finalans03 - The Ohio State University Department of...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
The Ohio State University Department of Economics Econ 805 Final Exam Answers Professor Peck Winter 2003 Here is the distribution of scores on the …nal exam: 100 6 90-99 5 80-89 6 70-79 4 60-69 6 50-59 6 40-49 7 30-39 8 1. Consider a pure exchange economy, which we will call the n-consumer economy, with k goods and n consumers. Each consumer’s utility function and endowment vector satis…es assumption A: Assumption A: The utility function is continuous, strictly monotonic, and strictly quasi-concave. The endowment vector is strictly positive. Now consider the pure exchange economy in which an n +1 st consumer, whose utility function and endowment also satis…es assumption A, joins the original n consumers. We call this economy the n+1-consumer economy. For the statements in (a) and (b), either sketch the argument for why the statement is true, or give a counterexample if the statement is false. ( a )( 1 5p o i n t s )F o r all i =1 ; :::; n ,consumer i receives at least as high a utility level at the competitive equilibrium of the n+1-consumer economy than at the competitive equilibrium of the n-consumer economy. (b) (15 points) Suppose that the initial endowment allocation of the n- consumer economy is Pareto optimal. Then for all i ; :::; n ,c on sum e r i receives at least as high a utility level at the competitive equilibrium of the n+1-consumer economy than at the competitive equilibrium of the n-consumer economy. Answer: (a) This statement is false. While it is possible for all of the …rst n consumers to be better o¤ at the C.E. of the n+1-consumer economy, we 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
can …nd a counterexample. For example, let k=2 and n=2 hold, and consider the following utility functions and endowments: u 1 ( x 1 ) = log( x 1 1 ) + log( x 2 1 ) ;! 1 =(2 ; 1) u 2 ( x 2 ) = log( x 1 2 ) + log( x 2 2 ) 2 =(1 ; 2) u 3 ( x 3 ) = log( x 1 3 ) + log( x 2 3 ) 3 ; 1) : It is easy to check that consumer 1 receives a higher utility, in the C.E. to the economy with consumers 1 and 2, than in the C.E. to the economy with all three consumers. Intuitively, the introduction of consumer 3 creates an unfavorable price shift, making the good that consumer 1 wants to buy more expensive relative to the good that consumer 1 wants to sell.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 07/17/2008 for the course ECON 805 taught by Professor Peck during the Spring '08 term at Ohio State.

Page1 / 7

finalans03 - The Ohio State University Department of...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online