ch6ans - Foundations of International Macroeconomics1...

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

View Full Document Right Arrow Icon
Foundations of International Macroeconomics 1 Workbook 2 Maurice Obstfeld, Kenneth Rogo f , and Gita Gopinath Chapter 6 Solutions 1. (a) We look at the symmetric e cient incentive-compatible contract. That contract maximizes an equally-weighted average of Home and Foreign expected utility, E { u ( C ) } +E { u ( C ) } , subject to the constraints η Y P ( ² ) η Y, which must hold for all N possible realizations of the shock ² . The Lagrangian for the contracting problem is L =m a x P ( ² ) N X 1=1 π ( ² i ) ' u £ ± Y + ² i P ( ² i ) / + u £ ± Y ² i + P ( ² i ) /“ N X 1=1 λ ( ² i ) £ P ( ² i ) η ( ± Y + ² i ) / N X 1=1 ( ² i ) £ P ( ² i ) η ( ± Y ² i ) / . The rst-order condition with respect to P ( ² i )is π ( ² i ) { u 0 [ C ( ² i )] + u 0 [ C ( ² i )] } λ ( ² i )+ ( ² i )=0 , (1) and the complementary slackness conditions are λ ( ² i ) £ η ( ± Y + ² i ) P ( ² i ) / =0 , 1 By Maurice Obstfeld (University of California, Berkeley) and Kenneth Rogo f (Prince- ton University). c MIT Press, 1996. 2 c MIT Press, 1998. Version 1.1, February 27, 1998. For online updates and correc- tions, see http://www.princeton.edu/ObstfeldRogo f
Background image of page 1

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

View Full DocumentRight Arrow Icon
( ² i ) £ η ( f Y ² i )+ P ( ² i ) / =0 . Despite the Forbidding Formalism oF the Kuhn-Tucker conditions, the solu- tion to the problem can be characterized rather simply. Consider the so- lution in states where the incentive constraints do not bind, that is when λ ( ² i )= ( ² i )=0 . Across these states, the rst-order condition (1) reduces to u 0 [ C ( ² i )] = u 0 [ C ( ² i )] , and so C ( ² i )= C ( ² i ) . There is thereFore a range [ e, e ] such that inside this interval C = C . The bound e is easily Found as the largest ² such that ² η ¡ f Y + ² ¢ , implying e = η 1 η f Y. (2) (b ) ±or ²>e , the incentive constraint P ( ² i ) η ( f Y + ² i )p r ev en t sFu l l insurance, so P ( ² i )= e + η ( ² i e )[whe rewehavesub s t i tu tedFo r f Y From equation (2)]. Since the equilibrium is symmetric, For ²< e , P ( ² i )= e + η ( ² i + e ). To graph the payments schedule that the contract implies, put P ( ² )on the vertical axis and ² onthehor izonta lax is .Thepaymentsschedu lepasses through the origin, has slope 1 over [ e,e ], and has slope η outside that interval. See gure 6.1. 2. This problem is completely parallel to the problem in the text. There are only two di f erences: the zero-pro t condition For lenders is now N X 1=1 π ( ² i ) P
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 10/21/2009 for the course ECON ECONOMICS taught by Professor Yu-chinche during the Winter '08 term at University of Washington.

Page1 / 13

ch6ans - Foundations of International Macroeconomics1...

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