0.3 0.7 Zach's preferences are representable by the utility function u = 91³927, where 9₁ and 92 denote his consumption of goods 1 and 2. (Answers to each of these questio decimal places.) Still assuming endowments of e₁ = 5 and e₂ = 9 and market prices p₁ = 20 and p₂ = 30, what is the maximised value of Zach's utility? O Au = 6.74 ○ Bu = 5.39
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- James's preferences over cake, c, and money, m, can be represented by the utility functionu (c, m) = c + m + µ (c − rc) + µ (m − rm)where rc is his cake reference point, rm is his money reference point, and the function µ (·) isdefined as µ (z) = z , z ≥ 0 and λz, z < 0 where λ > 0. 1. If his reference point is the status quo (that is, his initial endowment), what is themaximum price Sam would be willing to pay to buy a cake?2. If his reference point is the status quo, what is the minimum price Sam would be willingto accept to sell a cake he already owned?Now,suppose N=3 with a market clearing interest rate. The first two agents are the same as earlier. The third agent has an endowment of 20 in the first period and consumes 15 in the second period. If the first two agents each consumed 21 units in the first period, how much did the third agent consume in the first period? Plz do fastAlex preferences over cake, c, and money, m, can be represented by the utility functionu (c, m) = c + m + µ (c − rc) + µ (m − rm)where rc is his cake reference point, rm is his money reference point, and the function µ (·) isdefined as µ (z) = z , z ≥ 0 and λz, z < 0 where λ > 0. 1. If his reference point is the status quo (that is, his initial endowment), what is themaximum price Sam would be willing to pay to buy a cake?2. If his reference point is the status quo, what is the minimum price Sam would be willingto accept to sell a cake he already owned?
- An individual's utility function is given by: U (q1 , q2) = q11/2 . q2 Suppose we know that the individual is maximizing their utility by consuming 9 units of good #1 (q1=9) and six units of good #2 (q2=6). If the current price for good #1 is $1 (p1=1), what must be the price of good #2 (p2) and what must be the individual's current income (y) available to spend on the two goods? a.) p2 = b.) y=An individual is faced with a choice of buying housing in one of two markets; the private market where he may buy any amount of housing he pleases at the going price, and the public housing market where he will be offered, on a take-it-or-leave-it-basis, a particular amount of housing at a price lower than that which he would pay for it on the private market. Will he necessarily choose the public housing? If so, may we conclude that he will consume more housing than he would have purchased had he been forced to buy it on the private market? (With thanks to Dr Leslie Rosenthal.)Consider a two-person exchange economy in which initial endowments for both individuals are such that (e1 = e1) = (1,1). Suppose the two individuals have the following indirect utility functions: V1 (x, y) = ln M1 - a ln Px - (1-a) ln Py V2 (x, y) = ln M2 -b ln Px - (1-b) ln Py Where Mi is the income level of person i and Px and Py are the prices for goods x and goods y, respectively. a) Calculate the market clearing prices.
- Consider an economy with 2 goods and 2 identical agents, each of whom has the following utility function, u (x1; x2) = ln x1 + 2 ln x2. The aggregate endowments of the 2 goods are given by (1; 2). Suppose there is a social planner who cares about agents equally.(a) Set up the plannerís problem.(b) Calculate the first-best outcome 2. Consider an economy with 2 goods and 2 identical agents, each of whom has thefollowing utility function, 11(31, 3:2) = In 3:; + 2111332. The aggregate endowments ofthe 2 goods are given by (1, 2). Suppose there is a. social planner who cares aboutagents equally. (a) Set up the planner’s problem.(b) Calculate the first-best outcome (11.6., the social planner’s solution).Assume an individual has a utility function of this form U(C, L) = 20 + 4(C*L)1/2 This utility function implies that the individual’s marginal utility of leisure is 2(C/L)1/2 and her marginal utility of consumption is 2(L/C)1/2. The individual has an endowment of V=$80 in non-labour income and T = 16 hours to either work (h) or use for leisure (L). Assume that the price of each unit of consumption good p=$1 and the wage rate for each hour of work w=$10. a. How much utility does the individual receive if she consumes C = 100 and works h = 7 hours? b. Calculate the rate at which the individual is willing to sacrifice an additional leisure hour when she is already working 4 hours. c. What is this individual’s optimal amount of consumption and leisure?Assume an individual has a utility function of this form U(C, L) = 20 + 4(C*L)1/2 This utility function implies that the individual’s marginal utility of leisure is 2(C/L)1/2 and her marginal utility of consumption is 2(L/C)1/2. The individual has an endowment of V=$80 in non-labour income and T = 16 hours to either work (h) or use for leisure (L). Assume that the price of each unit of consumption good p=$1 and the wage rate for each hour of work w=$10. a. What is this individual’s optimal amount of consumption and leisure? b. Assume a cash grant welfare program is instituted which pays M = 20 dollars for individuals who do not work. Compute the new optimal labour supply for this individual under the welfare program. Assume that prior to the welfare program, p =$1, w =$10, and V =$80 (as in part c). Does the individual accept the welfare program and not work? Show why or why not.
- A consumer finds only three products, X, Y, and Z, are for sale. The amount of utility which their consumption will yield is shown in the table below. Assume that the prices of X, Y, and Z are $10, $2, and $8, respectively, and that the consumer has an income of $74 to spend. Product X Product Y Product Z Quantity Utility Marginal Utility per $ Quantity Utility Marginal Utility per $ Quantity Utility Marginal Utility per $ 1 42 NA 1 14 NA 1 32 NA 2 82 4 2 26 6 2 60 3.5 3 118 3.6 3 36 5 3 84 3 4 148 3 4 44 4 4 100 2 5 170 2.2 5 50 3 5 110 1.25 6 182 1.2 6 54 2 6 116 0.75 7 182 _0 7 56.4 _1.2 7 120 _0.5_ Why would the consumer not be maximizing utility by purchasing 2 units of X, 4 units of Y, and 1 unit of Z?A consumer finds only three products, X, Y, and Z, are for sale. The amount of utility which their consumption will yield is shown in the table below. Assume that the prices of X, Y, and Z are $10, $2, and $8, respectively, and that the consumer has an income of $74 to spend. Product X Product Y Product Z Quantity Utility Marginal Utility per $ Quantity Utility Marginal Utility per $ Quantity Utility Marginal Utility per $ 1 42 NA 1 14 NA 1 32 ___NA__ 2 82 4 2 26 6 2 60 __3.5_ 3 118 3.6 3 36 5 3 84 __3___ 4 148 3 4 44 4 4 100 __2___ 5 170 2.2 5 50 3 5 110 _1.25___ 6 182 1.2 6 54 2 6 116 _0.75__ 7 182 0 7 56.4 1.2 7 120 _0.5_ How many units of X, Y, and Z will the consumer buy when maximizing utility and spending all…Assume that the prices of good X, Y and Z are as follows R5,R1 and R4 respectively, and the Judith has an income of R37 to spend. HOW much of each good will judith consume in order to maximise her utility? What will be her total utility and marginal utility of the last rand spent on each good? Show all the calculations