0.3 0.7 Zach's preferences are representable by the utility function u = 91³927, where 9₁ and 92 denote his consumption of goods 1 and 2. (Answers to each of these questio decimal places.) Still assuming endowments of e₁ = 5 and e₂ = 9 and market prices p₁ = 20 and p₂ = 30, what is the maximised value of Zach's utility? O Au = 6.74 ○ Bu = 5.39
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- Rafe is optimally choosing to consume 6 apples and 3 bananas. The prices of apples and bananas are p. = 7 and pb - 7. Which of the following utility functions over quantities of apples (a) and bananas (b) could represent Rafe's preferences? = u(a, b)-a4/5 61/5 Ou(a, b) = a¹/5 64/5 Ou(a, b)-a2/3 b1/3 Ou(a, b)-a¹/3 2/3Suppose that Omar's marginal utility for cups of coffee is constant at 5.5 utils per cup no matter how many cups he drinks. In contrast, his marginal utility per doughnut is 10 for the first doughnut he eats, 9 for the second, 8 for the third, and so on (that is, declining by 1 util per additional doughnut) In addition, suppose that coffee costs $1 per cup, doughnuts cost $1 each, and Omar has a budget that he can spend only on doughnuts, coffee, or both. How big would that budget have to be before he will spend a dollar buying a first cup of coffee? Instructions: Enter your answer as a whole numberSuppose that Omar’s marginal utility for cups of coffee is constant at 5.5 utils per cup no matter how many cups he drinks. On the other hand, his marginal utility per doughnut is 11 for the first doughnut he eats, 10 for the second he eats, 9 for the third he eats, and so on (that is, declining by 1 util per additional doughnut). In addition, suppose that coffee costs $1 per cup, doughnuts cost $1 each, and Omar has a budget that he can spend only on doughnuts, coffee, or both. How big would that budget have to be before he would spend a dollar buying a first cup of coffee?
- A consumer can consume two goods, A and B, and has the utility function U-15A1/281/2, The consumer's budget is $900, the price of good A is $15 per unit and the price of good B is $45 per unit. (Assume A is the horizontal axis good and B is the vertical axis good. Both goods are infinitely divisible, but round numerical answers to 2 decimal places as necessary) What is the consumer's marginal rate of substitution? What is the consumer's marginal rate of transformation? What is the formula for the consumer's budget constraint? What is the consumer's utility-maximizing bundle given the utility function and budget constraint? A B HAnswer the following questions using the following information. Columns 1 and 2 in the table below show the marginal utility that Cody gets by purchasing products A and B. Column 3 shows the marginal utility Cody gets from saving Assume that the price of A is $13 the price of B is $10, and Cody has an income of $129. a) Find the following series of MU/$ for each column. Note: Keep as much precision as possible during your calculations. Your final answer should be accurate to at least two decimal places Column 1 Column 2 Column 3 Units of A MU MU/S Units of B MU MU/$ Number of $ saved MU MU/S 68 6.8 1 80 6.15 1. 13 0. 2 71 5.46 2 63 6.3 2 10 0. 3 66 5.08 3 56 5.6 3 7 4 61 4.69 4. 46 46 0. 54 4.15 40 4 45 3.46 31 3.1 6. 1 39 3 22 2.2 0. 29 2.23 8 17 1.7 8 b) What quantities of A and B will Cody purchase in maximizing his utility? Quantity of A: 0 Quantity of B: 0 c) How many dollars will Cody save? Dollars Saved = $0 SAVE AND CLOSEAssume that the prices of good X, Y and Z are as follows R5,R1 and R4 respectively, and the Judith has an income of R37 to spend. HOW much of each good will judith consume in order to maximise her utility? What will be her total utility and marginal utility of the last rand spent on each good? Show all the calculations
- 11) Stanley consumes only white and red wines and his utility function can be describedby U(R,W) = R0.40∙W0.60, where R is the number of bottles of red wine and W is the4number of bottles of white wine that he consumes per month. Suppose that his income is$500 and the price of a bottle of red wine $20 and the price of a bottle of white wine is$15. In this case, Stanley will purchase _____ bottles of red wine and _____ bottles ofwhite wine per month. Next, suppose that the price of red wine goes up to $35 per bottle.In this case, Stanley would consume ______ quantity of bottles of white wine comparedto the original situation.A) 10; 20; smallerB) 20; 10; smallerC) 10; 20; the sameD) 20; 10; the sameE) None of the above.Suppose that Omar's marginal utility for each additional cup of coffee is 1.5 utils per cup no matter how many cups he drinks. On the other hand, his marginal utility per doughnut is 11 for the first doughnut he eats, 10 for the second he eats, 9 for the third he eats, and so on (that is, declining by 1 util per additional doughnut). In addition, suppose that coffee costs $1 per cup, doughnuts cost $1 each, and Omar has a budget that he can spend only on doughnuts, coffee, or both. What is the minimum value of Omar's budget if he purchases one cup of coffee? Instructions: Enter your answer as a whole number.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
- 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.Alex's utility is U (xA, YA) = min {TA, YA}, where zA, and y, are his consumptions of %3D goods a and y respectively. Becky's utility function is U (zB, YB ) = TBYB where ap and yp are her consumptions of goods a and y. Alex's initial endowment is 20 units of x and 12 units of y. Becky's initial endowment is 12 units of x and 20 units of y. At the Walrasian equilibrium, a) Both of them consume 16 units of good y each. b) Alex consumes 8 units of good y and Becky consumes 16 units of y. c) Both of them consumes 12 units of good x each. d) Alex consumes 12 units of good x and Becky consumes 20 units of x. e) None of the above2. Jie has the utility function U, (a, b) = 2a + b and Daokui has the utility function U,(a, b) = v2ab, where a is the number of apples consumed and b is the number of bananas consumed. There are 10 units of apple and 10 units of banana in total. We draw an Edgeworth box with apple on the horizontal axis and banana on the vertical 4 axis and we measure Jie's consumptions from the lower left corner of the box. We assume that both apple and banana are infinitely divisible. Please answer the following questions. (a) Write down all pareto optimal allocations (you do not need to explain why). (b) If social welfare function is W min{U,(a, b), U(a, b)}, derive the social optimal allocation. Is this allocation pareto optimal? Suppose the endowment of Jie is 7 units of apple and 0 units of banana, and the endowment of Daokui is 3 units of apple and 10 units of banana. Please answer the following questions. (c) Assume that the price of apple is p, and the uniform price of banana is 1. Derive the…