Consider a small closed economy with two consumption goods: good 1 (meat) and good 2 (berries). There are two types of agents, h and g, and they have the same preferences over consumption, represented by the utility function: u(¤1,72) = In z1 + In z2. However, there are twice as many type-h agents as type-g agents. The only factors of production are their labour. When a type-h agent chooses to spend a fraction a of his day producing meat and the rest producing berries then his output is (yf', y;) = (2a, 2(1 – a)). A type-g agent is more productive. When she chooses to spend a fraction B of her day producing meat and the rest producing berries then her output is (vĩ, v5) = (38, 12(1 – B)). Remembering that there are twice as many agents of type h than those of type g, what is the equilibrium price p? a. p= 3. O b. p= 1. O c. p= 2. O d. p= 4. O O O O

Consider a small closed economy with two consumption goods: good 1 (meat) and good 2 (berries). There are two types of agents, h and g, and they have the same preferences over consumption, represented by the utility function: u(¤1,72) = In z1 + In z2. However, there are twice as many type-h agents as type-g agents. The only factors of production are their labour. When a type-h agent chooses to spend a fraction a of his day producing meat and the rest producing berries then his output is (yf', y;) = (2a, 2(1 – a)). A type-g agent is more productive. When she chooses to spend a fraction B of her day producing meat and the rest producing berries then her output is (vĩ, v5) = (38, 12(1 – B)). Remembering that there are twice as many agents of type h than those of type g, what is the equilibrium price p? a. p= 3. O b. p= 1. O c. p= 2. O d. p= 4. O O O O

