Question

1. Oscar and Elmo make up a simple exchange economy where the only goods are books and cookies. Total books 10 Total cookies 5 a) Elmo has 7 books and 2 cookies. Draw the Edgeworth box. Label the endowment with w and how much each person is consuming (or reading) at that point. Also label Elmo's origin (OE) and Oscar's origin (Oo), and label along which axis each good is increasing for each person b) On your graph from part a, draw an indifference curve for each person (label them lE and lo) such that the endowment is NOT Pareto Efficient. c) On your graph from part a, draw a point that represents a Pareto improvement relative to the endowment. Label it P d) Define Pareto improvement and explain how P1 satisfies that definition. e) At a Pareto Efficient allocation in this type of exchange economy, what must be true of the agents' Marginal Rates of Substitution (MRS)? f) Given the following marginal rates of substitution for the two individuals over the two goods, is the allocation where Elmo has 2 cookies and 7 books Pareto efficient? Justify your answer fully. MR5%,-2b + c g) What does the First Fundamental Theorem of Welfare Economics tell us about all initial allocations in a simple exchange economy? Under what (2) assumptions?

only need answers e, f, g

Answer 1

Answering all parts to have a better understanding.

Edge worth Box: - B^bar = 10, C^bar = 5 a) b) Let preferences are Strictly convex of both IC pass from initial endowment point w c) at P.O. MRS_B, e^O = MRS_B, c^E, the two IC are tangent to each other so the shaded Lens Region Represents all Pareto improvement allocations. D) Pareto improvement is defined as situation, where one individual could be made better off w/o making other one worse off Now of player D shifts to NEW IC, IO^' , then O is better off while elmo's welfare is unchanged Thus p1 shows Pareto Improvement e) at Pareto efficiency rightarrow two MRS are equal Ans f) Now MRS middot E = 2b + c, MRS^0 = 2c/b elmo allocation, (b, c)^E = (7, 2) MRS^E = (2 times 7) + 2 = 16, (b, c)^0 = (3, 3) , MRS^0^' = 2 times 3/3 thus MRS^0 notequalto MRS^E, Hence not Pareto optimal Ans G) According

G) According to the first fundamental theorem

If ( assumptions):

There is no market failure ( no case of public goods or externalities)

& No consumption externality,

Then every Competitive equilibrium is a Pareto efficient allocation.

Thus initial allocations aren't the Pareto efficient allocations..