please only do: if you can teach explain steps of how to solve each part use lengrange A consumer of two goods has utilityu(x₁, x2) = x²x₂.In addition to her wealth w, the consumer already owns k units of good 1, which she cannotsell (she can, however, purchase more). Thus, for example, if k = 2 and she uses her wealthto purchase 3 units of good 1 and 1 unit of good 2, then she receives utility (3+2)².1 = 25.(a) Sketch this consumer's utility-maximization problem in (₁,2)-space, where I repre-sents the total quantity consumed of good i (i.e. including the k units of good 1 that shealready owns).Solution: The sketch is similar to the typical one except that the budget line is shiftedto the right by k (leaving a gap from x₁ = 0 up to x₁ = k.)(b) Find this consumer's Marshallian demand, expressed in terms of quantity purchased (i.e.not including the k units of good 1 that she already owns).Solution: In terms of quantity consumed, the utility maximization problem is the samethe usual one given this utility function except that the wealth is w+kp₁ and the nonneg-ativity constraint on x1 is replaced with ₁ ≥k. Therefore, using the usual Cobb-Douglasdemand formula and subtracting k from ₁ to get the quantity purchased, and then check-ing the constraint x₁ ≥k, we obtainx(p, w) ==2w-kp1 w+kpi3p₁ 3p₂(0, #)P2if 2w > kp₁,otherwise.

Utility Function : U = x12x2 Budget Constraint : p1x1 +p2x2 = w Optimal consumption point is…

A consumer of two goods has utility u(x₁, x2) = x²x₂. In addition to her wealth w, the consumer already owns k units of good 1, which she cannot sell (she can, however, purchase more). Thus, for example, if k = 2 and she uses her wealth to purchase 3 units of good 1 and 1 unit of good 2, then she receives utility (3+2)².1 = 25. (a) Sketch this consumer's utility-maximization problem in (₁,2)-space, where ; repre- sents the total quantity consumed of good i (i.e. including the k units of good 1 that she already owns). Solution: The sketch is similar to the typical one except that the budget line is shifted

A consumer of two goods has utility u(x₁, x2) = x²x₂. In addition to her wealth w, the consumer already owns k units of good 1, which she cannot sell (she can, however, purchase more). Thus, for example, if k = 2 and she uses her wealth to purchase 3 units of good 1 and 1 unit of good 2, then she receives utility (3+2)².1 = 25. (a) Sketch this consumer's utility-maximization problem in (₁,2)-space, where ; repre- sents the total quantity consumed of good i (i.e. including the k units of good 1 that she already owns). Solution: The sketch is similar to the typical one except that the budget line is shifted

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

A consumer finds only three products, X, Y, and Z, are for sale. The amount of utility yielded by their consumption is shown in the table below. Assume that the prices of X, Y, and Z are $10, $2, and $8, respectively, and that the consumer has an income of $74 to spend. (a) Complete the following table by computing the marginal utility per dollar for successive units of X, Y, and Z to one or two decimal places. (b) How many units of X, Y, and Z will the consumer buy when maximizing utility and spending all income? Show this result using the utility maximization formula. (c) Why would the consumer not be maximizing utility by purchasing 2 units of X, 4 units of Y, and 1 unit of Z? Product X Product Y Quantity Utility Marginal Quantity Utility Marginal Utility Utility per$ per$ 1 23 4567 42 82 118 148 170 182 182 1 23 4 5 6 7 14 26 36 44 50 54 56.4 Product Z Quantity Utility Marginal Utility per$ 1 23456 7 32 60 84 100 110 116 120 3..
Linda loves buying shoes and going out to dance. 20 Her utility function for pairs of shoes, S, and the number of times she goes dancing per month, T, is: 18- 16- U(S, T) = 2ST 14- It costs Linda $75 to buy a new pair of shoes or to spend an evening out dancing. Assume that she has $750 to spend on shoes and dancing. E 12- 1.) Use the line drawing tool to draw Linda's budget line. Properly label this line. 10- 2.) Use the point drawing tool to locate Linda's optimal consumption bundle. Label this point 'R'. 8- 6- Carefully follow the instructions above, and only draw the required objects. 4- What is Linda's marginal rate of substitution? -. (Enter your response as an 2- integer. Note that the minus sign is already included.) 0- 12 10 Shoes (S) 14 16 18 20 React tv MacBook Air 80 DII F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 @ 23 2$ & 1 3 4 7 8 Q W E T Y { A S F H. J K C V M. く tion command command option ピーの Dancing (T) コ B. レ

