Consider a utility function for apples and bananas. You are given the following three bundles: (12, 4), (4, 12), and (8, 8). Under the standard assumptions of the well-behaved preference relationship. you should strictly prefer (8, 8) to (12, 4) and (4, 12). Briefly explain why?
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Marginal Rate of Technical Substitution
MRTS reaches a manufacturer when a part of the product is lowered to sustain the manufacturing level when the other part is extended. It is the level of the quantity that is lowered when one extra volume is used, and the output is unchanged.
Preferences and Utility Analysis
Before understanding what is preference and utility analysis, it is very important to understand the terms preference and utility separately.
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Consider a utility function for apples and bananas. You are given the following three bundles: (12, 4), (4, 12), and (8, 8). Under the standard assumptions of the well-behaved preference relationship. you should strictly prefer (8, 8) to (12, 4) and (4, 12). Briefly explain why?
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- 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2 Utility representations Recall that for a finite outome set X, the rank-score function U# (x) = #({x' = X : x ≥ x'}) is a utility function representation for any preference relation. In this problem we'll consider the case of a countably infinite outcome set X = {x¹, x², x³, ...}. 1. Write down a preference relation over X for which the rank-score function is a utility representation. Write down another preference relation for which it is not a utility representation. 2. Consider the preference relation over X defined by x¹ ≥ x¹ iff i ≤ j. Write down a utility representation which assigns non-positive utility to every outcome. Write down another utility representation which assigns non-negative utility to every outcome.I am unsure the direction the utility functions would go in , with this specific scenario
- 1. Pindyck and Rubinfeld (2018) Chapter 4 Appendix, Exercise #5 Jae has the following utility function: U(X,Y)= 20X+ 80Y – X² – 2Y?, where X is consumption of CDs, with a price of $1, and Y is consumption of movie videos, with a rental price of $2. Jae plans to spend $41 on both forms of entertainment. Determine the number of CDs and video rentals that will maximize Jae's utility. а.4 Part Question on Caesar * * PART 1 * * Caesar has preferences that are described by the utility function u = 3x 1 + 5x 2. Caesar strictly prefers the bundle (x 1, x 2) = (0, 6.6) to the bundle A. (3, 3) B. (5, 3.6) C. (0, 8.4) D. (11, 1.8) E. (8, 3.60) * * PART 2 * * What is the functional form of Caesar’s preferences, or indifference curves? A. Linear (perfect substitutes) B. Leontief (perfect complements) C. Satiation D. Concave, but not strictly concave E. Cobb-Douglas * * PART 3 * * Caesar’s preferences are A. strictly convex. B. definitely not well-behaved. C. definitely well-behaved. D. strictly concave. E. neutral. * * PART 4 * * Caesar has been consuming the bundle (x 1, x 2) = (10, 2.4). At this point, what is the marginal rate of substitution? A. – 0.25 B. –0.6 C. – 1.67 D. – 3.0 E. – 5.0.Question 2 David spends his budget on chocolate and chip. His utility function is given by ?(?1,?2)= 2?1?2, where ?1 is the number of chocolates he consumers per week, and ?2 is the number of chips he buys per week. A chocolate costs 10 SEK, and a chip costs 20 SEK. David’s weekly budge for consuming on these two goods is 120 SEK. (1) What is David’s budge line? Draw the budget line on a graph with chocolate amounts on the horizontal axis and chip amounts on the vertical axis. Write explicitly at which points budget line crosses the axis. (2) What is David’s marginal utilities for the two goods, respectively? What is his marginal rate of substitution between the two goods? (3) What is David’s optimal choice? Calculate the numerical answer for the optimal bundle. Also draw an indifference curve for David on the same graph as question(1) and show the optimal bundle.
- Suppose you have $10, which you can wager in a game called "double or quits." In this game, you roll a fair die. If you roll a 4, 5, or 6, you win the game, getting back your $10 plus $10 more for a total of $20. If you roll a 1, 2, or 3, you lose the game and your $10. Your utility function is shown on the following graph Utility 10 20 Income According to this graph of your utility function, would you be considered risk-averse or a risk-taker? Why? Risk averse because of increasing marginal utility of income Risk taker because of increasing marginal utility of income Risk taker because of diminishing marginal utility of income O Risk averse because of diminishing marginal utility of income2. Consider a consumer whose preference relation over the consumption set X = R can be repre- sented by the utility function: u (11, 12, 13) = A (x1 – #1)° (x2 – #2)® (r3 – 3)" where A, a, B and y are all strictly positive. (a) Why can you assume A = 1 and a + 3 + y = 1 without loss of generality? Do so for the %3D rest of the question. (b) Solve the UMP and derive the consumer's Walrasian demand. (c) Find the indirect utility function, the minimum expenditure function, and the Hicksian demand function.2. Maria likes to have one cup of coffee (x) and two slices of bread (y) each morning. Which of the following utility functions represents Maria's preference for (x, y)? (a) U(x, y) = min(8x, 2y) (b) U(x, y) = min (4x, 2y) - RIGHT ANSWER (c) U(x, y) = min(x, 2y) (d) U(x, y) = min(x, 2y)
- Anton, Betsy and Catherine are three college friends who regularly go the movies. At the movies, they can purchase skittles (x) and junior mints (y). The table below display the total utility each of them get from bundles of these two snacks (x, y). Bundle A = (1,1) B = (1,2) C = (1,3) D = (1,4) E = (1,5) Anton's Anton's Utility MUY (2) (1) 10 14 16 17 17.5 Betsy's Utility (3) 10 10 9 8 7 Betsy's MU, (4) Catherine's Utility (5) 10 12 15 19 24 Catherine's MUY (6) a) Yesterday the three friends went to watch the Barbie movie and they purchased the same bundle, bundle B = (1,2), with 1 bag of skittles and 2 bags of junior mints. Can you say who of the three friends experienced the highest utility from consuming bundle B? Explain. b) As you may have noticed, all bundles in the table contain 1 bag of skittles while they differ in the number of bags of junior mints. Fill in columns (2), (4) and (6) in the table by computing the marginal utility each friend receives from choosing a bundle…A consumer with income I=120 facing prices pX = 4 and pY = 8 for two goods X and Y (for each good she prefers more to less) chooses optimally to consume 12 units of X. If the prices change and now pX = 6 and pY = 4, what is the possible range for her optimal X consumption? (like, x >/ 7 or 10 >/ x >/7…etc. Use indifference curve analysis on a graph to reason about the possible locations of the new optimal bundle.)QUESTION 8 If the ulitity function is: U=41x₁ + 11x2 and considering the following bundles: A=(73,52) B=(31,61) C=(9,59) D=(5,46) E=(81,45) How much utility does the consumer get from bundle C?