. (b) Suppose there are two Bohemian roommates with identical preferences whoderive utility from the number of paintings hung on their hotel's walls (X) and thenumber of granola bars (Y) that they eat. The specific utility function underlyingtheir preferences is given by:U₁ (X,Y)= X1¹³ Y₁23 (for i=1.2)mesGiven that each roommate has $300 to spend and P=$100, Py = $ 0.20, explorethe consequences of various expenditure allocations. In particular provide adetailed analysis of the possibility leading to free ridership Will that solution beefficient? If so or if not, why? Calculate the efficient allocation. Whatarrangement for cost sharing would be Pareto superior?

Pareto efficiency, also known as Pareto optimality, is a concept from economics that represents a…

(b) Suppose there are two Bohemian roommates with identical preferences who derive utility from the number of paintings hung on their hotel's walls (X) and the number of granola bars (Y) that they eat. The specific utility function underlying their preferences is given by: U₁ (X,Y)= X1¹³ Y23 (for i=1.2) mes Given that each roommate has $300 to spend and Pr=$100 $030 explora =

(b) Suppose there are two Bohemian roommates with identical preferences who derive utility from the number of paintings hung on their hotel's walls (X) and the number of granola bars (Y) that they eat. The specific utility function underlying their preferences is given by: U₁ (X,Y)= X1¹³ Y23 (for i=1.2) mes Given that each roommate has $300 to spend and Pr=$100 $030 explora =

Exploring Economics

8th Edition

ISBN:9781544336329

Author:Robert L. Sexton

Publisher:Robert L. Sexton

Chapter10: Consumer Choice Theory

Section: Chapter Questions

Problem 9P

See similar textbooks

Similar questions

. 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.
I like drinking Smirnoff and Stoli Vodka, but I really only careabout the total amount of alcohol I get out of it. They areperfect substitutes. Smirnoff is sold in liter bottles that are100 proof (that’s 50% alcohol). Stoli is sold in liter bottlesthat are 80 proof (40% alcohol). What is my utility functionfor bundles of these two vodkas? What do my indifferencecurves look like?
Draw thes e utility functions a) u Cxiy) = 2. %3D
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…
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?
2. Consider a consumer whose preference relation over the consumption set X = R can be repre- sented by the utility function: u (x1, x2, 13) = A (x1 – T1)ª (x2 – ã2)° (x3 – ã3)" - where A, a, B and y are all strictly positive. (a) Why can you assume A = 1 and a + B+y= 1 without loss of generality? Do so for the rest of the question. (b) Solve the UMP and derive the consumer's Walrasian demand. (c) Find the indirect utility function, the minimum expenditure function, and the Hicksian demand function.
As a consumer you have RM34 per month to spend for snack i.e. either pizzas which costs RM6 each or chicken burger which cost RM4 each. Suppose further that your preference is given by the following Total Utility Table Quantity 1 2 3 4 5 6 7 Pizza 60 108 138 156 162 166 166 Chicken Burger 44 76 100 120 136 148 152 First, graph the budget constraint with Pizzas on the horizontal axis and Chicken burger on the vertical axis. What are the intercepts at horizontal axis and vertical axis. Using the table, please show the Marginal Utility of Pizzas and Chicken Burger for every quantity demand. Using the utility maximizing rule to identify the consumer equilibrium, that is, combination of pizzas and chicken burger that will maximize your Total Utility. Confirm that the consumer equilibrium generates the highest combined total utility of any affordable combination of goods.
Give examples by drawing a graph of each of the following. Please draw your graphs neatly using a ruler to draw the axes and label your graphs completely. In each case draw ar least three indiffer- ence curves and indicate clearly the direction of increasing prefer- ence. (i) the preferences being convex but not strictly convex. (ii) the preferences being strictly increasing but not convex.
Suppose that Kevin is a 10 years old boy. He is at the mall with his mom, and she gives him some money to get food from the food court. At the food court there is a hamburger place, and an ice cream shop. In the following table, I will show you Kevin's Total Utility for each quantity of Hamburgers and ice cream. Quantit Total y Utility 1 2 3 4 5 Hamburgers ($2) Margin al Utility 6 7 0 20 34 44 47 47 42 32 MU/P Quantit Y BM 0 1 2 3 4 5 6 7 Ice Cream ($1) Margin al Utility Total Utility 0 29 46 53 55 56 56 52 MU/P
1) Suppose that Abel and Eden spend their incomes on two goods, food (F) and clothing (C).Abel’s preferences are represented by the utility function U(F,C)=10FC, while Eden’spreferences are represented by the utility function U(F,C)= 0.20F2C2A) With food on the horizontal axis and clothing on the vertical axis, identify on a graph theset of points that give Abel the same level of utility as the bundle (10, 5). Do the same forEden on a separate graph.B) On the same two graphs, identify the set of bundles that give Abel and Eden the samelevel of utility as the bundle (15, 8).C) Do you think Abel and Eden have the same preferences or different preferences? Explain 2. Graphically show the effect of an increase in price of Coca Cola on the demand of PepsiCola 3. Assume a budget line is drawn for two commodities: X on the x-axis and Y on the y-axis. Ifthe income of the consumer is 120 Birr, the y-intercept is 3, and the slope of the budget lineis -0.5 then determined the price of commodity…
5. What kind of preferences are represented by a utility function of the form u(x1, x2) = x1 + V*2? Is the utility function v(x1, x2) = xỉ + 2x1Vx2+x2 a monotonic transformation of u(x1, x2)? 6. Consider the utility function u(x1, x2) = Vx1x2. What kind of pref- erences does it represent? Is the function v(1, x2) transformation of u(x1, x2)? Is the function w(x1, x2) = xỉx, a monotonic transformation of u(x1, x2)? = x²x2 a monotonic
solutions. Question 1 Calculating MRS for CD Utility Functions (a) If a consumer has a CD utility function 0.4 0.6 U(91,92) = 994926, calculate MRS1,2. (b) If a consumer has a CD utility function Ima kdown1 calculate MRS1,2. (c) If a consumer has an utility function noltan asd Tor sympy ,1-α U(91,92) = 91 92 llib et (.) orde (hing aid tol bholup U(91,92) = a ln(91) + (1 - a) ln(92), diw sonuanos of calculate MRS1,2. Is it the same as the result in the previous part? (Note: Recall that we discussed the concept of ordinal utility in class, which means only the order of utility matters, not its magnitude. In function is a monotone transformation on the CD utility function. Notice that In (qq) = a ln(9₁) + (1 - a) ln(92). This example verifies that a monotone transformation does not change *(S) sidshav the consumer's indifference curves.) wobei/ (d)