A maximizing consumer is endowed with gh= 20, 5h= 20 and has preferences described by the linear function d = 45. Initially i" = 2, i!= 3. Now i!= 1. Provided an Indifference Curve Analysis Diagram to illustrate and quantify the endowment, the initial bundle, the Hicksian substitution effect, the ordinary income effect and the endowment income effect as bundles E, A, B, C and D. Use arrows to clearly indicate the SE, Ordinary IE, Endowment IE and Total Effect Her SE moves her from x =________ to x = Her Ordinary IE moves her from x = to x Her Endowment IE moves her from x = ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Questions g) and h)

Question one A consumer maximises the following utility function: i. ii. iii. iv. V. U(x) = x Inx₁ + (1 - α)Inx₂ Such that W=P₁x1 + P₂x₂ Derive the Marshallian demand function Derive the indirect utility function Discuss the properties of the indirect utility function and Marshallian demand function. Show that the Marshallian demand function satisfies all the properties What assumption about preferences ensures that the Marshallian demand function is a function and not a correspondence?

Consider a three-commodity consumer setting with the expenditure function:e(p, u) = up1α p2βp3γ 1. Find the indirect utility function2. Find the Walrasian demand function3. Verify Roy's identity4. Recover consumer's direct utility function

Que Robert's utility function is U(x, y) = 2/T + y. In every graph for this question, set y in the vertical axis and z in the horizontal axis. (a) Obtain the marginal rate of substitution MRS. Obtain the equation of the indifference curves for Ū = 2 and Ū = 4 (solving for y as a function of 1). Draw these indifference curves, identifying the intersections with each of the axes. (b) Suppose p, = 2 and Robert's income is M = 6. In a new graph, show the total, income and substitution effects (on the demand of r) of a drop in the price of z from p, = 4 to Pz = 2. (c) Now, the store where Robert goes for shopping has changed the prices to p, = 2 and py = 6, however, it also has a new special offer: for any amount of Y that Robert buys, he gets the same amount of X for free. Robert's income is M = 6. Draw Robert's budget line. Write down the equation of this line. Find Robert's utility-maximising bundle. (d)(d.1) Arthur's income is M = 6 and he goes to the same store as Robert. His utility…

Clara has utility function preferences u(x, y) = x^(1/2)+ you ^(1/2). She has income m = 48 and pays pX= 4, pY= 2. Now pX falls to 2. Provide a labeled diagram that decomposes this price change using the Slutsky decomposition SE (A to B) and TE (B to C) and the Hicksian decomposition SE (A to H) and TE (H to C).

Suppose Lea is presented with the following four bundles A=(12, 4), B = (10,6), C = (10, 7) and E=(8,8). Lea's preferences satisfy strong monotonicity and strict convexity. It is also true that for Lea A-E Which of the following statements, if any, is correct? (If no statement is correct, select "None".) Select one or more: a. For Lea, bundle C is strictly preferred to bundle A. b. Lea is indifferent between bundles A and C. c. Lea's favorite bundle among the four stated is A. d. None. e. For Lea, bundle C is strictly preferred to bundle B. f. For Lea, bundle B is strictly preferred to bundle E. g. For Lea, bundle E is strictly preferred to bundle A.

John’s preferences for apples (A) and berries (B) are represented by U(A,B)= A+2B . Apples cost £2 and berries £1. Given that John’s monthly income is £30 answer the following questions: What type of goods are apples and berries for John? What is the proportion to which John is willing to exchange apples for berries? Illustrate and solve graphically John’s utility maximization problem. If his income increases every month by £10, how will John’s consumption choice be affected? Illustrate graphically the income expansion path and the Engel curve for each good. How will an increase in the price of berries to £6 affect John’s optimal consumption choice? (John’s income is £30) Graph John’s demand curve for each good. Assume that John wins a voucher of £20, redeemable only in apples. How would this affect John’s utility? (Assume that prices and income are as described initially) Assume that John is presented with two options: an apple voucher of £20 or just £6 to spend on any good he wants.…