Find the efficient allocation of consumption, Business Economics

Assignment Help:

There are two agents, A and B. Both have preferences represented by a von Neumann-Morgenstern utility function u(csj) = ln (csj), where csj is consumption of agent j in state s. Agents have risky endowments ωsj and zs = ωsA + ωsB is the aggregate amount of resources in state s. Suppose there are two possible states, 1 and 2, with probabilities Π1 and Π2.

a) Write down the problem that determines the efficient allocations of consumption in this economy (indicate with λA and λB the Pareto weights of the agents).

789_Find the efficient allocation of consumption.png

b) Find the efficient allocation of consumption when the Pareto weight of B is twice the weight of A.

c) Represent it in an Edgeworth box. What is the marginal rate of substitution (the slope of agents' indifference curves) at the optimum?

d) Why should agent A's consumption be lower than B's even when her income is higher than B's?

e) Suppose that prior to the realization of the uncertainty, agents can trade (buy or sell) two types of securities: asset 1 that promises a payment of 1 unit of resources if state 1 is realized (0 in state 2); asset 2 that promises a payment of 1 unit of resources if state 2 is realized (0 in state 1). Suppose further that the price of asset 1 is 2/3, the price of asset 2 is 1; agents decide how much to buy or sell of each asset taking their prices as given (think of there being many agents like A and B, no one has market power, so we have perfectly competitive markets). Look at the Edgeworth box. How much of each asset do you think agent A would buy or sell? What will agent B want to do? Would they manage to implement an efficient risk sharing?


Related Discussions:- Find the efficient allocation of consumption

Determine the total price effect , An agent has a utility function over goo...

An agent has a utility function over goods 1 and 2 of the form U = x c 1 x d 2 where c is your 1- digit number and d is your minimum number. The agent's income is equal to you

Diversity, How has the definition of diversity changed over time? Can a div...

How has the definition of diversity changed over time? Can a diverse workforce help a company compete more effectively? How?

Current vs. historical costs, Accountants prepare income statements typical...

Accountants prepare income statements typically in terms of historical costs, in terms of the purchase price, rather than in terms of the current price. The reasons given for this

Treatment of capital gains and losses, Capital gains and losses are regar...

Capital gains and losses are regarded as wind falls. Fluctuation in the stock market prices in one of the most common sources of the wind falls. In a progressive society accordin

Linea programming, use of linear programming in decision making

use of linear programming in decision making

Define term project initiation in project management method, Define the ter...

Define the term project initiation in project management methods. Project initiation: It is a main control point in a project as this is where the Project Board gives for

What are the predictions of balanced growth, What are the predictions of ba...

What are the predictions of balanced growth? When government can co-ordinate immediate investment in several industries one firm gives a market for another. It needs state pla

Why do markets work into promoting development, Why do markets work into pr...

Why do markets work into promoting development? Liberal economists dispute a free market economy works since this gives incentives for self-generating growth. Particularly the

Business Units, Make a general comparison analysis of all the business unit...

Make a general comparison analysis of all the business units

What are problems of the sustainability in economic growth, What are the pr...

What are the problems of the sustainability in economic growth? Sustainability Problem in Economic Growth: Recent economic growth makes threats the future quality of life. S

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd