please only do: if you can teach explain steps of how to solve each part use lengrange u(T1, T2, T3) = √√√1₂-2-³.As usual, goods 1 and 2 are perfectly divisible, meaning that ₁ and 2 can take on anynonnegative real values and need not be integers. Good 3 is indivisible and unique, meaningthat 23 must be either 0 or 1 (for example, good 3 could be an original painting).(a) Show that this consumer's preferences are monotone.Solution: The derivatives du/oxy and du/dr2 are positive for x1, x2 > 0. Increasing13 from 0 to 1 increases utility by 1/2. Therefore, if the quantity of all three goodsincreases, utility (strictly) increases.(b) Find this consumer's Marshallian demand.Solution: If x3 = 0, the optimal choice isIf x3 = 1, the optimal choice iswhich simplifies toW(31,82,83) = (201₁, 2012, 0).Therefore,x(p, w):Note that if p3>w, we must have x3 = 0. Otherwise, the optimal choice of x3 is 0 ifw-P3 w - P32p1 2p2(F1, F2, F3) = (²W W2p12p212w-P3 w-P3,2p1 2p2P3 ≥ √P1P2.w-Pa2p1 2pz²,₁1).(2P12P2,0)1) if p3 ≤ w and p3 ≤ √P1P2,if P3 w or P3 ≥ √P1P2

As usual, goods 1 and 2 are perfectly divisible, meaning that ₁ and 22 can take on any nonnegative real values and need not be integers. Good 3 is indivisible and unique, meaning that 23 must be either 0 or 1 (for example, good 3 could be an original painting). (a) Show that this consumer's preferences are monotone. Solution: The derivatives du/day and du/da2 are positive for x1, x2 > 0. Increasing 23 from 0 to 1 increases utility by 1/2. Therefore, if the quantity of all three goods increases, utility (strictly) increases. (b) Find this consumer's Marshallian demand. Solution: If x3 = 0, the optimal choice is (#₁, #2,83) = (25₁, 252,0). If x3 = 1, the optimal choice is (#1, #2, #3) = W 2p1 1 w - P3 2p2

As usual, goods 1 and 2 are perfectly divisible, meaning that ₁ and 22 can take on any nonnegative real values and need not be integers. Good 3 is indivisible and unique, meaning that 23 must be either 0 or 1 (for example, good 3 could be an original painting). (a) Show that this consumer's preferences are monotone. Solution: The derivatives du/day and du/da2 are positive for x1, x2 > 0. Increasing 23 from 0 to 1 increases utility by 1/2. Therefore, if the quantity of all three goods increases, utility (strictly) increases. (b) Find this consumer's Marshallian demand. Solution: If x3 = 0, the optimal choice is (#₁, #2,83) = (25₁, 252,0). If x3 = 1, the optimal choice is (#1, #2, #3) = W 2p1 1 w - P3 2p2

