Fiona requires a minimum level of consumption, a threshold, to derive additional utility: U(X, Z) is 0 if X + Z < = 5 and is X + Z otherwise. Draw Fiona's indifference curves. Which of our preference assumptions does this example violate?
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- Lionel eats ham (x) and cheese (y). The utility function U(x,y)=0.25x + 2y^0.5 represents his preferences.a) What is Lionel’s MRS? Holding y constant, how does his MRS change as ham (x) is increased?b) What does your answer in (a) imply about his indifference curves as you hold y constant and increase x? In (c) and (d) you are asked about the Marshallian and Hicksian Demands for cheese (y). Do NOT calculate the demand functions to answer these questions. Use your answers to (a) and (b) to explain your answer. c) Holding prices constant, what is the effect of an increase in income on his Marshallian demand for cheese (y)? Briefly explain your answer.d) Holding prices constant, what is the effect of an increase in utility on his Hicksian demand for cheese (y)? Briefly explain your answer.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.)Abby likes tangerines and oranges. For every 4 tangerines, Abby is equally happy to consume 2 oranges instead. Let x be the number of tangerines, and y be the number of oranges. (a) Graph Abby's indifference curves. Make sure to mark the direction of the preferred bundles. (b) Write down an utility function that represents Abby's preferences. (c) Write down another utility function different from your previous answer but also represents Abby's preferences. (d) Does v(x, y) = x + y represent Abby's preferences? (e) What is Abby's marginal rate of substitution? (f) Suppose that px = 1, py = 1, and Abby has Y = 20. Compute Abby's optimal consumption bundle.
- Amrita, a utility maximizing consumer, consumes only two normal goods, Breakfast Cereal and Bread Loaf. She is currently consuming 12 packets of Cereal and 16 bread loafs a week. If the price of Cereal increases (and everything else stays the same) we would expect Amrita to consume fewer bread loafs per week. Do you agree? Why/Why not?Suppose Al is currently consuming five movies and two concerts per month. If his utility function is given by U = 15MC, where Mrepresents the number of movies seen and C represents the number of concerts attended, Al's total utility is equal to: 75 15 150 10 30We claimed in the text that if preferences were monotonic, then a diag-onal line through the origin would intersect each indifference curve exactly once. Can you prove this rigorously? (Hint: what would happen if itintersected some indifference curve twice?)
- Donald likes fishing (X1) and hanging out in his hammock (X2). His utility function for these two activities is u(x1, x2) = 3X12X24. (A) Calculate MU1, the marginal utility of fishing. (B) Calculate MU2, the marginal utility of hanging out in his hammock. (C) Calculate MRS, the rate at which he is willing to substitute hanging out in his hammock for fishing. (D)Last week, Donald fished 2 hours a day, and hung out in his hammock 4 hours a day. Using your formula for MRS from (c) find his MRS last week. (E) This week, Donald is fishing eight hours a day, and hanging out in his ham mock two hours a day. Calculate his MRS this week. Has his MRS increased or decreased? Explain why? (F) Is Donald happier or sadder this week compared to last week? Explain.1. For each of the following scaling functions for a von Neumann-Morgenstern utility func- tion, determine the Marginal Rate of Substitution between X1 and X2 and the equation for an indifference curve through the consumption bundle (100,100) (solve for X2 on the left hand side of the equation). State 1 is the bad outcome that occurs with probability 0.2 and State 2 the good outcome that occurs with probability 0.8. Graph these indif- ference curves and comment on what you see. Is a consumer with these preferences risk averse, risk neutral, or risk loving? (a) V(X) = InX (b) V(X)= VX (c) V(X)= X (d) V(X)= X²True or false Law of diminishing margnal utility law states that utility derived from each successive consumption will keep falling.
- If Utility=.5lnX+3Z+10+4VW then Marginal utility from X is...... and the Mu of Z is...... Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a b с 10; 3 3,4 5/X; 3 d 2/VW; 3Mylie’s total utility from singing the same song over and over is 50 utils after one repetition, 90 utils after two repetitions, 70 utils after three repetitions, 20 utils after four repetitions, −50 utils after five repetitions, and −200 utils after six repetitions. Write down her marginal utility for each repetition. Once Mylie’s total utility begins to decrease, does each additional singing of the song hurt more than the previous one or less than the previous one?