An agent consumes quantity (x1,X2) of goods 1 and 2. Here is his utility function: U(x1, x2) =Vx1 + 2 *x2, his budget constraint is p1x1+p2x2 = m.a. Calculate the agent's Marshallian demand (x*1 , x*2 ).b. When would the agent's consumer's problem have a corner solution?

Utility is the satisfaction derived from a good that a consumer has purchased. A rational consumer…

Answered: An agent consumes quantity (x1,X2) of…

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 2.1 A consumer has a utility function u(x1, x2) = VT1 + x2 and faces a budget constraint y = P1x1 + P2x2. Assuming an interior solution to the consumer's utility maximisation problem (i.e. excluding the possibility of any corner solutions where x = 0 or x = 0), solve for x(p, y) and x(p, y), the consumer's Marshallian demand functions. 2.2 Derive the consumer's indirect utility function. 2.3 Derive the consumer's expenditure function. 2.4 Suppose the assumption of an interior solution, as set out in question 2.1 above, is no longer maintained. Discuss how (under what conditions) a corner solution to this specific utility maximisation problem may arise (i.e. where x = 0 or x = 0). Then re-write the solutions for xi(p, y) and x(p, y) (the consumer's Marshallian demand functions), as well as the new indirect utility function v(p, y), so as to allow for the occurrence of a corner solution.
Let a consumer's utility function be U (x, y) = x'/²y/2. The consumer's income is I = 160 and prices for the two goods are, respectively, p, = 1 and py = 4. (a) Write down the utility maximization problem and compute the optimal consumption basket. (b) Suppose now the price of good y is equal to p, = 16 (while the price of good r stays constant). Compute the new optimal consumption basket.
Given the total utility function for a consumer, consuming two goods is U = x+2y + xy+2 the prices of x and y are 4 TL and 6 TL respectively (Px = 4 and Py = 6), and the total budget of the consumer (B) is 130 TL; a) Write the constraint ( budget) function. b) Write the lagrangian function. c) What are the first-order conditions for utility maximization? d) Find the critical values of x, y and \lambda (x*,y*and \lambda *) according to the first order conditions. e) is the second order suficent condition for maximum utility satisfied 2 4 10 [ [:] 8 Write the appropriate commands to create A and d matrixes in R software. A-1. din R language? Given A = 1 3 And d = How can you formulate the equation X =
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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
A consumer consumption bundle contains good X and Y. Suppose the price of good X goes up and a consumer goes on consuming the exact same amount of X as before. Check the correct statement(s).A) Both X and Y are inferior. B) X is an inferior good.C) In the special case where X is Leisure, and Y is "all other goods", X is an inferior good.D) The consumption of Y decreases.E) It is impossible that the consumption of X remains unchanged when the price of × goes up.F) The substitution effect is negative
Anthony seeks to maximize the following utility function u(x, y) = x'/3y2/3 subject to the budget constraint Pæa + PyY = I 1 where pr, Py, x, y, I > 0. a) Find Anthony's utility-maximizing bundle (x*, y*) as a function of pæ, Py, and I. b) Show that y* is decreasing in py and increasing in I (hint: use partial derivatives). c) What share of Anthony's income is spent on x? What share is spent on y? In other words, calculate Pa and Pu. Are these shares a function of prices? Pyy* Note: The above utility function is Cobb-Douglas, and all Cobb-Douglas functions have these share formulas for any values for the exponents. d) What is the impact of a change in pr on Anthony's utility?
A consumer’s utility only depends on the consumption of goods A and B according to the following Cobb-Douglass utility function: U(A, B) = A1/4 B 3/4. The price of goods A and B are $20 and $40, respectively. The consumer has a budget of $1200 that he can use to consume the two goods. a. Write down the budget constraint and plot it. b. Calculate the optimal bundle and maximized utility for the consumer. c. A new tax of $10 is imposed on the price of good B. Compute the new optimal bundle of good A and B for the same consumer. What is the utility loss due to the tax? d. Show that the consumer would prefer a lump sum income tax that raises the same revenue as the tax on good B. Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.
Two friends, Karol and Manuel, like to drink kombucha (x₁) and matcha (x₂). Both X₁ and X2 are expressed in ounces. The following utility function represents Karol's preferences: 1 1 2 2 u (x1, x2) = x1 x3 The following utility function represents Manuel's preferences: u (x₁, x2) = √√x1 + x2 Karol's income in dollars is denoted by mk, and Manuel's income is denoted by mm. Both face the same prices in the market, denoted by p₁ and p2, for kombucha and matcha, respectively. Both prices are expressed in dollars per ounce. Assume p₂=1 throughout the whole question. 1) Draw Karol's and Manuel's indifference curves in separate graphs and describe any important similarities or differences between the two.

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An agent consumes quantity (x1,X2) of goods 1 and 2. Here is his utility function: U(x1, x2) = Vx1 + 2 * x2, his budget constraint is p1x1+p2x2 = m. a. Calculate the agent's Marshallian demand (x*1 , x*2 ). b. When would the agent's consumer's problem have a corner solution?

An agent consumes quantity (x1,X2) of goods 1 and 2. Here is his utility function: U(x1, x2) = Vx1 + 2 * x2, his budget constraint is p1x1+p2x2 = m. a. Calculate the agent's Marshallian demand (x1 , x2 ). b. When would the agent's consumer's problem have a corner solution?