The consumer buys bundle x'at prices p'i = 0,1. Separately for parts (a) to (do, state whether these indicated choices satisfy WARP: (a) Po = (1,3), x° = (4,2); p' = (3,5), x' = (3,1). (b) Po = (1,6), x° = (10,5); p' = (3,5), x' = (8,4). (c) P0 = (1,2), x° = (3,1); p' = (2,2), x' = (1,2). (d) Po = (2,6), xº = (20,10); p' = (3,5), x' = (18,4). %3D %3! %3D
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- A consumer has utility u(x,y,z)= ln(x) + 2ln(y) + 3ln(z) over the three goods, x,y and z and pZ = 1 . Optimally sheconsumes 30 units of z. What is her income? How much money does she spend on x?(HINT: MUX =??, MUY =??, MUZ =??and remember the “equivalent bang for the buck” condition)(b) Forget about (a). Suppose you have t = 29 hours in total to spend on 3 projects X, Y and Z to make some money.If you spend x hours on project X, you make 2√? dollars;If you spend y hours on project Y, you make ?√? dollars;If you spend z hours on project Z, you make ?√? dollars;Writing down your “utility function” u(x,y,z) and the constraint, solve the utility maximization problem; what isthe optimal amount of time to spend on x ? on y? on z ?4. Suppose a person has $8 to spend only on apples and bananas. Apples 1 cost $0:4 each, and bananas cost $0:1 each. Furthermore, his preferences for apples (A) and bananas (B) can be represented by U = pAB. a) If A = 5 and B = 80, what will utility be?b) If A = 10, what value of for B will provide the same utility in part a? c) If A = 20, what value of for B will provide the same utility in parts a and b?d) Graph the indi§erence curve implied by parts a through c.e) Give the budget constraint, which of the points identiÖed in parts a through c can be bought by this person?f) show through some examples that every other way of allocating income provides less utility than does the point identiÖed in part b. graph this utility maximizing situation.Let MUA = z = 10 − x and MUB = z = 21 − 2y, where z is marginal utility per dollar measured in utils, x is the amount spent on product A, and y is the amount spent on product B. Assume that the consumer has $10 to spend on A and B—that is, x + y = 10. How is the $10 best allocated between A and B? How much utility will the marginal dollar yield?
- Mats, who has reference-dependent preferences over beer and money, goes to the local pub with a friend, but is not planning on drinking any beer or spending any of his 50 Euro in cash. Let his end-of-evening outcomes in pints of beer consumed and cash be c1 and c2, respectively, and let his reference point in pints of beer and cash be r1 and r2, respectively. Then, Mats’ utility is given by v(6c1 − 6r1) + v(c2 − r2), where v(x) = x for x ≥ 0, and v(x) = 1.5x for x < 0. (a) Suppose that the price of beer is pB. Calculate Mats’ utility from drinking one pint of beer at this price. What is Mats’ utility from drinking no beer? And, comparing these two utility values, what is the maximum price pB that Mats would pay for one beer? (b) Suppose that Mats unexpectedly gets a pint of beer as part of a promotion at the pub, and incorporates its consumption into his reference point in beer. [Hint: this means that (r1, r2) = (1, 50).] Suppose that Mats could sell the beer at a price pS.…Harmon's utility function is U(x1, x2) = x1x2. His income is $80. The price of good 2 is p2 = 4. Good 1 is priced as follows: the first 15 units cost $4 per unit and any additional units cost $2 per unit. What consumption bundle does Harmon choose? a) (12.5, 12.5). b) (25, 12.5). c) (12.5, 25). d) (15, 10). e) none of the above.True/False/Uncertain: 1. In taking an exam, Atack, a rational student, allocates his time to the various questions so as to equalize hismarginal point utility per minute on all questions. 2. The marginal utility of food to Zecher depends only on the amount of food (and not on the amount ofhousing) and the marginal utility declines as more food is consumed; likewise for housing. Therefore,both food and housing are normal goods. (Hint: Express the optimality condition for Zecher’s [UMP], MUF/MUH = PF/PH. Notice that PF/PH is fixed. If all of an increase in income is spent on F, can the equality be maintained?)
- Mr. Dogan has 4000 TL to spend. He considers buying meat whose price is 400 TL per kg. and cheese whose price is 160 TL /kg. Given this a) What condition (equality) leads him to a utility maximization. State the condition numerically and tell clearly what each of the variables mean in that equation b) Now suppose that income of Mr. Dogan and price of meat does not change but price of cheese is down to 130 TL/kg. Do the equality and optimal basket found in a still maximize the utility? If not; what is the new condition for utility maximization (write the condition as a numerical equation defining the variables in the equation)Suppose the consumer's utility function is given by U(x,y) = X3/5y2/5, and the exogenous variables are given by M = 500, Px = 5, and Py = 4. Price of y changes to Py = 2. What is the income effect ony?O A.-14.53O B. +14.53O C. +24.21O D. +25.79O E. None of the above Note:- Please avoid using ChatGPT and refrain from providing handwritten solutions; otherwise, I will definitely give a downvote. Also, be mindful of plagiarism. Answer completely and accurate answer. Rest assured, you will receive an upvote if the answer is accurate.Let the following table represents the total utility of a given consumer, in the cardinal utility approach. Q 1 2 3 4 5 Tux 8 14 18 20 20 Tuy 6 10 13 15 16 Mux Muy Mux/px Muy/py D) Assuming the consumer has any amount of money (enough budget) how many of X and Y should the consumer buy, to maximize utility? E) What is the total utility of X and Y? F) Let now price of X is 4 birr per unit and price of Y is 2 birr per unit and budget of the consumer for consumption of X and Y is 20 birr. Given budget constraint how many of X and Y should the consumer buy to maximize utility? G) What are the total utility of X and Y
- Suppose that you have highly nonconvex preferences for ice cream andolives, like those given in the text, and that you face prices p1, p2 and havem dollars to spend. List the choices for the optimal consumption bundles.22. Peanut butter (PB) sells for 10 dollars per pound and Oysters (O) sell for 50 dollars perpound. Suppose Pat buys 5 pounds of peanut butter and one pound of oysters each month.With this consumption bundle, his MRSP B,O = 3. Which of the following is true (assumingPat’s preferences satisfy all the basic assumptions of consumer theory)?(a) Pat could increase his utility by buying more oysters and less peanut butter.(b) Pat could increase his utility by buying more peanut butter and less oysters.(c) Pat could increase his utility by buying more peanut butter and more oysters.(d) Pat could increase his utility by buying less peanut butter and less oysters.Ewa spends all her 600 PLN bonus on the purchase of sweets and cosmetics. Draw the Ewa's budget line, knowing that her favorite sweets cost PLN 10 per pack and the price of cosmetics is PLN 25. •How will Ewa's situation be affected by the PLN 50 bonus increase? •What will happen if the price of cosmetics increases to PLN 30? •How, from the point of view of initial situation, we will evaluate the following quantitative combinations: –30 packages of sweets and 15 cosmetics –60 packages of sweets and 24 cosmetics –20 packages of sweets and 10 cosmetics –10 packages of sweets and 15 cosmetics