c and d please For problems 1, 2, 3, we consider an agent Ann who consumes goods and y and has a utilityU (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'sdemand?(d) Find Ann's demands for x and y as functions of P₂, Py, and I. (Partial credit if you do thisonly for I = 30, P₂z = 5 and Py = 2.)

Optimal consumption bundle: The optimal consumption bundle is such that at that bundle the…

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 x costs P₂ and good y costs Py. (1) Ann has I to spend. (a) Write out Ann's utility maximization problem. (b) Find: MU, MUy, and MRS zy- (e) 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 Pz, Py, and I. (Partial credit if you do this only for I = 30, P₂ = 5 and Py = 2.)

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 x costs P₂ and good y costs Py. (1) Ann has I to spend. (a) Write out Ann's utility maximization problem. (b) Find: MU, MUy, and MRS zy- (e) 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 Pz, Py, and I. (Partial credit if you do this only for I = 30, P₂ = 5 and Py = 2.)

Microeconomics

13th Edition

ISBN:9781337617406

Author:Roger A. Arnold

Publisher:Roger A. Arnold

Chapter7: Consumer Choice: Maximizing Utility And Behavioral Economics

Section: Chapter Questions

Problem 6QP

See similar textbooks

Similar questions

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.)
1 Alice has a monthly lunch budget of 360 dollars which she spends on either burgers (B) or pizza (Z). The price of each pizza is 16. dollars and the price of each burger is 8 dollars. Alice's utility is given by: u(B, Z) = B'/2 +4Z!/2 + 47!/2 a) Find Alice's budget constraint. Set up the Lagrangian and find her optimal consumption. What is her new consumption if the price of burgers becomes 16 dollars?
1 Consider a consumer who consumes only two goods, 21 and z2. His utility function is u (21, 22) = In z1 + 2. where In represents the natural logarithm. 1.a Derive the consumer's MRS of good 1 for good 2 using calculus to calculate his marginal utility from z and his marginal utility from z2. 1.b If the price of z1 is $2 per unit and the price of z2 is $4 per unit, and the consumer's income is $100, What is the equation of this consumer's budget line? 1.c What are the optimal consumption choices, z and z5, for this consumer? Show your work.
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…
Alan likes eating chocolates and oranges. His utility is described by U(x₁, x2) = (x1 - y)2, where ₁ is chocolate and 2 is oranges. Chocolates are addicitive, so y represents a reference point, any amount of chocolates consumed less that y does not increase utility. The price of ₁ is p₁ and the price of 22 is P2. Alan's income is m. • State the optimization problem. • Find the utility maximizing values of chocolates, x₁, and oranges, 2. • Test whether these will indeed yield maximum utility. Determine how a changes as y changes. Why do you think so?
2 COOKIES AND TEA Consider a consumer, Jennie, who only consumes tea (t) and cookies (c). Jennie's utility func- tion is U(t, c) = min{5t, c}. The min function gives you the smaller of the two arguments.¹ For example, the min{1,3} = 1 since 1 is less than 3. She has $10 to spend, the price of a cup of tea is normalized to $1, and the price per cookie is $2. Assume she can buy tea and cookies in fractions. a. Graph the set of the tea and cookie pairs that yield the utility level of 5 with tea on the x-axis and cookies on the y-axis. Now graph an indifference curve associated with the level of utility equal to 7. b. Given the market prices that Jennie faces and her income, how much tea and how many cookies will Jennie choose to consume? Show her optimal choice graphically with cookies on the x-axis and tea on the y-axis. [Note: You cannot use the standard Lagrangian technique here because the slope of the indifference curve is not defined at the kink. Try working with the graph of the…
Please no written by hand and no emage Consider a consumer that consumes 2 teaspoons of sugar with each cup of coffee. For each cup of coffee with sugar the consumer gains 10 utils.a) Write down the utility function that gives the total utility if the consumer consumes S teaspoons of sugar and C cups of coffee. The consumer has assigned £7 per week to be spent on drinking coffee with sugar. The current price of coffee is £0.50 per cup and each spoon of sugar costs £0.10. b) Calculate the optimal weekly consumption bundle for this consumer.c) Does the consumer view C and S as complements or substitutes?
Suppose Paco has an annual entertainment budget of I. He spends his entertainment budget on only 2 goods: video games and movies. The price of a video game is P, and the price of a movie is Pm. Paco's utility function for video games (v) and movies (m) is: U(v, m) = 4v²m. a. Derive Paco's demand functions for video games and movies as functions of only exogenous variables. b. Write Paco's indirect utility function.
2. Vibha consumes three goods X, (shirts), X, (food in pounds), and X, (shelter in square feet). Vibha's utility function is given by: U (X,, X, X,) = 5ln Xt 3ln X + 2ln X, where In (x) or log. (x) is the natural logarithm. Vibha's weekly income is $100. Let the price of X, = P, = $10, the price of X, = P, = $2, and the price of X, = P; = $4. What is the equation for Vibha's budget constraint? а. b. |How many shirts, pounds of food, and square feet of shelter, will Vibha consume, as a rational consumer?
3) Oğuz has the utility function U(x1,X2) = x:*x2². (X: nuts, X2: berries). %3D a) If Oğuz has 25 units of nuts and 17 units of berries, the price of nuts is 2 and the price of berries is 1 liras, what would be the optimal consumption of Oğuz? b) Assume the prices change, so that nuts cost 1 and berries cost 3 liras. What is the new demand? In this change, What is the pure substitution effect? What is the income effect? c) In the change calculated in part (b), what is the pure substitution effect? d) In the change calculated in part (b), what is the income effect? In the change calculated in part (b), what is the endowment effect?
I. You only consume two goods and your preferences are represented by utility function U(x₁, x₂) = (x0.5 + x2.5)² for x₁ > 2 and x₂ > 0. 1
I need help with my homework assignment that i dont undertsand. Suppose a consumer has a utility function given by U(X,Y) = MIN(X, 2Y). The consumer has $90 to spend (M = $90). The Price of good Y is PY = $1. Using a graph, sketch the consumer’s demand curve for Good X. Make sure to identify three points on the demand curve. Make sure your graph is neat, accurate, and scaled properly.