yyQUESTION 1 Consider the standard utility maximization problem: maxU = U(x,y) subject to Px+Py = B, where PP denote the price of goods x and y, respectively, and B represents the consumer's available income. (a) Write theLagrangian function and obtain the first-order conditions. (6 marks) (b) Assume that U = xy, P = 1,P = 4 andB=120. Find A along with the optimal levels of purchase x and y. Calculate U. (10 marks) (c) Using theBordered Hessian matrix, verify that the second-order conditions for a maximum are satisfied. (9 marks)yand

Step 1:Step 2: The determinant of the Hessian matrix is negative. Hence, it is concave down. and…

Answered: y y QUESTION 1 Consider the standard…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Provide (any) two utility functions for each following description. (a) A consumer has a perfect substitute preference for good 1 and good 2. (b) A consumer has a perfect complement preference for good 1 and good 2. (c) For any prices of goods and incomes, a consumer always spends the same portion of his income on each good (i.e, for example, p1x1/m = a and p2x2/m = b for any p and m). Give full typed explanation
Question 5 Solving Consumer's Choice Problem under CES Utility, Numerical (sympy solution not required) The consumer with income Y has a preference represented by CES utility function U(91,92) = (90.4 + 92.4) 04. Given prices for the two goods, denoted by P₁, P2, solve the consumer's optimal choice problem following the steps below. (a) Write down the consumer's maximization problem, i.e be clear about (1) the choice variables, (2) the objective function and (3) the constraint. (b) Write down the Lagrangian for this optimization problem. (c) Derive the three first-order conditions. (d) Solve for the optimal consumption bundles q₁,92 . (e) Now we analyze the properties of demand. How does q respond to changes in P₁, P2 and Y? Specifically, does q increase or decrease if 1. p₁ increases? 2. P2 increases? 3. Y increases? For simplicity, we only analyze q, results for q are similar. (Hint: comparative statics, calculate, etc.)
A consumer has preferences over bundles of two goods with indifference curves defined by X2 = for k>0. (a) Find a utility function representing these preferences assuming that the consumer's pref- erences are monotone. (b) Give an example of a utility function representing non-monotone preferences with the same indifference curves. (c) Show that indifference curves of the form x2 = x + k for k € R cannot arise from monotone preferences.
(b) It is thought that a consumer measures the utility, u(x, y), of possessing a quantity, z, of apples and a quantity, y, of oranges by the formula u(x, y) = rªyla, where a is a constant. Suppose that apples cost p dollars each and oranges q dollars each. If the consumer has M dollars to spend on apples and oranges, use the method of Lagrange multipliers to find the quantity of each that he will buy in terms of a, p, q and M. [You are not required to justify the use of the method of Lagrange multipliers here.] For equally priced apples and oranges when he has one dollar to spend, he is actually observed buying one apple and two oranges. What value of a does this imply?
3. Let there be two goods x and y with prices px and py respectively, and let M be the consumer's income. Let the consumer's preferences be represented by the utility function min(2x, y). Find the consumer's expenditure function. Note: you cannot use the Lagrange method as the utility function is not differentiable - but you have used the min U = utility function before. (4)
b) An individual wish to maximise the following utility function: U = 2x}x2 %D Subject to the budget constraint 5x, + 7x2 = 172 a. Derive the Marshallian demand functions for the two goods. b. Calculate the maximum utility level c. Show graphically your answer to parts 'a' and 'b'
Please help me to solve questions (a) (b) (e). (especially question e). thank you!
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?
1. Which of the following utility functions does not admit corner solutions (x = 0 or x = 0) given a positive income m > 0? a) u(x1, x2) = x, + 2x2, b) v(x1, x2) = X1X2, c) w(x1,x2) = max{x1,x2}, d) y(x1, x2) = Inx1 + x2.
Help!
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.

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