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

Consider an economy composed of 16 consumers. Of these, 5 consumers each own one right shoe and 11 consumers each own one left shoe. Shoes are indivisible. Everyone has the same utility function, which is Min(2R, L}, where R and L are, respectively, the quantities of right and left shoes con sumed. A) (10%) Is the status quo (where each individual has his own shoe) Pareto efficient? If so, briefly explain why. If not, provide a Pareto improvement b) (10%) Characterize all Pareto efficient allocations
a) Consider a couple whose behaviour follows the unitary household model. Their preferences can be represented by the utility function: U(CM; CH) = min (CM, CH), where CM, denotes market goods and CH denotes home production. Each spouse can work up to 50 hours per week, and those 50 hours can be divided between market work and home production. Joe and Anna are each paid £20 per hour for market work. Joe produces £20 of home production per hour, while Anna produces £30 per hour of home production. How many hours are each of the spouses allocating to home production and market work? b) Suppose that Anna is offered a pay raise, so that her hourly market wage increases to £25, and nothing else changes. Will that change the identity of the spouse who works more hours on the market? Explain your answer. [Hint there is no need to calculate the full solution to this case]
Consider an economy with 3 agents, Mohammed (M), David (D) and Susan (S). There are two goods available, good x, and good y. The marginal rates of substitution (where good x is on the horizontal axis and good y is on the vertical axis) are given by for Mohammed, for David and for Suzan. Mohammed and David are both consuming twice as much of the good x than good y, while Susan is consuming equal amounts of x and y. (image of functions and equations attached) A. What are the conditions for Pareto efficiency in an exchange economy? Are these consumption levels economically efficient? B. Can these consumption allocations be observed in a perfectly competitive equilibrium in an exchange economy without production? Explain.
Consider a couple whose behaviour follows the unitary household model. Their preferences can be represented by the utility function: U(CM; CH) = min (CM, CH), where CM, denotes market goods and CH denotes home production. Each spouse can work up to 50 hours per week, and those 50 hours can be divided between market work and home production. Joe and Anna are each paid £20 per hour for market work. Joe produces £20 of home production per hour, while Anna produces £30 per hour of home production. (a)How many hours are each of the spouses allocating to home production and market work? and Suppose that Anna is offered a pay raise, so that her hourly market wage increases to £25, and nothing else changes. Will that change the identity of the spouse who works more hours on the market? Explain your answer.
Aanchal and Bradyn are two homo economicus engaged in exchange over sour snakes (x) and peanut butter cups (y). Their utility functions are given by the following: Aanchal: u A = x ^1/4 A y ^3/4 A Bradyn: uB = x^1/4B y ^3/4 B Aanchal has an initial endowment of 5 peanut butter cups and 13 sour worms. Bradyn has an initial endowment of 10 peanut butter cups and 7 sour worms. g. What is Bradyn’s marginal rate of substitution of peanut butter cups (yB) for sour snakes (xB)?
Consider the utility functions below of two individuals, A and B, and bundles of goods Q and R. UA=X0.5Y0.5; UB=X+2Y; Bundle Q (10, 10); Bundle R (10, 15). Suppose the total X and total Y available in the economy are both equal to 20. a. If initially both individuals are consuming bundle Q, then a pareto-improvement is possible through reallocation of goods, i.e. individual A gives B some of his good X in exchange for some of individual B’s good Y. (True or False? Explain through mathematical examples).b. Pareto-optimality is achieved if we give individual B Bundle R and the remaining goods X and Y available in the economy is given to individual A. (True or false? Explain through a graphical example)
A possible explanation for the indecency might be the fact that the consumers are not all alive at the same time and therefore some mutually advantageous trades cannot occur. Consider an economy where consumer t receives an endowment of 1 unit of the single consumption good at time t and obtains utility only from consumption at times t and t + 1. All consumers meet at time 0 to trade. What is the equilibrium? Is exigency restored?
Consider the production of handmade rugs and assembly robots in India and Canada. Assume that Canada is relatively abundant in capital and that India is relative abundant in labour. Furthermore assume that the production technology for rugs and robots is the same in both countries. Draw production possibilities frontiers for each country keeping the production of rugs in the horizontal axis and the production of robots in the vertical axis. Assuming that consumer preferences are the same in both countries, add indifference curves and relative price lines under autarky. What are the differences in the relative price of rugs between the countries under autarky?
Assume an economy producing only two goods (shoes and computers) with a fixed amount ofproductive resources and technology and employing all its productive resources to the maximum.Production in this economy is subjected to the law of diminishing marginal returns and resourcesare assumed to be fully optimized. In addition, the cost of sacrificing shoes for computers andvice versa is 1. On the basis of the foregoing assumptions, answer the following questions: Mention three (3) conditions under which the sacrifice ratio between the goods will bezero.
Suppose the household’s preferences are given the following forms: u(c)=log(c), v(l)=log(l), that ß=2/3, and that the production functions are given by: F1(L)=L1/2 and F2(K)=K1/2. a) What are the equilibrium conditions? Derive them. b) What are the quilibrium quantities?
2. Consider the two-good model of the utility maximization program subject to a budget constraint. The utility function U of a hypothetical rational consumer and his/her budget constraint are given, respectively, by: U = x1x2, (U) B = p1x1 + p2x2, (B) where xi = the consumer’s demand for consumption good i (i = 1, 2), pi = the price of consumption good i (i = 1, 2), and B = the (exogenously given) budget of the consumer. In this maximization program, assume the following data: B = 240, p1 = 10, p2 = 2. (a) Using the Lagrangian function L, derive the first-order (necessary) conditions for a (local) maximum of the utility function. (b) Compute the optimal values of all choice variables, i.e., x*1 , x*2, and λ* , in the program, where λ signifies the Lagrange multiplier. (c) Using the information of the bordered Hessian matrix H¯ , verify the second order (sufficient) condition for a (local) maximum of the utility function. Note:- Do not provide handwritten solution. Maintain accuracy…
Can you help me with this question. Im finding it quite difficult. In a two-good economy there are two equal-sized groups of people: type a have preferences given by 2 log(xa1) + log(xa2) and type b have preferenceslog(xb1)+2log(xb2) where xhi means consumption by a type h person of good i. The division of property is as follows: each a-person has an endowment of (30, k) units of the two goods; each b-person has an endowment of (60, 210−k) units, where k is some given number between 0 and 210. Assume that there is no production and that people can freely exchange goods to maximise their utility. If there is a competitive equilibrium, what are the individuals’ incomes (ya, yb) in equilibrium as a function of k?