Sam's extended family spends $3,200 per month on wine and beer. Their utility function is given by U = 200WB, where W represents the number of bottles of wine that they buy, and B represents the number of cases of beer that they buy. Wine costs $25 per bottle and beer costs $32 per case. Sam's family wants to maximize their utility. Calculate how many bottles of wine and how many cases of beer they should buy. Show your calculation(s).
Jane spends $210 per month on wine and beer. Her utility function is given by TU = 100WB, where W represents the number of bottles of wine that she buys and B represents the number of cases of beer that she buys. If wine costs $10 per bottle and beer costs $15 per case, she will maximize utility by buying: 10 bottles of wine and 13.33 cases of beer. equal amounts of wine and beer. none of the above. 10.5 bottles of wine and 7 cases of beer. 2 bottles of wine and 3 cases of beer.
Zeynep is at the supermarket buying her bi-weekly groceries. As she arrived at the store right before closing, not much is left on the shelves; so her purchases are limited to beef, B, and an assortment of organic vegetables, V. Beef costs £50/kg and vegetables Ł10/kg. Her utility function is expressed as U(B,V) = B0-6v0.3. She has ±150 to spend. Please answer the following questions using this information: A) Given the vegetables cost less than beef, explain why Zeynep would not only buy vegetables. B) Write Zeynep's constrained maximization problem (objective function subject to her budget constraint). C) Using the Lagrangian technique, find how much beef and vegetables would Zeynep buy? D) Show that for the preferences represented as above, demand for beef is a function of only its own price, pg, and income, m, but not the price of vegetables, py. Note: Rather than using the given prices and income, use PB, Py and m. Find and comment on the comparative statics, i.e., how do changes…
U=X^0.7*Y^0.8 utility function (EXAMPLE: U=XL In the Utility function given above, U=Utility level, X and Y are two goods such as apples and pears) (e.g. apple and pear),Px and Py represent the price of goods X and Y, respectively. (M) shows income The budget equation is shown as M=PxX+PyYpx=5py=10M=800a) Find the Y quantities that maximize the Utility according to the above. b) Calculate how much a one-unit increase in the constraint will increase the level of utility. c) Calculate the maximum benefit level
Kate’s utility function includes coffee (c) and sugar (s). She only consumes coffee and sugar together, and she only consumes in the ratio of one unit (cup) of coffee with two units (spoons) of sugar. Her utility function is What is her marginal utility of sugar if she has 4 cups of coffee and 6 spoons of sugar? Remember that unit are infinitely divisible (you can have parts of units). (a) 0 (b) 1 (c) ½ (d) 2
Ice cream and cakes are perfect substitutes for a child, and 2 units of ice cream is always worth 3 units of cakes (however many ice creams or cakes she might have, she would be willing to give up 2 ice creams to get 3 more cakes to keep the same utility level) . (a) Write down a utility function u(x,y) that represents the child's preferences, where x is the number of ice creams and y is the number of cakes she has. (b) If the prices are px= 8 and py =5, and she has $140 to spend on the two goods this summer, what is her optimal bundle? (c) If the price of ice creams decreases slightly, down to px = 7, what happens to her optimal bundle in this case? Did it change "slightly" compared to (b)?
There are two shows on Netflix that Jeff can watch, Show 1 and Show 2. x₁ measures the number of episodes watched of Show 1 and x2 measures the number of episodes watched of Show 2. Jeff's preferences can be represented by u(x₁, x₂) = x² + ax². Jeff has 5 hours available for watching Netflix today. Each episode of Show 1 lasts 30 minutes, while each episode of Show 2 lasts one hour. For all question parts, round to three decimal places if necessary.
There are two shows on Netflix that Jeff can watch, Show 1 and Show 2. x₁ measures the number of episodes watched of Show 1 and x₂ measures the number of episodes watched of Show 2. Jeff's preferences can be represented by u(x₁, x₂) = x² + ax². Jeff has 5 hours available for watching Netflix today. Each episode of Show 1 lasts 30 minutes, while each episode of Show 2 lasts one hour. For all question parts, round to three decimal places if necessary. For parts (a) - (f), let a = 1. Draw Jeff's indifference curves for the utility levels u = 4, 9, 16. Draw a straight line between the bundles (x₁, x₂) = (4,0) and (x₁, x₂) = (0,4). Now, use your picture to determine whether the following two statements are true or false. Answer "1" for true. Answer "0" for false. a) Statement 1: Jeff's preferences are strongly monotone. b) Statement 2: Jeff's preferences are strictly convex. c) Find the bundle at which one of Jeff's indifference curves is tangent to the budget line. (x₁, x₂)=( d) Evaluate…
of 55 The vending machine in Katherine's office building offers cans of pop and candies. Katherine's utility function is U = 3PC, where P is the amount of pop consumed per week and C is the amount of candy consumed per week. Pop costs $1 and candy costs $0.5 per bag. If Katherine has $10 to spend, she will consume
Suppose a consumer's utility is given by: u (x1, x2) = a/xT + b/x2 Where a= 8, and b = 4 %3D What is the value of MU1 (x1, X2)when x1=9 and x2=8. (Note: The answer may not be a whole number, so round to the nearest hundredth) (Note: The numbers may change between questions, so read carefully)