Page < 2Question 1:Consider a pure exchange economy with two consumption goods, X and Y, and twoconsumers, A and B. There are 20 units of X and 20 units of Y in the economy. Thepreferences of the consumers are represented by the following utility functions:UA(XA, YA) = 4XA + 3YAof 3UB (XB, YB) = 5(XB)4 (YB)²Q1 a) Suppose that initially consumer A has 5 units of X and 15 units of Y, and that consumer Bhas 15 units of X and 5 units of Y. Is this allocation Pareto efficient? Let Px and Pybe the pricesof goods X and Y, respectively. Write down expressions for the two individuals' budgetconstraints.

A utility function is a representation to define individual preferences for goods or services beyond…

UA(XA. YA) = 4XA + 3YA UB (XB. Ya) 5(X)^ (Y₂)² Q1 a) Suppose that initially consumer A has 5 units of X and 15 units of Y, and that consumer B has 15 units of X and 5 units of Y. Is this allocation Pareto efficient? Let Px and Py be the prices of goods X and Y, respectively. Write down expressions for the two individuals' budget constraints.

UA(XA. YA) = 4XA + 3YA UB (XB. Ya) 5(X)^ (Y₂)² Q1 a) Suppose that initially consumer A has 5 units of X and 15 units of Y, and that consumer B has 15 units of X and 5 units of Y. Is this allocation Pareto efficient? Let Px and Py be the prices of goods X and Y, respectively. Write down expressions for the two individuals' budget constraints.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter13: General Equilibrium And Welfare