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

4.If we observe a consumer choosing (x1, x2) when (y1, y2) is available one time, are we justified in concluding that (x1, x2) > (y1, y2)?
Suppose a person has $8 to spend only on apples and bananas. Apples cost $.04 each and bananas cost $.01 each. Furthermore, his preferences for apples (A) and bananas (B) can be represented by U = the square root of AB. a.) If A =5 and B=80, what will utitly be? b.)lf A =10, what value of B will provide the same uititly in part a? c.) If A=20, what value of B will provide the same utility in parts a and b?
Neha and Sonam consume only Coke and Pepsi in a two person and two goods exchange economy. Neha consumes these two goods in fixed proportions such that she consumes 2 bottles of coke with 1 bottle of Pepsi. Sonam's utility function is given by U = 4P + 3C . In the economy, there is a total of 100 bottles of Pepsi and 200 bottles of Coke. If Neha initially had 60 bottles of Pepsi and 80 bottles of coke, then in the equilibrium position, Sonam will consume: A. between 50 to 60 bottles of Pepsi B. between 52 to 60 bottles of Pepsi C. between 54 to 60 bottles of Pepsi D. between 56 to 60 bottles of Pepsi
Ginny likes to eat Bertie Bott’s Every Flavour Beans (b), and Chocolate Frogs (f). Herpreferences over these lollies are Cobb-Douglas, and can be presented by the utility functionu(b, f) = 1/5(b − 2)(f + 3). Each Every Flavour Bean costs 25 Knuts and each Chocolate Frogcosts 12 Knuts. Ginny has 314 Knuts to spend. Assume that beans and frogs are both perfectlydivisible goods.(a) Find Ginny’s optimal bundle.(b) Suppose that Ginny is mugged by Draco on her way to the lolly cart, so that by the timeshe is there, she is left only with 75 Knuts. What is her optimal bundle now?(c) Now, consider the general case, where Ginny’s income is m, the price of Every FlavourBeans is pb, and the price of Chocolate Frogs is given by pf . In other words, treat ChocolateFrogs as the numeraire. Find Ginny’s demand for each good in terms of m, pb and pf .(d) Find the good on which Ginny will always spend more than half of her income.(e) Find the own-price, cross-price, and income elasticities of good 2.
Ginny likes to eat Bertie Bott’s Every Flavour Beans (b), and Chocolate Frogs (f). Herpreferences over these lollies are Cobb-Douglas, and can be presented by the utility functionu(b, f) = 1/5(b − 2)(f + 3). Each Every Flavour Bean costs 25 Knuts and each Chocolate Frogcosts 12 Knuts. Ginny has 314 Knuts to spend. Assume that beans and frogs are both perfectlydivisible goods.(a) Find Ginny’s optimal bundle.(b) Suppose that Ginny is mugged by Draco on her way to the lolly cart, so that by the timeshe is there, she is left only with 75 Knuts. What is her optimal bundle now?(c) Now, consider the general case, where Ginny’s income is m, the price of Every FlavourBeans is pb, and the price of Chocolate Frogs is given by pf . In other words, treat ChocolateFrogs as the numeraire. Find Ginny’s demand for each good in terms of m, pb and pf .(d) Find the good on which Ginny will always spend more than half of her income.(e) Find the own-price, cross-price, and income elasticities of good 2…
ote: - You are attempting cuestios suro 12 Neha and Sonam consume only Coke and Pepsi in a two person and two goods exchange economy. Neha consumes these two goods in fixed proportions such that she consumes 2 bottles of coke with 1 bottle of Pepsi. Sonam's utility function is given by U=4P+BC. In the economy, there is a total of 100 bottles of Pepsi and 200 bottles of Coke. If Neha initially had 60 bottles of Pepsi and 80 bottles of coke, then in the equilibrium position, Sonam will consume: A. between 50 to 60 bottles of Pepsi B. between 52 to 60 bottles of Pepsi C. between 54 to 60 bottles of Pepsi D. between 56 to 60 bottles of Pepsi Answer 04:09 PM 19-10-2021
1. Jie thinks a cup of coffee is just as good as five cups of orange juice. Let M stand for the number of cups of coffee and N stand for the number of cups of orange juice. Among the following utility functions, how many of them represent his preferences? (1) U(M,N) %3D тах(М,5N} (2) U(M, N) = M + 5N (3) U(M,N) = (3M + 15N)2 (4) U(M, N) = 5M2 + N A.0 B.1 С.2 D.3
2. Diana and Jennie are stranded on a desert island. Each has in his possession some slices of ham (H) and bread (B). Diana is a choosy eater and will eat ham and bread only in the fixed proportions of 2 slices of bread to 1 slice of ham. Her utility function is given by Up = min(H, B/2). Jennie is more flexible in his dietary tastes and has a utility function given by U, = 4H + 3B. Total endowments are 100 slices of ham and 200 slices of bread. a. Draw the Edgeworth box diagram that represents the possibilities for exchange in this situation. What is the only exchange ratio that can prevail in any equilibrium? b. Suppose Diana initially had 40H and 80B. What would the equilibrium position be? c. Suppose Diana (much the stronger of the two) decides not to play by the rules of the game. Then what could the final equilibrium position be?
Consider the classic consumer's choice problem of an individual who is allocating Y dollars of wealth amongst two goods. Let c1 denote the amount of good 1 that the individual would like to consume at a price of Pı per unit and c2 denote the amount of good 2 that the individual would like to consume at a price of P2 per unit. The individual's utility is defined over the consumption of these two goods (only). Suppose we allow the individual's happiness to be measured by a utility function u(c1, c2) which is increasing and strictly concave in both goods while also satisfying the Inada condition, limcı→0 du(c1,c2) = limc1→0 du(c1,c2) dc2 = 0. The Inada conditions simply say that the slope of the utility function becomes vertical in the direction of the good that has its consumption level go to zero. By assuming increasing and strictly concave utility in both directions, we are assuming that the shape of the utility function is such that, holding constant the amount of one good, as the…
Problem 1. Two consumers, Alice and Bob, have utility functions given by u₁(x, y) = x¹/²y¹/4 and ug (x, y) = 4x² + y², respectively, where x and y are the number of apples and bananas respectively. Suppose that apples and bananas cost p₁ and p2 dollars each respectively and that both consumers have M dollars to spend on apples and bananas. (a) On the same axes, sketch Alice's budget set and some contours u₁(x, y) = c for positive values of c. By referring to your sketch explain why the method of Lagrange multipliers can be used to find the maximum value of u₁(x, y) subject to her budget constraint. Hence use the method of Lagrange multipliers to find Alice's optimal bundle. (b) On the same axes, sketch Bob's budget set and some contours up (x, y) = c For positive values of c. By referring to your sketch, find Bob's optimal bundle.
(c) If the preferences are concave, will the consumer ever consume both of the goods together?
3- Assuming that the equation F(U, x, X2 = f(x1, x2,, ... Xn): ******* **** ,xn) = 0 implicitly defines a utilityfunction U 073 a) Find the expressions for 60, 6U and 6x4 " 3 6x2 6xn 6x2 6xn b) Interpret their respective economic meanings. c) Now. assume the utility function is U(x, y) = y√x. Does the consumer believe that more is better for each good? Do the consumer's preferences exhibit a diminishing marginal utility of x? Is the marginal utility of y diminishing?