2 Indifference Curves in Consequence Space(A) If the utility function is v (c) = c2, where c is income, suppose aperson's preference ordering over actions or prospects in a two-stateworld is given by:U(q, G; T, 72) = T, (4) + 7,(6,)+ T2Depict the indifference curves in a diagram with q on the horizontalaxis and c, on the vertical axis (probabilities held constant). Show thateach indifference curve touches the axes and is everywhere bowedtoward the origin.(B) If U = ET,v(c,) and v(.) is a strictly concave function, show that ifthe individual is indifferent between (c, , c2 ) and (c, c) he will strictlyprefer the convex combination (Ac, + (1 – 1)c, rc, + (1 – )C).Hence draw a conclusion about the shape of the indifference curvesin the (c, ) plane.

Given Indifference Curves in Consequence Space

Answered: Indifference Curves in Consequence…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.CR: Chapter 9 Review

Problem 7CR

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*A Consumer is willing to trade 3 unit of x for unit 1 of y ,when she has 6 unit of x and 5 unit of y.she also willing to trade in 6 unit of x for 2 unit of y,when she has 12 unit of x and 3 unit of y.she is indifferent between bundle (6,5) and bundle (12,3).what is the utility function of for goods x and y? hint: what is the shape of indifference curve?*
Each person tries to balance his or her time between leisure and work. The tradeoff is that as you work less your income falls. Therefore each person has indifference curves which connect the number of hours of leisure, 1, and income, s. If, for example, you are indifferent between 0 hours of leisure and an income of $1125 a week on the one hand, and 10 hours of leisure and an income of $750 a week on the other hand, then the points 1 = 0, s = 1125, and 1= 10, s = 750 both lie on the same indifference curve. The table below gives information on three indifference curves, I, II, and III. Weekly Income Weekly Leisure Hours I II III II 1125 1250 1375 0 20 40 750 875 1000 10 30 50 500 625 750 20 40 60 375 500 625 30 50 70 250 375 500 50 70 90 (a) On a sheet of paper, or using a calculator or other technology, graph the three indifference curves. (You will need these to answer part (d) of this problem.) (b) You have 95 hours a week available for work and leisure combined, and you earn…
4. Let the utility function for two goods, X and Y be given by U (x, y) = 4yx² + 1. On Monday Nigel purchases 2 units of X and 8 units of Y. (a) If on Tuesday Nigel purchases 2 units of good Y, how many units of good X must he purchase to obtain the same level of utility he obtained on Monday? (b) Graph the indifference curve for this level of utility over the do- main D = {(x, y) = R²|0 ≤ x ≤ 10,0 ≤ y ≤ 10}.
The value y (in 1982–1984 dollars) of each dollar paid by consumers in each of the years from 1994 through 2008 in a country is represented by the ordered pairs. (1994, 0.675) (1995, 0.654) (1996, 0.643) (1997, 0.618) (1998, 0.611) (1999, 0.599) (2000, 0.585) (2001, 0.562) (2002, 0.559) (2003, 0.539) (2004, 0.529) (2005, 0.513) (2006, 0.493) (2007, 0.482) (2008, 0.462) (b) Use the regression feature of the spreadsheet software program to find a linear model for the data. (Let trepresent time. Round your numerical values to four decimal places.) y = (c) Use the model to predict the value (in 1982–1984 dollars) of 1 dollar paid by consumers in 2010 and in 2011. (Round your answers to two decimal places.)
Two countries, Korea and Vietnam, are engaging in international trade.They produce two goods: automobiles and cloth. We observe a relativeabundance of cheap labor in Vietnam and a relative abundance of capitalin South Korea. Draw a graph that shows the above situation in South Korean economy with a P P F and two relative prices (one before trade and theother after trade). The quantity of automobiles (QAuto) is on thehorizontal axis and the quantity of cloth (QCloth) is on the verticalaxis.
Suppose there are two people, Selma and Burak, who must split a fixed income of 200. The marginal utilities of income for Selma and Burak are as follows: MUs = 600- 2*Is MUB = 600- 4*IB where IS and IB are incomes of Selma and Burak respectively. What is optimal distribution of income if social welfare function is additive? Draw the MUof Selma and Burak in the Edgeworth box and show part (a). What is the optimal distribution if society values only the utility of Selma? What is the optimal distribution if society values only the utility of Burak? This example refers to ……… ………. rationale for income redistribution and it is Pareto ………….
Group I nesting boxes were well separated from each other and well hidden by availablebrush. There were a total of 480 eggs in group I, of which a field count showed about275 hatched. Group II nesting boxes were placed in highly visible locations and groupedclosely together. There were a total of 874 eggs in group II boxes, of which a field countshowed about 272 hatched. Find a point estimate ˆp1 and ˆp2 for the proportion of eggsthat hatch in group I nest boxes and group II nest boxes. Let p1 and p2 be the populationproportion of hatched count in boxes I and II respectively. Find a 99% confidence intervalfor p1 − p2.(a) List the given information with appropriate symbols.(b) What is the probability distribution of ˆp1−pˆ2, difference between sample proportions?(c) Write the expression for the population mean of ˆp1 − pˆ2 distribution. Use propersymbols. (d) Find the population standard deviation of ˆp1 − pˆ2 distribution. Use proper mathematical symbols.(e) Find the margin of error of…
Let x1 and x2 be the payoffs of two investment
If an individual’s preferences are described by the utility function U(X1 , X2 ) = X12 + X22, graph the indifference curve for U = 20 and U= 40. Find the optimal consumption quantities if P1 = US$2.50 ; P2 = US$ 7.50; and M = US$ 60.
The monthly income associated with the sale of two products is described with the function in two variables / = 21a + 19b, where a and b are quantities sold of products A and B, respectively. Furthermore, it is known that the cost of producing these products is modeled by C = 3a² +6b². With this information answer: Write the criterion of the monthly profit function from the sales of products A and B, use as variables a and b What is the only critical point of the utility function? What is the value of the discriminant of the utility function evaluated at that critical point (Value of D used to classify the critical point) At this critical point. Is a relative maximum, a relative minimum, or neither determined?
2. In a simple regression analysis where Yisa dependent and an independent variable)if the Y intercept is positive then A. there is a positive relation between X and Y B. if Y is increased must also increase C. None D. if x increased y must also increase
The following table shows the marks obtained by 10 students of a college in Accountancy (X) and Statistics (Y) out of a maximum of 50 marks: Accountanc 24 32 24 26 34 28 30 30 35 37 y Statistics 20 27 24 24 27 24 32 25 31 36

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