values, change in Consumer Surplus is smaller than EV. There is not enough information to determine an answer.
Derive Ryan's demand function for q₁, given his utility function is where o = = (9₁) P + (9₂)P, 1 1-p The demand curve for q₁ as a function of P₁, P2, and Y is (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_ 9₁ = character.) U= Let the price of q₁ be p₁, let the price of q2 be p2, and let income be Y.
Given the following utility function: and marginal utilities: A consumer facing the following prices: chooses to consume: U = 2X + 2Y Assume that graphically good X is on the horizontal axis and good Y is on the vertical axis. Given this consumption bundle, the marginal rate of substitution is equal to - Given this value, the consumer should consume MU, = 2, MU, = 2 P, = $2, P, =5 15 units of good X and 19 units of good Y. (Round your answer to two decimal places. Note that the minus sign is already included). in order to maximize his/her utility.

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