There are 40 people living in a village each having preference over apples and shirts represented by U(a,b) = a1/3s2/3, where a and s are amount of apples in pounds and shirts consumed, respectively. The price of a shirt is $10. Each villager has $300 income. Apples are supplied to the village by a farmer, whose supply function is S(pa) = 1000pa. Part a1 What is the equilibrium price of apples? How many pounds of apples does each villager consume? Part a2 What is the aggregate net consumer surplus at the equilibrium? Part a3 What is the price elasticity of demand at the equilibrium? Part b1 Suppose 50 more people move in to the village. What is the equilibrium price now? Part b2 Are consumers better or worse off now? Why? If a consumer is worse off, by how much additional income he/she needs to be compensated in order to be as well off as in Part a.

There are 40 people living in a village each having preference over apples and shirts represented by U(a,b) = a1/3s2/3, where a and s are amount of apples in pounds and shirts consumed, respectively. The price of a shirt is $10. Each villager has $300 income. Apples are supplied to the village by a farmer, whose supply function is S(pa) = 1000pa. Part a1 What is the equilibrium price of apples? How many pounds of apples does each villager consume? Part a2 What is the aggregate net consumer surplus at the equilibrium? Part a3 What is the price elasticity of demand at the equilibrium? Part b1 Suppose 50 more people move in to the village. What is the equilibrium price now? Part b2 Are consumers better or worse off now? Why? If a consumer is worse off, by how much additional income he/she needs to be compensated in order to be as well off as in Part a.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter13: General Equilibrium And Welfare

