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- 5. Sheila and Bruce are taking a canoe trip. Sheila brought 10 boxes of peanuts (x) and 15 bags of chips (y). Sheila's utility function is U*(x,y) = lnvx*+ Invy°. Bruce also brought 20 boxes of peanuts and 5 bags of chips. Bruce's utility function is UB(x.y) = min[x', y'I. a) Illustrate the endowment point and draw a sample set of indifference curves through the endowment point. b) If Sheila and Bruce trade what will be the pattern of mutually beneficial trade? c) If the terms of trade are the number of bags of chips (y) per box of peanuts (x) then what is the largest value that these terms can be for a mutually beneficial trade in this economy? d) Find one mutually beneficial trade where the terms of trade are 1 bag of chips (y) per 2 boxes of peanuts (x). Suppose that Sheila and Bruce set up two competitive markets for peanuts and chips. Below you will show that if the price of peanuts (x) is $1 and the price of chips (y) is $2 then the markets for both peanuts and chips will clear.…4 Emily goes camping on the weekend and eats marshmallows (M) and crackers (C) there. She wants to match 1 marshmallow with 2 crackers, but does not eat in different proportion (i.e., perfect com- plement). The price of a marshmallow is 10 cents and the price of a cracker is 5 cents, and she spend up to $3 in total. a) Write down a utility function which represents Emily's preferences over marshmallows and crackers. b) How many marshmallows and crackers is she going to consume? (Hint: the first-order conditions will not help; draw the budget constraint and the indifference curves and look at the highest one that intersect the budget constraint). c) What is the exact value of Emily's indirect utility?Let's suppose that an individual prefers bundle of goods A over another bundle of goods B. Let's suppose that the individual prefers the bundle of goods C to the bundle of goods B. Then we can say the individual prefers C to A because more is better than less the individual prefers A to C because more is better than less two answers are correct no answer is correct O the individual prefers A to C; because of transitivity the individual prefers C to A because of transitivity
- Let the following table represents the total utility of a given consumer, in the cardinal utility approach. Q 1 2 3 4 5 6 7 TUX 8 14 18 20 20 18 16 TUY 6 10 13 15 16 16 14 MUX MUY MUX/PX MUY/PY Calculate the MUX and MUY and fill the table in the 4th and 5th rows. If the two products (X&Y) are free goods how many of X and Y should the consumer take to maximize utility? What is the maximum utility of X and Y if they are free? Let now price of X is 4 birr per unit and price of Y is 2 birr per unit. Calculate MUX/PX and MUY/PY and fill the 6th and 7th row. Assuming the consumer has any amount of money (enough budget) how many of X and Y should the consumer buy, to maximize utility? What is the total utility of X and Y? Let now price of X is 4 birr per unit and price of Y is 2 birr per unit and budget of the consumer for consumption of X and Y is 20 birr. Given budget constraint how many of X and Y should the consumer buy to maximize utility?4. Sheila and Bruce are going backpacking. Sheila and Bruce each have 24 power bars (x) and 24 ounces of water (y). Their preferences can be represented by: U*(x°,y°) = la xS + la y and U(x",y) = 3lm x# + la y" a) Find Sheila and Bruce's MRS at endowment. Illustrate in an Edgeworth box diagram, the endowment point and the indifference curves through that point. b) What is the pattern of trade associated with mutually beneficial trades? c) Find one mutually beneficial trade where the terms of trade are 2 ounces of water (y) per 1 power bar (x). Instead of trading directly, Sheila and Bruce trade in a market. Sheila and Bruce are price takers on both the power bar and water markets. Each can buy and sell goods at the same price. Let P, be the price of a power bar and P, be the price of an ounce of water. d) Are the prices Px = 4 and Py-1 General Equilibrium prices? Briefly explain. You do NOT need to find the GE prices to answer this question. Do use the MRS at %3D endowment. e) Write…he Calculus of Utility Maximization and Expenditure Minimization -End of Appendix Problem uppose that there are two goods, X and Y. The price of X is $2 per unit, and the price of Y is $1 per unit. There are two onsumers, A and B. The utility functions for the consumers are UA(X,Y)= X05.05 UB(X,Y)= X0.8y0.2 Consumer A has an income of $100, and Consumer B has an income of $300. Using Lagrangians, solve for the optimal bundles of goods X and Y for both consumers A and B. a. The optimal bundle for consumer A is X = 25 and Y* = 50 - b. The optimal bundle for consumer B is X = 120 and Y* = 60
- Suppose that you are thinking about joining COSTCO. You must pay a membership fee, but once you joined you can buy products at a lower price. Assume you would buy only one good, say, paper towels at COSTCO. After careful consideration you think that you are indifferent between joining and not joining COSTCO. Illustrate your dilemma with a graph that includes two budget lines (with or without COSTCO) and an indifference curve. Make sure that you labelled the axes and all the shapes in your graph.Joon has preferences over two goods only-beer and pizza, both of which he loves. His initial budget line goes through bundles A and B; he chooses A. When prices change such that he faces budget line through bundles B and D, Joon chooses B. Qpizza a f b B h g D I Qbeer We want to determine which bundles are better for Joon than bundle B and which bundles are worse. For each of the areas on the graph, labeled from (a) to (j) we can say, given the information provided, that1. A consumer has an income of $3024 to spend each day. The only two goods the consumer is interested in purchasing are goods A and B. The marginal-utility schedules for these two goods are shown in the table below. The price of B does not change and is $378. The marginal utility per dollar from B is also shown in the table. But the price of A varies as shown in the table. The marginal utility per dollar from A when the price of A is $1512 and $756 is shown in the following table. Good A Good B Quantity MU MU/$1512 MU/$756 MU MU/$378 1 24 2 15 3 12 4 8 5 6 6 4 48 32 24 16 8 4 ||||| ||||| |||
- 3. We 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 it intersected some indifference curve twice?)Matt has $14 to spend on fruit today at the grocery store. The only fruits he likes are apples and oranges. Both cost $2 per pound. Matt's preferences between these fruits are presented in the table below. How many apples and oranges will he buy if he were a utility maximizer? a b с Pounds of Apples 1 2 3 4 5 Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. d Pounds of Oranges 1 2 3 4 5 Apples = 1 pound, Oranges = 2 pounds Apples = 2 pound, Oranges = 5 pounds Apples = 1 pound, Oranges = 1 pound Marginal Utility from Apples Apples = 3 pounds, Oranges = 3 pounds. 200 300 380 440 480 Marginal Utility from Oranges 100 200 250 280 300GLASS-1: Short Individual Assessment 10 A B E D 1 2 4 cheeseburgers 1. Refer to the figure as you answer the following questions: Bundle C is preferred to Bundle A because Bundle C represents a more balanced Bundle. Do you agree or disagree with this statement and why? Calculate the MRSXY between points A and B, and between points C and D. Interpret your computed values. c. What assumption about preferences would allow you to say that Bundle E is preferred to Bundle B? Briefly explain. Bundle E has one less cheeseburger than Bundle D. What assumption(s) would still allow you to say that Bundle E is preferred to Bundle D? Briefly explain. а. b. d. Consider the utility function of individual A given by UA (X,Y) = Xº.5y0.5 in answering the items below: 2. Calculate the marginal utility for each good (MU,x & MUy) of individual A and the marginal rate of substitution (MRSxY). Interpret your computed values If Px = 0.5, Py = 1, and I = 10, solve for X*, Y*, and U* using the Lagrange a. b.…