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. %3D (c) Does Jane have enough money to attain a utility level of 20? Justify your answer. (d) Assume the price of y marginally increases. Find the total, income and substitution duo to the change in Du.
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- 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.Morgan has the following utility function: u(x, y) = 5 ln(x) + 3y. Her income is given by I = 15 and the prices originally are pr = 2 and py = 3. = (a) What are Morgan's Marshallian demands? (b) How much of each good is Morgan currently consuming? (c) What is the utility level that Morgan can achieve? (d) Assume the price of x increases to p = 4, find Morgan's new levels of consumption. X X (e) Find the total, substitution and income effects for good x caused by the price change. Consider this price change a "large" price change (Apz = Pz - Px=4-2=2).Jen from Thunder Bay consumes housing (H) and food (F). Her studentstipend is $600/month. She has a utility function of U(H, F) = F1/3H2/3.The initial price of food is pF = 1 and the price of housing is pH = 10. (a) Determine how much food and housing she consumes.(b) Suppose the government decides to subsidize her housing by 50%.This has the effect of lowering the price she actually pays for housingto $5. If the price of food is $1 and the price of housing is $5, calculateJen’s utility maximizing bundle of goods.(c) How much does the Government spend on this program (just on Jen)?(d) Calculate her utility level using the utility function above and thequantities consumed.(e) Calculate Jen’s utility maximizing bundle and her resulting utilitylevel if the government chooses to simply give her the money theywould have spent on the program (rather than subsidize housing).How much utility does Jen get?(f) Given the two programs cost the same, which one is better for Jen?Illustrate the…
- Moe's income is $320 per week and he spends it on two goods, X and Y. Good X costs $8 and good Y costs $4 per unit. His utility function is U = 4.5XY. (a) Calculate Moe's utility-maximizing purchases of X and Y. (b) Calculate Moe's constrained utility- maximum if his income decreases by $2.00? (c) If the price of Y doubles, with no change in the price of X, by how much would his income have to increase to enable him to maintain his initial level of utility (as in part (a) above)?Ricky has utility function u=x'y. This implies that MUx=2xy. MUy=x². His income is 100. The price of y is 10. (a) Find his demand for x at price 20. (b) Find his demand for x at price 30. (c) Write down his demand function for x: that is, write down his demand for x as a function of the price of x.Joan has a monthly income of €100 that she allocates to two goods: meat and potatoes. Suppose meat costs €4 per pound and potatoes €2 per pound. Suppose also that her utility function is given by the equation U (M, P) = 2M + P. An outbreak of potato rot raises the price of potatoes to €4 per pound. What combination of meat and potatoes maximizes her utility? A. M = 25, P = 0 B. M = 20; P = 30 C. M = 20; P = 10 D. Any combination of meat and potatoes that satisfies her budget constraint
- Economics A consumer’s demands x, y for two different goods are chosen to maximize the utility function U (x,y) = √x + √y (x ≥ 0, y ≥ 0) subject to the budget constraint px+qy = m (where p,q,m > 0).(a) Find the utility-maximizing demands for both goods, as well as the Lagrange multiplier λ, all as functions of the three variables (p,q,m). Simplify all expressions as much as possible.(b) Find the maximized utility U*(p, q, m). Simplify the expression as much as possible(c) Show that (dU/dm)* is the Lagrangian multiplier λ.Suppose you have the following indirect utility function: V(Pa, Py, I) = In PxPy What are marshallian demands for x and y? I (a) (9x9y) = (22) (b) (9,9y) = (In, In 2) (c) (9, 9y) = (exp(2p/py), exp(2ppy)) I (d) (9x, gy) = (2pr+py' px+2py) What is the expenditure function for the associated expenditure minimization problem? (a) E(pa, Py, U) = (P + Py) ln(U) (b) E(pa, Py, U) = √exp(U)Papy (c) E(pa, Py, U)= (p²+p²) In(U) (d) E(pa, Py, U) = exp(U)²papy What are the individual's Hicksian demands for goods x and y? (a) (h₂, hy) = ((BU)¹/², (PU) ¹/²) (b) (ha, hy) = (RU, DU) (c) (ha, hy) = ((2 exp(U))¹/², (exp(U))¹/²) -1/2 (d) (hx, hy) = ((P₂PzU)−¹/², (P₂PzU)-¹/2) Are x and y complements or substitutes?Let U(x, y) = 3x + y be the utility function of a consumer, whohas a budget of I. As a function of I, find the consumer’s Walrasian demand when the prices are px = py = 1. The price of good x increases to 2, find the new Walrasian demand for the new prices px= 2 and py = 1. Decompose this change into an income and a substitution effect.
- Rohit likes playing badminton with his friends. His utility function for playing badminton every week is given by U(t) = 11t - 212. where t is measured in hours. They play on a badminton court, which they can rent per hour. Suppose the current price to play on the badminton court is $2.50 per hour. a) How many hours should Rohít play if he wishes to maximise his utility? b) Explain what we mean by the principle of diminishing marginal utility. Does the principle apply in Rohit's case? Explain why? In a diagram with income in Dollars on the horizontal axis and quantity on the vertical axis, show the relationship between Rohit's budget and the number of hours that would maximise his consumer surplus.1-). Apples (A) and Toys (T): U(A,T)=A"T". Suppose you want to reach a utility level of 1000. Price for an apple is 3 TL, price for a toy is 1 TL. Please find your HICKSIAN demand for toys and apples. Show all your calculations. Suppose that you have the following utility forNgan's preferences over Coffee (C) and Redbull (R) are given by U(C, R) = aC + a²R Ngan's income is given by M and prices are given by PC and PR. Assuming Ngan is maximizing her utility, under which condition will she only consume coffee? (i.e. C* - M Pc Po PR and R* = PR > PC Pc = aPR Pc PR > a ay 0)