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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- K should be used to TL? 3. A consumer's preferences are represented by the utility function, U(X,Y)= Xay. Budget constraint is M = PxX+ P,Y. Based on this information; E a) Derive the Marshallian demand function. b) Calculate zero degree homogeneity for Marshallian demand for X. c) Derive the Hicksian demand function.Pete consumes goods 1 and 2. Pete thinks that 3 units of good 1 is always a perfect substitute for 4 units of good 2. Which of the following utility functions is the only one that would not represent Pete's preferences? A B D E U (x₁,x₂) = 40x₁+30x - 10000 2 U(x₁,x₂) = 4x₁+3x₂+ 1000 2 U (x₁,x₂) = min {4x₁, 3x₂} U(x,x)=16x² +24xx₂+9x² More than one of the above does not represent Pete's preferences.This question will let you examine/explore a more interesting utility func- tion than the simple example discussed in class as there will be both cross-price elas- ticity and an inferior good. Suppose you are told a consumer has the following utility function: U (9x9₂) = 9x + √√9₂ +9₂ You should assume income is Y, the price of good z is Pr, and the price of good z is P₂. This question will ask about several concepts discussed in lecture. (a) What is the Marshallian demand for goods x and z? I.e. find (9) for both interior solutions and corner solutions. Note: the outcome is "ugly" for the interior section and both corner should include constraints, i.e. limits using Y relative to f(P2, P₂). Hint: if solving using MRS = MRT, can use this information again in part (d).
- Suppose that you go to a restaurant with your friends. a) One of your friends always eat exactly one chicken wrap (C) and drinks two cups of ayran (A). He never changes this combination of food choice. (i) Write the utility function of your friend to represent his preferences. (ii) Draw couple of indifference curves of your friend on graph with appropriate labels. (iii) Determine the demand function of your friend for each product as a function of prices and income. Denote prices as Pc, Pa; income as M. b) Suppose that one of your friends does not care if she consumes spaghetti(S or noodle(N).She wants to consume either two-dish spaghetti or two-dish noodle or any combination of both which adds up to two dishes. (i) Write the utility function of your friend to represent his preferences. (ii) Draw couple of indifference curves of your friend on graph with appropriate labels. (iii) Denote prices as Pn, Ps; income as M. If Pn < Ps, then determine the demand…Given the utility function U = 10X1.5Y0.5, a. show and discuss if the individual is experience diminishing marginal utility. b. calculate the MRSXY and interpret your computed value. Would you say that this individual prefers more balanced bundles over extremes? Support your claim. c. and suppose prices of goods PX = 10, PY = 5, and income I = 400, solve for the optimal levels of X, Y, and U using the Lagrange Multiplier Method and graphically illustrate the resulting substitution, income, and net effects if the price of good Y is doubled, cet. par.Problem 2 Joan has the following utility function: u(x, y) = 5x + 3y. (a) Find Jane's marshallian demands. (b) Find Jane's hicksian demands. Consider that income is I = $8, and prices are given as p = $4, Py = $2. (c) Does Jane have enough money to attain a utility level of 20? Justify your answer. (d) Assume thè price of y marginally increases. Find the total, income and substitution effect for r due to the change in py.
- Derive the relationship between the quantity of X demanded and the price of X if the consumer’s indifference map vis-à-vis X and Y has curves concave to the origin. Let X be games of golf per annum and Y all other goods. Draw the indifference map and budget constraint of: (a) an amateur who pays to play golf; (b) a professional who is paid to play golf. May we conclude that golfers turn professional because they dislike the game?Demonstrate that the demands obtained in exercise 2.4 are homogeneous of degree zero in prices. Show that doubling prices does not affect the graph of the budget constraint. Exercise 2.4 Let a consumer have preferences described by the utility function and an endowment of 2 units of good 1 and 2 units of good 2. a. Construct and sketch the consumer’s budget constraint. Show what happens when the price of good 1 increases. b. By maximizing utility, determine the consumer’s demands. c. What is the effect of increasing the endowment of good 1 upon the demand for good 2? Explain your finding.I need asnwers of e,f,g Assume there is consumer, his utility function is u(x,y) =8 * x0.5+y , and his budget constraint is px*x +y = m, which implies py = 1. a.Please derive the Marshallian demand function of x. b.Please derive the indirect utility function. c. Please derive the expenditure function If originally m = 40, px=2. d. What is his original highest utility level? Now px has decreased to 1, m and py do not change. e. What is his new maximum utility level? f. Based on (c) (d) and (e), what is his compensating variation? g.Based on (c) (d) and (e), what is his equivalent variation?
- Consumer satisfaction from consuming goods X and Y is as follows:U=10X+14Y-X2-Y2 and consumer income 3X+Y=12Look for:1. The marginal utility function for goods X and Y?2. What are the values of X and Y for maximum utility?3. Prove with the results of X and Y obtained whether optimal customer satisfaction is achieved?Suppose an individual has the following utility function: U(X,Y)= min{X, 2Y}, and they choose marshallian demands gx,gy. Suppose you have an increase in px. Which of the following is true about the change in demand for good X, gx? (a) No substitution effect, because they only consume one of the goods. (b) No substitution effect, because they always consume the goods in fixed proportion. (c) No income effect, because they only consume one of the goods. (d) No income effect, because they always consume the goods in fixed proportion. Which of the following production functions exhibits constant returns to scale? (a) f(k,l) = 0.310.7 (b) f(k, l) = kl (c) f(k, 1) = ln(k)+ln(1) (d) f(k, l) In(k) + In(1) =For problems 1, 2, 3, we consider an agent Ann who consumes goods and y and has a utility U (x, y) = x²y. In these problems, Good costs P and good y costs Py. (1) Ann has I to spend. (a) Write out Ann's utility maximization problem. (b) Find: MU, MUy, and MRSxy. (c) Write out Ann's tangency condition. What is the other equation needed to solve for Ann's demand? (d) Find Ann's demands for x and y as functions of Pr, Py, and I. (Partial credit if you do this only for I = 30, P₂ = 5 and Py = 2.)