A consumer has preferences over two goods represented by the utility function u(x₁, x₂) = x1 +2√x₂. (a) Sketch this consumer's indifference curves. (b) Find the Marshallian demand function x(p, w). (c) Sketch the wealth expansion path; that is, fixing prices p, sketch the demands x(p, w) in (1,2)-space as wealth w varies.
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- A decision maker has preferences represented by the utility function u(x,y) = xy over two goods and she is indifferent between the bundles (1,a), (b,4), (c,2) and (8,1). (a) Find the values a, b and c. (b) Brittney claims that another utility function, v(x,y) = (xy)^2 + 2xy - 5 , also represents the same preferences hence has the same exact indifference curves as u. Verify that the four bundles above are on the same indifference curve according to v, too, indeed.Joanna is playing blackjack for real money. She has reference-dependent preferences overmoney: if her earnings are m and her reference point is r, then her utility is v(m − r), wherethe value function v satisfies v(x) = √x for x ≥ 0, and v(x) = −2√−x for x ≤ 0a) Graph Joanna’s utility function as a function of m − rb) Does Joanna’s utility function satisfy loss aversion? Does it satisfy diminishingsensitivity?Suppose that Joanna has linear probability weights (that is, she does NOT have prospecttheory’s non-linear probability weighting function). Hence, if she has a fifty-fifty chance ofgetting amounts m and m′, and her reference point is r, her expected utility is1/2v(m − r) + 1/2v(m′− r) (2)For parts (c), (d), and (e), assume that Joanna’s reference point is $0 (that is, no winsor losses) and answer the following questions for each part: (i) What is the g for whichJoanna would be indifferent between not gambling and taking fifty-fifty win $g or lose$4 gamble? (ii) Does this reflect…For a > 0, consider a consumer whose utility function amounts to u(x1, x2) = − exp(−ax1x2). Can you take first order conditions to solve the utility maximization problem? Explain your argument. Next solve the utility maximization problem, and derive Marshallian demands and the indirect utility function. Given your calculations, state and use the duality theorem to find the expenditure function and Hicksian demand Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.
- Khan lives in a world with two consumption goods x and y. Her utility function is U (x, y) = √x² + y². a. If px = $3,py = $4, and her income, I, is equal to $50, what will be the quantities of x and y that Maya should buy to maximize her utility? Make sure that you write out the Lagrangian and the first-order conditions. (Hint: It may be easier to maximize U² than U). Have you found a true maximum? Explain your answer.Student question Time Left :00:09:43Suppose there are two consumers, A and B. The utility functions of each consumer are given by: UA(X,Y) = 2X + Y UB(X,Y) = Min(X,Y) The initial endowments are: A: X = 5; Y = 3 B: X = 2; Y = 2 a. Illustrate the initial endowments in an Edgeworth Box. Be sure to label the Edgeworth Box carefully and accurately, and make sure the dimensions of the box are correct. Also, draw each consumer’s indifference curve that runs through the initial endowments. Is this initial endowment Pareto Efficient? b. Now suppose Consumer A gets all of both goods. Is this allocation Pareto Efficient? (You do not need to draw a new graph or illustrate this on the existing graph. Simply answer “yes” or “no.”) c. Now suppose Consumer B gets all of both goods. Is this allocation Pareto Efficient? (You do not need to draw a new graph or illustrate this on the existing graph. Simply answer “yes” or “no.”)For each of the following statements, define all of the underlined terms. Then, explain why the statement is true or false. a. If a consumer views two goods as perfect substitutes, then their optimal choice will be a corner solution if MRS ≠ MRT. b. The substitution effect from a price increase states that the consumer will always choose a smaller amount of that good to consume. However, the income effect states that consumption can move in either direction. c. Suppose Alf and Bo have convex indifference curves. Alf likes units of "X" more than units of "Y" but Bo likes units of "Y" much more than units of "X." Then, in the optimum, Alf's marginal rate of substitution will be different from Bo's even if they face the same prices. d. Economists assume that preferences are ordinal. This implies that given two utility functions and one is a monotonic transformation of the other, then they represent the same preferences over bundles of goods.
- Irene spends all of her income M on soda and chips. The price of soda is 2 per unit. Irene’s utility function is U (s, c) = 5 ln(1 + s) + ln(1 + c).Hint: throughout the question, you can assume M 》= 50 and pc 《 = 8 (these assumptions just rule out the possibility of corner solutions, but do not affect the way we solve the problem). (a) Derive Irene’s demand function for chips (as a function of her income and the price of chips). (b) Are chips an inferior good for Irene? Is the magnitude of the (total) effect of a decrease in price of chips greater or smaller than the corresponding substitution effect? (c) Obtain Irene’s inverse demand function for chips when her income is M = 50. Show that this function is decreasing and convex. (d) Is Irene’s Engel curve upward sloping or downward sloping? Explain in detail.Suppose a consumer with a utility function U(x,y) =x^(0.5)y^(0.5) and an income of $1,000.00. Considering that products X and Y are sold by the kilo and that their prices are 50.00 and 100.00 respectively, calculate: a) Maximizing amounts of x and y for the consumer b) Graphically sketch the consumer balance c) What would be the impact on the utility of this consumer, if a policy of distribution of good X was established so that each period the consumer "earns" 20 units of X at no cost? What will your new balance be?Emma has a utility functionU(x1, x2, x3) = logx1+ 0.8 logx2+ 0.72 logx3over her incomes x1, x2, x3 in the next three years. This is an example of(A) expected value;(B) quasi-hyperbolic utility function;(C) standard discounted utility;(D) none of the above. Emma’s preferences can exhibit which of the following behavioral patterns?(A) preference for flexibility;(B) context effects;(C) time inconsistency;(D) intransitivity.
- I need help with this homeowrk question i am unsure if i have it correct. Suppose a consumer’s utility function is given by U(X,Y) = X^1/2*Y^1/2. Also, the consumer has $36 to spend, and the price of good X is P(x) = $4. Let good Y be a “composite” good (good Y is the “numeraire”) whose price is P(y) = $1. So, on the Y-axis, we are graphing the amount of money that the consumer has available to spend on all other goods for any given value of X.if P(x) increases to 9 and the new bundle of the customers demands are 2 units of x and 18 units of y, how much additional money would the consumer need in order to have the same utility level after the price change as before the price change? (Note: this amount of additional money is called the Compensating Variation.) and of the total change in the quantity demanded of good X, how much is due to the substitution effect and how much is due to the income effect? (Note: since there is an increase in the price of good X, these values will be…. Answer all parts (a) (c) of this question. (a) Consider an agent whose preferences over any couple (x1, x2), where 2₁ ER+ and x2 € R+, e.g., apples and oranges, is such that she prefers the bundle that is closest to having the same number of apples and oranges. Write a utility function u: R² → R+ which represent these preferences. A politician remarks "Our recent increases in the wage rates of teachers has been a total suc- cess! The shortage of teachers has been reduced drastically. Another, similar wage increase should eliminate this shortage entirely" (b) Explain and illustrate in a diagram what is meant by "income effects" and "substitution effects" of a wage rate change. (c) Explain and illustrate how you would model the labour supply decision of a potential teacher. Do you agree that the wage increase will increase the labour supply in this case? Carefully outline the assumptions underlying your argument.If consumption preference is concave (such as Narcotics drugs), this violates the assumption of consumer preference (assumed to be convex) ,how business policy (eg choosing prices, promotions/sales) or government policy (eg taxes) might be affected.