1. For what kind of preferences will the consumer be just as well off facing a quantity tax asan income tax?2. Someone is willing to maximize his/her utility. Assume he/she knows his/her u(x,y) =%3Dx0.Sy0$ (Cobb-Douglas)(a) Find his/her optimal consumption given the income = 20, Px=2, Py=4!%3D(b) Depict his/her optimal consumption graph!3. Suppose that x and y (from your answer in number 2) are now perfect complement withu(x,y) = min(x,y).(a) Find his/her optimal consumption (given the same income and prices)!(b) Depict his/her optimal consumption graph!Best of Luck!

"Since you have asked multiple questions, we will solve the first question for you. If you want any…

Answered: 1. For what kind of preferences will…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question 2 There are two goods, apple and banana, whose quantities are denoted by X, and X, and prices are P and Pg respectively. An individual spends his income denoted by M on these goods. His indirect utility function is known to be: M2 V = V(P,. P. M) = 2P,P2 (ey者% a Derive his Marshallian (Uncompensated) demand functions for X, and X2 b. Find the consumer's Expenditure function c. Find the consumer's Hicksian (compensated) demand functions for X, and X2 ops famce d. Derive the direct utility function of this consumer 告/
Assume that the preferences of a consumer can be expressed by the utility function 0.75 utx), 4 + x (i) Show that based on this utility function, the demand functions are for the benefits provided by 81 p x = 4 3 81 р; т and x P2 P der 1 p is the price per unit 1 x, 2 p is the price per unit 2 x and m are the income of the consumer. (ii) Explain what is meant by the cross-price elasticity of a good. Calculate the cross-price elasticity of the goodigiven in question (i), and give an interpretation of the result.
Suppose that consumer uses 2 units of X and 5 units of Y always in fixed proportion. Suppose also that Px = 1. Py respectively? = 2 and I = 120. What would be the optimal consumption of X and Y at the equilibrium, 20, 50 40, 40 24. 60 50. 35
Given f(x,y) = 2x2 - 5xy + 5y2, and Px= 7, Py= 6 and income, I = 169. Construct the budget contraint and Lagrange function and solve for the equilibrium values of x and y. (a) What is the equilibrium value of x? (Give your answer to two decimal places, if required) (b) What is the equilibrium value of y? (Give your answer to two decimal places, if required) (c) What is the value of the determinant of the bordered Hessian matrix? (Give your answer to two decimal places, if required) (d) Based on the value of the Bordered Hessian, comment whether the obejective function is maximised or minimised.
suppose the government of a desert community wants to punish excessive water useage, where "excessive" is defined as any usage greater than 100 gallons/week. to do this, the government paces a flat $100 income tax on anyone who consumes more than 100 gallons/week of water in any given week (so this tax could theoretically be levied 52 times per year). people who use less than 100 gallons of water each week will not face this $100 special tax. For these problems, consider the decisions between water consumption, X(sub)w and consumption of a composite good, X(sub)c, where P(sub)w =$2/gallon and the composite good's price is numeraire. suppose michael lives in this desert community and has a weekly income of $1000. 1. graphing michels budget contraint over (X(sub)w , X(sub)c) bundles, what is the slope of his budget conraint for bundles containing MORE than 100 gallons of water? 2. What is the slope of michaels budget constraint at the point (X(sub)w, X(sub)c)=(100,750)? 3. what is the…
1. A consumer wishes to maximize the utility U(X1, X2) = (X1 + 20)(X2 + 30) subject to the available income (M= 600) and prices (pi = 5, p2 = 4). Find the optimal consumption levels and marginal utility of income. ASsuming a local maximum is attained, prove that it is also a unique global maximum.
Frank's utility function for WWE wrestling event tickets (x,) and NASCAR race tickets (2) is of the following Cobb - Douglas form: U(x,, ) = x 1 2 0.25 0.75 x 2 his income is Y, the price of WWE tickets is p₁, and the price of NASCAR tickets is p₂. a. Mathematically derive his 1 demand functions for x, and x2. No graphs! You are not required to use Lagrangian Function, you can just use the demand formulas for the Cobb - Douglas utility function (Chapter 5, fourth slide). b. Using your answers from part (a), find the demand functions for x and x2, and mathematically prove that they have the proper negative slope.
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Given f(x,y) = 2x2 - 6xy + 9y2, and Px= 7, Py= 5 and income, I = 175. Construct the budget contraint and Lagrange function and solve for the equilibrium values of x and y. (a) What is the equilibrium value of x? (Give your answer to two decimal places, if required) (b) What is the equilibrium value of y? (Give your answer to two decimal places, if required) (c) What is the value of the determinant of the bordered Hessian matrix? (Give your answer to two decimal places, if required) unanswered d. Based on the value of the Bordered Hessian, comment whether the objective function is maximized or minimized. Answer in one word.
2. Consider a society with only two people one rich and one poor-who have the same util- ity functions. These utility functions exhibit diminishing marginal utility. Suppose that taxes are set such that the total amount of utility that each person loses is the same. Does it follow that the tax will be progressive? Explain.
2. Suppose there are n identical consumers, each with a utility function u(x, y): = ax = x²+y. Each consumer has different disposable income w. The price of good x is p dollars, and the price of composite good y is equal to 1 dollar. Assume a > 0 and b > 0. (Hint: Question 1) (a) Calculate the marginal utility of good x and good y. Then, calculate the marginal rate of substitution between good x and good y. (b) Calculate the individual demand of consumer 1 for good x. (c) Calculate the aggregate demand for good x. (d) Draw a graph showing the market demand curve for good x. (e) Discuss whether an increase in disposable income for each consumer lead to an increase in the consumption of good x? This increase in disposable income can result from various factors, such as a decrease in taxes, government stipends, or other forms of income support. (f) Discuss the effect on demand for good x if there is an increase in the price of good x. This increase in the price of good x can result from…

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