(b) Examine the validity of the following statements, giving reasons: (i) If a person consumes two commodities both of which are undesirable, the indifference map will look exactly the same as when both the commodities are desirable. (ii) If the utility function for two commodities is of a Cobb-Douglas form, then the Engel curve is a straight line passing through the origin. 2/5 (iii) The production function, y = x +xx+/7, exhibits decreasing returns to scale.
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- 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.An individual's utility is given by: U (q1, q2) = a(q1)+ b(q2), where a and b are constants. When prices are P1= 4 and P2=1, the individual can only maximize utility by purchasing all good #2. When the prices are P1=3 and P2=1, the individual can only maximize utility by consuming all good #1. Which of the following statements below must be true? A. Goods #1 and #2 are complements B. a < b C. 3 < a/b <4 D. The indifference curves exhibit diminishing MRSAnother instance when people are likely not to spend a dime (or a minute) on an item is when they have a dislike for mixing the item with other items available. In this case, we say the consumer has ‘non-convex preferences’ and indifference curves are bowed out from the origin. In plain language, the consumer has a preference for binging. We often feel this way towards our favorite social media app. Consider a kid who has four hours a day to spend on social media. They enjoy spending time on Snapchat (x) or spending time on Twitter (y). a) Write the kid’s time constraint and illustrate it in a graph where you measure time spent on Snapchat along the horizontal axis and time spent on Twitter along the vertical axis. This kid’s utility from time spent on Snapchat and time spent on Twitter is U(x,y) = 4x2+ y2. b) In your graph, draw a couple of the kid’s indifference curves. Notice how the kid’s |MRSY,X| increases along each curve as he spends more time on Snapchat and less time on…
- Tony is throwing a party at his Fraternity and is trying to choose what booze to buy. A bottle of vodka has three times the alcohol as a six-pack of beer. Assume that Tony only cares about the total amount of alcohol in his basket. (use vodka on the X-axis and beer measured in six-pack on the Y-axis) a) Devise a utility function to represent these preferences. b) Suppose a bottle of vodka costs $40, a six-pack of beer costs $10, and the budget is $200. Write the budget constraint. c) Solve Tony’s utility maximization problem and find the optimal combination. d) Suppose that a bottle of vodka cost has increased to $50. What will be his new optimal combination.Suppose that U(f,c) = f + 8c^(1/2)is a utility function that describes Amelia’s preferences over two goods: fish(f)and custard (c). For the following, think of fish as the good graphed on the horizontal axis.a. Derive an expression for her marginal utility (Uf)from a small increase in f holding c fixed. Also find themarginal utility for custard (Uc).b. What is Amelia’s marginal rate of substitution (MRS)? Give a brief (2 sentences maximum) intuitivedescription of what MRS represents. If Amelia has 4 units of custard, holding her utility constant, howmany units of custard would she be willing to give up in order to get one more unit of fish?c. Graph Amelia’s indifference curve for a utility level of 40. Be sure to specify at least 3 bundles of goodson the indifference curve.d. Does the fact that Amelia’s indifference curve intersects with the custard axis violate any of the 5properties of indifference curves? Briefly support your answer.e. Give another utility function that represents…While visiting family in Mexico, your professor has a budget of $ 255 ($ = pesos) that he spends on tacos and tequila. The price of tacos is $ 6 and a shot of tequila is priced at $ 16. During his visit the price of tacos changes to $ 5. Assume your professor has a Cobb-Douglas utility function with (tacos) parameter a = ( 27 / 100). How many shots of tequila does your professor purchase ? (Assume both goods are commodities.) (Answer is : 11.63)
- 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).Smith and Jones are stranded on a desert island. Each has in her possession some slices of ham (H) and cheese (C). Smith prefers to consume ham and cheese in the fixed proportion of 2 slices of cheese to each slice of ham. Her utility function is given by Us = min(10H, 5C). Jones, on the other hand, regards ham and cheese as substitutes – she is always willing to trade 3 slices of ham for 4 slices of cheese, and her utility function is given by UJ = 4H + 3C. Total endowments are 100 slices of ham and 200 slices of cheese. a. Draw the Edgeworth Box diagram for all possible exchanges in this situation. What is the contract curve for this exchange economy? b. Suppose Smith’s initial endowment is 40 slices of ham and 80 slices of cheese (Jones has the remaining ham and cheese as her initial endowment). What mutually beneficial trades are possible in this economy and what utility levels will Smith and Jones enjoy from such trades? c. Now imagine a new endowment in which Smith has 60 slices…Consider an individual with preferences represented by the following utility function: U (x1, 12) = x{x; The individual faces prices: P1 = 0.5; p2 = 1 And has income: M = 250 If the price of good one increases to p1 =1 For this change in price, mark all of the following answers that are correct. (EV = equivalent variation; CV = compensating variation) O In absolute value, EV is greater than Cv O In absolute values, change in Consumer surplus is smaller than CV. O In absolute value, CV is greater than EV In absolute values, change in Consumer Surplus is smaller than EV. There is not enough information to determine an answer.
- Consider the following utility function: U = 100x°.50,0.50 A consumer faces prices of P, = $2 and P, =$1 Assuming that graphically good X is on the horizontal axis and good Y is on the vertical axis, suppose the consumer chooses to consume 6 units of good X and 11 units of good Y. Then the marginal rate of substitution is equal to: MRS = (Enter your response rounded to two decimal places. Do not forget to include the negative sign.) Use absolute values. 15 stv МacВook Air 80 DI esc F1 F2 F3 F4 F5 F6 F7 F8 @ %23 2$ & 1 2 4 6 7 8 Q W T Y tab A S F H J K aps lock C V M control option command B H1.2 Ann and Bob each own 10 bottles of beer and, altogether, they own 20 bags of peanuts. There are no other people and no other goods in the economy, and no production of either good is possible. Using a to denote bottles of beer and y to denote bags of peanuts, Ann's and Bob's preferences are described by the following utility functions: UA (XA, YA) = TAYA and UB (XB, YB) = 2xB+ YB. In each of the following cases, determine the market equilibrium price ratio and allocation and depict the equilibrium in an Edgeworth box diagram. (a) Bob owns 20 bags of peanuts and Ann owns no peanuts. (b) Bob owns 15 bags of peanuts and Ann owns 5 bags. (c) Ann owns 20 bags of peanuts and Bob owns no peanuts.Consider the following utility function: U= 4X + Y. A consumer faces prices of P, = $2 and P, =1. Assuming that graphically good X is on the horizontal axis and good Y is on the vertical axis, suppose the consumer chooses to consume 10 units of good X and 19 units of good Y. Then the marginal rate of substitution (MRS) is equal to: MRS = (Enter your response rounded to two decimal places. Do not forget to include the negative sign.) étv Help Me Solve This eText P MacBook Air 80 DII esc F2 F3 F6 F8 F1 F4 F5 F7 @ 23 2$ & 1 2 4 6 7 8. Q W E R T Y U tab A S G caps lock C V shift fn control option command ーの エ B レ