Rue's utility function is U(z, y) min{z, 3y}. Jules' utility function is U(z,y) min{z, y). (a) Which of the bundles A (4, 0.5), B = (3, 2) and C (2, 4) does Rue prefer? Which of the bundles does Jules prefer? (b) For Rue, draw the indifference curve, denoted as I1, that contains the bundles that she likes exactly as well as bundle (4,2). On the same graph, draw the indifference curve I2 for Rue that passes through bundle (6,3) and draw the indifference curve I, for Rue that passes through bundle (8,3). Does her preference satisfy convexity?
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- 10. Consider the utility function U(x, y) = xy + x. Which of the following bundles is noton the same indifference curves as the others. Note: The first entry is the amount of x, thesecond is the amount of y.(a) (5,1)(b) (2,4)(c) (4,2)(d) (2.5,3)9 of 15 Laura has an income of 100 and she has to spend it to buy daisies (x₁) and daffodils (x2). Her preferences are represented by a Cobb Douglas utility function u(x1,x2)= x1x2. If daisies are twice as expensive as the daffodils, what would her optimal bundle be? O Buy only daffodils O Buy only daisies O Buy twice as many daffodils as daisies O Buy twice as many daisies as daffodils O Buy same amount of daisies and daffodils O No answer.Eren’s two main hobbies are taking vacations overseas (V) and eating expensivemeals (M). His utility function is given as: U(V,M) = V2MLast year, the average price of taking a vacation overseas was US$200 and the averageprice of an expensive meal is $50. However, due to supply problems in Onions, theaverage price of an expensive meal rose to $75. The average price of a vacation did notchange. His income, which is $1500, did not change. Suppose that the Department of Welfare wants to know how much should begiven to Eren to offset his change un utility due to the price increase of an expensivemeal. Calculate the compensative variation (CV).
- Eren’s two main hobbies are taking vacations overseas (V) and eating expensivemeals (M). His utility function is given as: U(V,M) = V2MLast year, the average price of taking a vacation overseas was US$200 and the averageprice of an expensive meal is $50. However, due to supply problems in Onions, theaverage price of an expensive meal rose to $75. The average price of a vacation did notchange. His income, which is $1500, did not change. Calculate for the equivalent variation (EV) for the price change.2. Eren's two main hobbies are taking vacations overseas (V) and eating expensive meals (M). His utility function is given as: U(V,M) = V²M Last year, the average price of taking a vacation overseas was US$200 and the average price of an expensive meal is $50. However, due to supply problems in Onions, the average price of an expensive meal rose to $75. The average price of a vacation did not change. His income, which is $1500, did not change. a. b. C. Calculate the change in consumer surplus from consuming the expensive meals considering the price change (Hint: you need to compare his optimal consumption bundle before and after the price change to get the change in CS). Suppose that the Department of Welfare wants to know how much should be given to Eren to offset his change un utility due to the price increase of an expensive meal. Calculate the compensative variation (CV). Calculate for the equivalent variation (EV) for the price change.ASAP 1. Consider a consumer with utility u(x1,x2) = .5lnx1 + .5lnx2 (b) Now, consider an equivalent representation of the above utility functionx51 x52 Does this utility function have the "increasing difference property"? Howabout the "strict increasing difference" property?
- Eren’s two main hobbies are taking vacations overseas (V) and eating expensivemeals (M). His utility function is given as: U(V,M) = V2MLast year, the average price of taking a vacation overseas was US$200 and the averageprice of an expensive meal is $50. However, due to supply problems in Onions, theaverage price of an expensive meal rose to $75. The average price of a vacation did notchange. His income, which is $1500, did not change. Calculate the change in consumer surplus from consuming the expensivemeals considering the price change (Hint: you need to compare his optimalconsumption bundle before and after the price change to get the change in CS).Lorelai's choice behavior can be represented by the utility function u(x1, x₂) = 0.9ln(x₁) + 0.1x2. The prices of both x₁ and x₂ are $10 and she has an income of $80. 1. What preference does this utility function represent? (Hint: the utility function is not linear, but at least linear in good x₂.) 2. Drawinwg indifference curves: you can copy down the graph on your paper using econgraphs. Set the preferences and parameters accordingly as given in the question. Click on "snap to optimal bundle" to see the optimal choice. Click on "show indifference curve map." Draw the lowest four indifference curves as you see from the graph. 3. Find the marginal utility of x₁ and x₂. What is the maximum number of x₁ so that MUX₁ is bigger than or equal to MUX₂ 4. Given her income of $80, how many units of x₁ can she buy? Would she buy any positive number of x₂ in light of the answer from Q5.3? Find the optimal bundle. 5. Suppose instead her income is $100. Would she buy any positive number of x2?…4. Minnie enjoys dessert by eating chocolate cake (C) and apple pie (P) according to the utility function U = Min [C, P]. In any given week, Minnie %3D spends £20 to purchase these two products. Assume that Minnie is a utility maximiser and has to pay 50p for a unit of apple pie and £2 for a unit of chocolate cake. (i) Consider the bundle C = 20 and P = 5. Is this the utility maximizing choice subject to Minnie's budget?. %3! (ii) Suppose that Minnie chooses the exact bundle that maximizes her utility. How would the utility maximizing choice of C be affected if price of P went up? (iii) Explain under which conditions the tangency condition does not work. Given that the tangency condition does not work, discuss how we can find out the optimal consumption bundle for a consumer.
- 2. Suppose John's utility function is UX,Y) = 4/XY , where X is consumption of beer and Y is consumption of pizza. For this utility function, ( Calculus Kahuna say: MUx = 2\Y/X and MUy = 2\X/Y ) a) Find three different bundles: (X,Y) = (2, 4½), (2, 3), (4, 24) and find the utility they provide John. Plot the three bundles and connect them with an indifference curve. J-L. IIII -+-+- - -4-L 7-T-T-r הרד - דר -LJ-J-L- 1-L -LJ-J-I ---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)Consider the following utility functions: (1) u(x₁, x₂) = x₁ + 2x2. (2) u(x1, 1₂) = 2125 12.75 (3) u(x₁,1₂)=-1²-1₂. (4) u(x1, 1₂) min{x1, 2x2). For utility functions (1) to (3), give the equations of the indifference curves correspond- ing to utility level k, where 22 is expressed as a function of 2₁ and k. For utility functions (1) to (4), draw two indifference curves for each function. That is, draw four graphs (one for each utility function) and two indifference curves on each graph.