Using a choice diagram (like the one from Perloff used in the slides and copied below for your convenience) explain why EV=CV for quasilinear preferences,
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- Problem 1 Last week, neither Alistair nor Bodana purchased blueberries (x). Both consumers had $30 to spend on blueberries and/or raspberries (y), the price of the two fruits was $3 per pack and both consumers bought raspberries only. Alistair's utility for blueberries and raspberries is UA(x,y) = x+2y. Bodana's utility for blueberries and raspberries is UB(x,y) = x +12ln(y). a) In two separate graphs, illustrate Alistair's and Bodana's optimal choices. Your graphs must illustrate the consumers' budget constraints and their indifference curves at the optimal bundle. b) At their optimal bundle, what is Alistair's marginal rate of substitution of raspberries for blueberries (- MUx/MUy)? At their optimal bundle, what is Bodana's marginal rate of substitution? This week, blueberries cost $3 per pack just like last week, however raspberries now cost $4 per pack. c) How many packs of blueberries and raspberries will Alistair buy this week? Clearly justify your answer. d) Using the…Huang is determining how much Coke and Pepsi he will buy. Use the information in italics to answer the bolded question below. • Huang's preferences for Coke (C) and Pepsi (P) are represented by the following utility function: U = 2C + 3P • Huang has $12 to spend on soft drinks. • The price of Coke (P) is $0.50/can. • The price of Pepsi (Pp) is $1.00/can. Which of the following statements referring to Huang's preferences is incorrect. O Huang does NOT experience diminishing MRS. If Huang gives up two cans of Pepsi, he needs to purchase 3 cans of Coke to remain equally satisfied. Pepsi and Coke are perfect substitutes for Huang O None of the above statements are incorrect.Reese thinks peanut butter and chocolate are great when separate, but when they combine they are even more epic. In other words, Reese likes to eat either peanut butter or chocolate, but when he eats them together, he gets additional satisfaction from the combination. His preference over peanut butter (x) and chocolate (y) is represented by the utility function: u(x, y) = xy + x + y Which of the following is NOT true about Reese’s preference? (a) The MRS decreases when x increases.(b) The preferences are homothetic.(c) The marginal utility of y is higher when x = 10 than when x = 5.(d) For any a > 0, Reese prefers the bundle (x =a/2 , y = a/2 ) over either the bundle (x = a, y = 0) or (x = 0, y = a).
- 4. Two individuals, Amir and Budi, consume two goods, clothes (X) and shoes (Y). The utility functions for the two individuals are given as: Utility function of Amir, UA = 15X0.25Y0.75Utility function of Budi, UB = 25X0.5Y0.5 The current price for clothes (Px) is Rp 100,000 and the current price for shoes (PY) is Rp 150,000 a. Determine marginal rate of substitution (MRSXY)between clothes (X) and shoes (Y) for Amir and Budi! Please explain. b. Amir is currently consuming 5 units of clothes (X) and 10 units of shoes (Y), whereas Budi is consuming 12 units of clothes (X) and 8 units of shoes (Y). At this current consumption, have Amir and Budi reached the efficient allocation of clothes and shoes? If they have, explain why. If they have not, calculate the optimal allocation and explain. c. Considering the relative price between of clothes and shoes, at the current consumption, have Amir and Budi reached exchange equilibrium? Please explain d. Use the Edgeworth Box to illustrate the…Illustrate with Example: According to law of diminishing marginal utility, as you consume more and more units of a commodity, total utility would go on increasing, but at a diminishing rate.With the aid of a diagram, describe a corner solution and explain the axioms of consumer choice.
- Fang likes playing badminton with her friends. Her utility function for playing badminton every week is given by U(t) = 11t – 2t2, where t is measured in hours. They play on a badminton court, which they can rent per hour. Suppose the current price to play on the badminton court is £2.50 per hour. How many hours should Fang play if she wishes to maximise her utility? Explain what we mean by the principle of diminishing marginal utility. Does the principle apply in Fang’s case? Explain why. In a diagram with income in pound sterling on the horizontal axis and quantity on the vertical axis, show the relationship between Fang’s budget and the number of hours that would maximise her consumer surplus.Please refer to the following information to answer the question (in bold) below: You enjoy consuming apples (A) and oranges (O). Suppose that your utility function over both goods is given by . Your marginal utility function for apples is Your marginal utility function for oranges is O You utility increases due to the price change U (A, 0) = AO³ You utility decreases due to the price change MUA = 0³ . Currently, the price of apples is $10/peck, the price of oranges is $5/pound, and your income is $160. Assume that apples are your horizontal axis good and oranges are your vertical axis good. Let's say the price of oranges rises to $10/pound of oranges. Comparing the utility you receive from your old consumer equilibrium bundle to your new consumer equilibrium bundle, how does the increase in the price of oranges impact your level of satisfaction as a consumer? MUO = 340² ЗАО2 You utility is unaffected by the price change You utility could either rise or fall due to the price change
