Question 1. The utility functions of each consumer are given by: UA(X,Y)= X¹/2*y1/2 UB(X,Y)=X+Y Suppose there are two consumers, A and B. The initial endowments are:
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- 1. Is it impossible for two indifference curves to intersect one another? why? 2. What does it mean that preferences are complete? Now would the real-life implica- tions of this assumption look like?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.…Suppose Ann likes both pancakes (P) and waffles (W) and is always willing to substitute two pancakes for one waffle. Write the equation for Ann's utility function. a. b. Given her preferences, what is Ann's marginal utility of an additional pancake? What is Ann's marginal utility of an additional waffle? с. With pancakes on the horizontal axis and waffles on the vertical axis, graph Ann's indifference curves for U=4 and U=8. d. What is Ann's marginal rate of substitution?
- 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.We claimed in the text that if preferences were monotonic, then a diagonal line through the origin would intersect each indifference curve exactlyonce. Can you prove this rigorously? (Hint: what would happen if itintersected some indifference curve twice?)Michael derives utility from only two goods, hamburger (Qh) and fanta (Qf). The marginal utility that Michael receives from cake (MUh) and donuts (MUH) are given as follows: MUh = Qd MUf = Qh Michael has an income of R500 and the price of hamburger (Ph) and fanta (Pf) are both R100. What is Michael's budget constraint? (1) Select one: a. 500 = 100Qh + 100Qf b. 500 = 100PH+ 100PF c. 500 = (Ph)(Qf) d. 500 = (QhXQf).
- 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* = 60Explain how consumer equilibrium is reached using marginal utility analysis.uestion1:Donna and Jim are two consumers purchasing strawberries and chocolates. Jim’s utility function is U (x, y) = xy and Donna’s utility function is U (x, y) = x2y where x denotes strawberries and y denoteschocolates. Jim’s marginal utility functions are MUX=y and MUy=x while Donna’s are MUX=2xy and MUy=x2. Jim’s income is $100, and Donna’s income is $150. What is the optimal bundle for Donna if the price of strawberries is $2 and the price of chocolate is $4? What is the optimal bundle for Jim, and for Donna, when the price of strawberries rises to $3?Question2:Consider a one-period eco
- Donna and Jim are two consumers purchasing strawberries and chocolate. Jim’s utility function is ?(?,?) = ?? and Donna’s utility function is ?(?,?) = ?2? where x is strawberries and y is chocolate. Jim’s marginal utility functions are MUx=y and MUy=x while Donna’s are MUx=2xy and MUy=x2. Jim’s income is $100, andDonna’s income is $150. What is the optimal bundle for Donna if the price of strawberries is $2 and the price of chocolate is $4?What is cardinal utility theory?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 = 2Y/X and MUy = 2\X/Y ) a) Suppose Y=3. Calculate John's utility for X=4,9,16, and 25. For a given level of Y, does good X display diminishing marginal utility?