Section: Chapter Questions

Problem 13.4P

See similar textbooks

Similar questions

Ginny likes to eat Bertie Bott’s Every Flavour Beans (b), and Chocolate Frogs (f). Herpreferences over these lollies are Cobb-Douglas, and can be presented by the utility functionu(b, f) = 1/5(b − 2)(f + 3). Each Every Flavour Bean costs 25 Knuts and each Chocolate Frogcosts 12 Knuts. Ginny has 314 Knuts to spend. Assume that beans and frogs are both perfectlydivisible goods.(a) Find Ginny’s optimal bundle.(b) Suppose that Ginny is mugged by Draco on her way to the lolly cart, so that by the timeshe is there, she is left only with 75 Knuts. What is her optimal bundle now?(c) Now, consider the general case, where Ginny’s income is m, the price of Every FlavourBeans is pb, and the price of Chocolate Frogs is given by pf . In other words, treat ChocolateFrogs as the numeraire. Find Ginny’s demand for each good in terms of m, pb and pf .(d) Find the good on which Ginny will always spend more than half of her income.(e) Find the own-price, cross-price, and income elasticities of good 2.
Ginny likes to eat Bertie Bott’s Every Flavour Beans (b), and Chocolate Frogs (f). Herpreferences over these lollies are Cobb-Douglas, and can be presented by the utility functionu(b, f) = 1/5(b − 2)(f + 3). Each Every Flavour Bean costs 25 Knuts and each Chocolate Frogcosts 12 Knuts. Ginny has 314 Knuts to spend. Assume that beans and frogs are both perfectlydivisible goods.(a) Find Ginny’s optimal bundle.(b) Suppose that Ginny is mugged by Draco on her way to the lolly cart, so that by the timeshe is there, she is left only with 75 Knuts. What is her optimal bundle now?(c) Now, consider the general case, where Ginny’s income is m, the price of Every FlavourBeans is pb, and the price of Chocolate Frogs is given by pf . In other words, treat ChocolateFrogs as the numeraire. Find Ginny’s demand for each good in terms of m, pb and pf .(d) Find the good on which Ginny will always spend more than half of her income.(e) Find the own-price, cross-price, and income elasticities of good 2…
3 Consider a pure exchange economy with 2 consumers and 2 goods. Consumer ? owns 8 units of good 1 and 1 unit of good 2, and his preference is represented by the following utility function: uA(x1, x2) = x1*x2. Consumer ? owns 2 units of good 1 and 4 units of good 2, and his preference is represented by the following utility function: uB(x1,x2)=x1+x2. Assume that the two consumers are allowed and able to trade with each other, and that good 1 is the numeraire. In this case, both consumers act as price-takers. Price takers: a market participant that is not able to dictate the prices in a market. Therefore, a price taker must accept the prevailing market price. Please find the competitive equilibrium of this pure exchange economy.
ote: - You are attempting cuestios suro 12 Neha and Sonam consume only Coke and Pepsi in a two person and two goods exchange economy. Neha consumes these two goods in fixed proportions such that she consumes 2 bottles of coke with 1 bottle of Pepsi. Sonam's utility function is given by U=4P+BC. In the economy, there is a total of 100 bottles of Pepsi and 200 bottles of Coke. If Neha initially had 60 bottles of Pepsi and 80 bottles of coke, then in the equilibrium position, Sonam will consume: A. between 50 to 60 bottles of Pepsi B. between 52 to 60 bottles of Pepsi C. between 54 to 60 bottles of Pepsi D. between 56 to 60 bottles of Pepsi Answer 04:09 PM 19-10-2021
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
5 Three Goods Consider a pure exchange economy with three goods: x1, x2 and x3. Consumer A’s utility function is U A = min {x1, x2}. He starts with one unit of x1 and none of the other goods. Consumer B’s utility function is U B = min {x2, x3}. He starts with one unit of x2 and none of the other goods. Consumer C’s utility function is U C = min {x1, x3}. He starts with one unit of x3 and none of the other goods. Find the general equilibrium prices and allocation
Bob goes to the supermarket to buy milk and cereal. He has $20 tospend. A consumption bundle consists of a quantity of milk, x (liters),and a quantity of cereal, y (grams). For all of the following questionsyou can assume that the consumption set is R2+. This means that milkand cereal can be consumed in any non-negative quantity. (a) The price of milk at the supermarket is px = 4$/liter. The priceof cereal is 0.2cents/gram. Draw Bob's budget set. What is theslope of the budget line? (b) Bob notices that the supermarket has a special coupon. A couponstates: "Buy 1 liter of milk and get 1 box of cereal for free". A boxof cereal has 2000 grams of cereal in it. Each shopper is limitedto one coupon. Draw Bob's budget set with 1 coupon. (Hint: Becareful with units again). (c) Due to popular demand, the supermarket extends its special offer. Each customer is now allowed to use 2 coupons. Draw Bob's budget set with 2 coupons.
Analyze how pareto efficiency is achieved from consumption activities in an economy
Give typing answer with explanation and conclusion Consider an exchange economy consisting of two people, A and B, endowed with two goods, 1 and 2. Person A is initially endowed with ωA = (0,10) and person B is initially endowed with ωB = (11,0). They have identical preferences, which are given by U^A(x1,x2) = U^B(x1,x2) = x1^2*x2. Suppose that p2 =1. Under the competitive equilibrium, what is p1? Round answers to two decimal places.
You'd like to study social networks. Consider the following 7 people {A,B,C,D,E,F,G} in a social network graph. (These people can be thought of as "nodes" or points drawn on a piece of paper.) Here, we'd like to model "followers." How many different ways can we draw arrows between two people from these 7? Here, "A-->B" (A is a follower of B) is not the same as "B-->A" (B is a follower of A). Order matters here
If marlow obtained 9 units of utility per dollar spent on apples and 6 units of utility per dollar spent on oranges, then Marlowe
Q. 4 Two consumers, A and B, live in a pure exchange economy with two good, x and y. Consumer A is endowed with 0 unit of x, 14 units of y; Consumer B is endowed with 4 unit of x, 6 units of y. They both have the utility function U=x1/4y3/4. What will be consumer A’s consumption of good X?