Section: Chapter Questions

Problem 13.13P

See similar textbooks

Similar questions

Q1 Consider the market for orange juice. In this market, the supply curve is given by QS = 100PJ −20PO and the demand curve is given by QD = 1000−150PJ +100PC, where J denotes orange juice, O denotes Orange, and C denotes coffee. Assume that PO = 10 and Pc = 8. Calculate the equilibrium price and quantity in the Orange juice market. Suppose that a poor harvest season raises the price of oranges to Po = 15 Is it possible to reach a market equilibrium if the price of orange juice PJ remains unchanged? Why? How much quantity of orange juice will finally be exchanged on the market? Find the market price necessary to restore equilibrium. Deduce the equilibrium quantity of orange juice. Draw a graph to illustrate your answers. Q2 Suppose the price elasticity of demand for the market of mobile phones is 0.90. If all mobile-phone companies simultaneously increased their prices, will total revenue in the industry increase or decrease? If a single mobile-phone…
Consider a two-person exchange economy in which initial endowments for both individuals are such that (e1 = e1) = (1,1). Suppose the two individuals have the following indirect utility functions: V1 (x, y) = ln M1 - a ln Px - (1-a) ln Py V2 (x, y) = ln M2 -b ln Px - (1-b) ln Py Where Mi is the income level of person i and Px and Py are the prices for goods x and goods y, respectively. a) Calculate the market clearing prices.
Let there be 3 people in the economy. Let the utility function of person 1 be u=min(x,y), utility of person 2 be = max(x,y) and the utility function of the 3rd consumer be U=x+y. Let the endowment points be A(5,5), B(5,5) c(5,5). An example of a pareto efficient allocation is: A) A(5,5), B(5,5) c(5,5) B) A(5,5), B(5,0) c(10,5) C) A(5,5), B(0,5), c(5,10) D) None of the above The correct answer is D. Explain clearly. Also, please state the pareto effient outcome not mentioned in the options (if it exists).
Consider a pure exchange economy, where each consumer has preferences described by a Cobb-Douglas utility function. Both consumers have exactly the same endowment. In such an economy, an equitable distribution of goods (where each individual consumes exactly half of each good) is a Walrasian equilibrium allocation. a. always for any consumers' preferences b.only if consumers' preferences are exactly the same c. never d. non of the above
Question 2 Demonstrate, by way of example, and explain fully, taking noting of the underlying assumptions, how you would derive Hicksian and Marshallian demand functions. What are the differences between these? Question 3 In the Walrasian world, Pareto optimal allocations are crucial in establishing an equilibrium outcome with respect to welfare. Give an exposition of the two Welfare Theorems, demonstrating also that they are Pareto efficient
The U.S. imports lumber among other goods from Canada. The lumber has been the topic of political dialogue between the 2 countries in the past few days. So let’s take X as ‘lumber’ and Y as ‘other goods’. Suppose the Canadian lumber and other exportable goods are produced with the following production Possibilities frontier (PPF): X2 + Y2 = 900 Suppose the U.S. utility function for the Canadian lumber, X, and other exportable goods, Y, is: U = X Y a. Derive the conditions necessary to determine the ‘Optimal Product Mix’ discussed in chapter 10. b. Draw the PPF (partial just the first quadrant) with Y on the vertical axis. On the same graph, draw at least one indifference curve so as to show the “optimal product mix’. Can this graph represent the ‘pure exchange’ economy? Explain why or why not. c. Now draw in a price line that can make the ‘optimal product mix’ a competitive exchange equilibrium. Can…
Consider an Edgeworth box economy, where preferences and endowments are given by. ( attached below ) In the following, use the normalization p2 = 1.(a) Find all the Pareto optimal allocations (use x1 to parameterize thePO allocations). (b) Suppose the government wants individual 1 to have the bundle x1 = (5, 9). Show whether the government can induce this outcome an equilib- rium with transfers. Find the supporting prices and transfers if possible. (c) State the Second Fundamental Theorem of Welfare and explain how the result in part (b) relates to that theorem. (d) Suppose the government does not care what bundle individual 1 gets and only wants to ensure that the individual 1 receives utility level equal to 45. Show whether this can be achieved as an equilibrium with transfers. Find the supporting prices and transfers if possible.
A fixed amount of a good has to be allocated between two individuals, h = 1; 2 with utility functions Where xh is the amount of the good allocated to consumer h. a. How should be allocated to maximize a utilitarian SWF? Illustrate the answer graphically. How do the optimal values of x1 and x2 change among the cases a1 2, a1 = a2, and a1 > a2? b. What is the allocation maximizing the Bernoulli-Nash SWF ? Illustrate graphically. How do the optimal values of x1 and x2 change with the preference parameters a1 and a2? c. What is the allocation maximizing the maxim in-Rawlins SWF? Illustrate graphically. How does the allocation change with preference parameters a1 and a2?
Kindly help on these two question... The result that every competitive equilibrium is pareto efficient. a) the second fundamental theorem of welfare economics. b) Edgeworth's condition c) The first fundamental theorem of welfare economics d) Waras's law 2) Assume that there are two consumers ( A and B) in an economy that have preferences that can can be represented as cobb-douglas utility functions. Also assume that there are two firms that have concave production possibility frontiers over goods x and y . Which of the following conditions must be true for an allocation to be distributivity efficient? Select all that apply. a) all goods in the economy are consumed. b) producers must be operating on their production possibilities frontier. c) all consumers must have marginal rates of substitution that are equal. d) all producers must have marginal rates of transformation that are equal . e) consumers must value goods at the margin at the same rate it costs society to produce them
Q3Use a matrix method to find the equilibrium prices and quantities where the supply and demand functionsfor Good 1, Good 2 and Good 3 are asQd1 = 50 − 2P1 + 5P2 − 3P3, Qs1 = 8P1 − 5Qd2 = 22 + 7P1 − 2P2 + 5P3, Qs2 = 12P2 − 5Qd3 = 17 + P1 + 5P2 − 3P3, Qs3 = 4P3 − 1
Two individuals, Fred and Helen, are in an economy with no production, and each have the utility function U = 10XY. Prices of both X and Y are set at $1. Initial endowments for Fred are 10 units of X and 6 units of Y. Helen has 8 units of X and 12 units of Y. Find the general equilibrium prices and allocation, then show that the G.E. allocation is Pareto efficient.
Considering the given possible uses of candy, which of the four choices could be Pareto Efficient (assuming candy is a “good”)? Among the four choices, which policy would yield the highest value according to a “Rawlsian” welfare function? (assuming that sweet/candy is a “good”) Explain. CHOICE 1: Every student gets one candy. The remaining candies are thrown in the bin. CHOICE 2: One student gets all the candies CHOICE 3: Every student gets two candies except for one student, who gets no candy; the remaining go in the bin. CHOICE 4: All the candies go in the bin