Set X2 as the numeraire, i.e., assume p₁ = p and p2 = 1. Write each consumer's budget line equation given the equilibrium price ratio. (h) Find the equilibrium allocation, ((x, x½), (x{, x²)).
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- QUESTION 4 Linguini and Colette consume only éclair (x,) and profiterole (x2). Linguini has utility function UA = x4x4 and Colette has utility function UB = 2xfx. Linguini is endowed with 10 éclair (x,) and 3 profiterole (x), while Colette is endowed with 20 éclair (x,) and 9 profiterole (x2). (a) Draw an Edgeworth box with x, on the horizontal axis and x, on the vertical axis. Position Linguini on the bottom left corner and Colette on the top right comer. Indicate the total number of units of x, and x2. Label the endowment allocation. (b) Derive the equation of the contract curve, ie., find x(x). In your graph in (a), draw the contract curve.Assume, as in Exercise 22.1, that a consumer has utility function F or fruit and chocolate. Determine the consumer's demand functions q1(P1, P2, M) and q2(P1, P2, M). Determine also It* in terms of P1, P2 and M. Find the indirect utility function and show that It* = 8Vj8M. Suppose, as before, that fruit costs $1 per unit and chocolate $2 per unit. If the income is raised from $36 to $36.5, determine the precise value of the resulting change in the indirect utility function. Show that this is approximately equal to (O.5)λ*, where λ* is evaluated at P1 = 1,P2 = 2 and M = 36. Exercise 22.1 A consumer purchases quantities of two commodities, fruit and chocolate, each month. The consumer's utility function is For a bundle (X1, X2) of X1 units of fruit and X2 units of chocolate. The consumer has a total of $49 to spend on fruit and chocolate each month. Fruit cost $1 per unit and chocolate costs $2 per unit. How many units of each should the consumer buy…Farah has $100 to spend each month on bread and chicken. Suppose the price of bread is $4 a loaf and the price of chicken is $5 per pound. Draw her budget constraint and label it BC0. Put bread on the horizontal axis and chicken on the vertical axis. Be sure to identify the intercept values. Suppose Farah is a utility maximizer and she consumes 10 loaves of bread and 12 pounds of chicken. On the same graph you drew in part (a), draw an indifference curve to identify her optimal bundle. Label this bundle "E." Is her budget exhausted? Verify your answer. Now suppose Farah's income falls so that she can now devote only $80 to the two goods. Prices however remain unchanged. In the same diagram, graph her new budget constraint and label it BC1. Be sure to identify any new intercept values. Following the change in income, can Farah consume the same bundle "E"? Explain your answer. What must happen to her total utility following the decrease in her income?
- 10.6 For every two boxes of strawberries that she consumes, Millicent insists on having one pitcher of cream. She does not, however, insist on consuming the same amount every week. Her utility function is U = min{$₁,2c₁}min{$2,2c2} where s₁ and s2 are the number of boxes of strawberries she consumes this week and next week and c₁ and c₂ are the number of pitchers of cream she consumes this week and next. Strawberries cost $2 a box and cream costs $1 a pitcher. She has a present value of $100 to spend on these goods in the next two weeks. The weekly interest rate is 1%. How many boxes of strawberries will she consume this week? (a) 10 (b) 20 (c) 22 (d) 14.1 (e) 6.06Now suppose that Jason's utility is entirely based on number of hours of skiing (X) and skating (Y). 3 hours of skating gives him the same utility as 8 hours of skiing. 11. Use max {ax; bY} function to describe his preferences. 12. Solve for his equilibrium consumption bundle in the general form. (Hint: you have to look at 3 different cases) 13. Suppose that 1 hour of skating costs him 20 and 1 hour of skiing costs him $10. Suppose that he has $800 to spend. What will he end up choosing in this case? How much utility (U*) will Jason get from this activity? Show your answer mathematically and sketch a graph to illustrate your answer. r 5Krissy spends all her income on holiday lights (L) and fishing bait (B). Lights are priced at $2, while a pack of bait costs $1. Assume that Krissy has $30 to spend and her utility function can be represented as: U(L,B) = L²B² with: MU=2LB² and MU=2L²B (Assume B is on the y-axis when graphing). How much utility does Krissy obtain from the optimal bundle? Note: enter number(s) only and convert any fraction to a decimal.
- Justin Barlow, a careful maximizer of utility, consumes only two goods, Krispy Kreme Doughnuts and coffee. He has just achieved the utility-maximizing solution in his consumption of the two goods when the price of Krispy Kreme Doughnuts falls by 50%. As he adjusts to this event, he will most likely * consume more of both Krispy Kreme Doughnuts and coffee consume less of both Krispy Kreme Doughnuts and coffee consume more Krispy Kreme Doughnuts and less coffee consume less Krispy Kreme Doughnuts and more coffee O consume the same amount of Krispy Kreme and coffee2. 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.Milo spends £27 on stamps (S) and maple candy (C). His preferences for these goods are given by the following utility function: U(S, C) = min (S, 3C). Suppose that price per unit of S is £1.1 and the price per unit of C is £2.1. a) Write down Milo's budget equation and draw the corresponding budget line. Clearly label the axes and calculate the coordinates of the points of intersection of the budget line with each axis. In your graph, indicate the consumption bundle of 12 stamps and 6 maple candies. Can Milo afford this bundle? Explain. b) Find Milo's optimal consumption bundle, both algebraically and graphically. Explain your reasoning. c) If the price of a stamp increases to £1.4, how should Milo's income change for him to be as well off as before this change in prices? d) Discuss the implications of the price change from c) on Milo's optimal choice. In your discussion, include the analysis of the substitution and income effects as well as Milo's demand for stamps and/or maple candy.
- Tina consumes only two goods , x and y, and her utility function is u(x1,x2) = x12+x22. (1) Find the demand function that solves first order conditions with budget constraint. (2) Please show that Tina's utility function is not convex. (3) Find the utility at the corner (spending all money on either x1 or x2) and compare the utility with the solution of (1).QUESTION 4 Linguini and Colette consume only éclair (x,) and profiterole (x,). Linguini has utility function UA = xfxf and Colette has utility function U® = 2xf x%. Linguini is endowed with 10 éclair (r,) and 3 profiterole (x,), while Colette is endowed with 20 éclair (x,) and 9 profiterole (x,). (a) Draw an Edgeworth boz with x, on the horizontal azis and x2 on the vertical azis. Position Linguini on the bottom left corner and Colette on the top right corner. Indicate the total number of units of x, and x2. Label the endowment allocation. (b) Derive the equation of the contract eurve, ie., find x (xt). In your graph in (a), draw the contract curve. Suppose the price of éclair (x,) is $1 and the price of profiterole (x,) is $2. (c) Find each consumer's utilitymaximising basket. (d) How much of each good does each consumer want buy or sell? Are the markets in equilibrium at the given prices? (e) Verify that Walras' law holds at these prices. Now we will solve for the competitive…Enrique is a movie buff. He likes to watch on demand movies from his cable company, which cost $5 each, and so likes to go to the local movie house, which charges $15 a ticket. Suppose that given his budget and his tentative spending plans, the marginal utility from a cable movie is 15 utils and the marginal utility of a movie at the local cinema is 45 utils. Assuming he is spending his entire budget, Enrique is currently maximizing his utility Enrique can increase his utility by buying more cable movies and watching fewer cinema movies Enrique can increase his utility by buying more cinema movies and fewer cable movies