A consumer has the following utility function U (x1, x2) = (x1 + 3) (x₂+4) Prices of the two goods X₁ and x₂ respectively are p₁ and p2 and the consumer has income m. We assume that all prices and income are strictly positive. Furthermore, throughout this question we assume that m is high enough so that both goods are consumed in strictly positive amount in equilibrium. (a) Solve the consumer's optimization problem and express the demand for the two goods in terms of prices and income. Compute the missing values of elasticities in the following table assuming M = 10, p₁ = 2, and p2 = 1. Show your work. Income elasticity Absolute value of own price elasticity Cross price elasticity X₁ Ts X₂ (b) While x2 is produced locally, x₁ is transported from a different region. Assume P₂ = 1. Building a new railroad (that connects the regions) will reduce transportation cost which in turn will reduce the price of good 1 from p₁ = 2 to p₁ = 1. Railroad will be funded by taxes which will reduce each consumer's disposable income from m = 10 to m = 10- T. A utility-maximizing consumer will accept higher taxes as long as

A consumer has the following utility function U (x1, x2) = (x1 + 3) (x₂+4) Prices of the two goods X₁ and x₂ respectively are p₁ and p2 and the consumer has income m. We assume that all prices and income are strictly positive. Furthermore, throughout this question we assume that m is high enough so that both goods are consumed in strictly positive amount in equilibrium. (a) Solve the consumer's optimization problem and express the demand for the two goods in terms of prices and income. Compute the missing values of elasticities in the following table assuming M = 10, p₁ = 2, and p2 = 1. Show your work. Income elasticity Absolute value of own price elasticity Cross price elasticity X₁ Ts X₂ (b) While x2 is produced locally, x₁ is transported from a different region. Assume P₂ = 1. Building a new railroad (that connects the regions) will reduce transportation cost which in turn will reduce the price of good 1 from p₁ = 2 to p₁ = 1. Railroad will be funded by taxes which will reduce each consumer's disposable income from m = 10 to m = 10- T. A utility-maximizing consumer will accept higher taxes as long as

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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?
Q2. Suppose a consumer seeks to maximize the utility function U (x, y) = (x + 2) (y + 1), where and y represent the quantities of the two goods consumed. The prices of the two goods and the consumer's income are pa, py, and I. Write out the consumer's budget constraint and the Lagrangian function for the problem.
Consider the following utility function: U= 100x0.50,0.50 A consumer faces prices of P, = $2 and P, =$1. Assuming that graphically good X is on the horizontal axis and good Y is on the vertical axis, suppose the consumer chooses to consume 6 units of good X and 11 units of good Y. Then the marginal rate of substitution is equal to: MRS = 1.83. (Enter your response rounded to two decimal places. Do not forget to include the negative sign.) Use absolute values. The consumer should consume to maximize utility. more Y and less X the same amount of X and Y more X and less Y O étv MacBook Air 80 esc F1 F2 F3 F4 F5 F6 F7 F8 # $ % & 1 2 7 Q W E T Y tab S D F G caps lock C V M ft control option command つつエ B N
Ricky has utility function u=x'y. This implies that MUx=2xy. MUy=x². His income is 100. The price of y is 10. (a) Find his demand for x at price 20. (b) Find his demand for x at price 30. (c) Write down his demand function for x: that is, write down his demand for x as a function of the price of x.
Consider the following utility function: U = 100x°.50,0.50 A consumer faces prices of P, = $2 and P, =$1 Assuming that graphically good X is on the horizontal axis and good Y is on the vertical axis, suppose the consumer chooses to consume 6 units of good X and 11 units of good Y. Then the marginal rate of substitution is equal to: MRS = (Enter your response rounded to two decimal places. Do not forget to include the negative sign.) Use absolute values. 15 stv МacВook Air 80 DI esc F1 F2 F3 F4 F5 F6 F7 F8 @ %23 2$ & 1 2 4 6 7 8 Q W T Y tab A S F H J K aps lock C V M control option command B H
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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
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.
Suppose the function for the utility from good c is denoted as U(c)=2c2. Which of the following expressions indicates the marginal utility of c? 1/c2 1/square root of c All of the above are correct.
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A consumer has utility (see image) on ice creams (x) and cakes (y). (a) Are the indifference curves bowed towards the origin? (b) Derive his demand function (as a function of prices px, py and budget I) for ice cream (x). (c)(Looking at the demand function you found in (b), Is ice cream a normal good? Are ice cream and cakes substitutes or complements? Calculate the income elasticity of market demand at the point px = 2, py = 1 and I = 12.
Consider the following utility function: U= 4X + Y. A consumer faces prices of P, = $2 and P, =1. Assuming that graphically good X is on the horizontal axis and good Y is on the vertical axis, suppose the consumer chooses to consume 10 units of good X and 19 units of good Y. Then the marginal rate of substitution (MRS) is equal to: MRS = (Enter your response rounded to two decimal places. Do not forget to include the negative sign.) étv Help Me Solve This eText P MacBook Air 80 DII esc F2 F3 F6 F8 F1 F4 F5 F7 @ 23 2$ & 1 2 4 6 7 8. Q W E R T Y U tab A S G caps lock C V shift fn control option command ーのエ B レ