homework10

# homework10 - ECO 475 Homework 10 Jay H Hong Due Dec 2 2009...

This preview shows pages 1–2. Sign up to view the full content.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ECO 475 Homework 10 Jay H. Hong Due: Dec 2, 2009 1 More on Lucas Tree Now consider the Lucas tree model with some modifications. News arrives at time-zero unexpectedly that a fraction χ of existing trees will die at the beginning of date T (before dividends are paid). This is one time unexpected shock in the sense that the remaining trees live forever if survive. We call a tree which dies at T a type A tree and a tree that lasts forever a type B . All trees give a constant stream of dividend, ¯ d , when alive. (1) Assume that the lifetime of each type of tree (either T or ∞ ) is also announced at date zero. What is the price of a type A tree ( P A,t ) for each t (0 ≤ t ≤ T )? (2) At T , type A tree dies. Therefore there will be only type B tree in the economy. What is the price of fruit at time T ? (This fruit comes from type B tree, of course.) (3) What is the price of a type B tree ( P B,t ) in each t ? ( Hint: For type B tree, its dividend stream is unchanged. However, its share price (price of tree) will be affected because the price of fruit is changed.) (4) Now assume that the dead trees (type A ) will be replaced, instantaneously, by equally many new, better trees (without any cost). New trees yield (1 + z ) ¯ d – more fruits than old trees ( z > 0). Assume that the share of better tree can be traded after T . Calculate the stock market’s value for every t before and after T . (The stock-market value is a weighted average of the value of trees.) 2 Economy with Two types of Agents...
View Full Document

## This note was uploaded on 09/06/2011 for the course ECO 475 taught by Professor Hong during the Fall '07 term at Rochester.

### Page1 / 3

homework10 - ECO 475 Homework 10 Jay H Hong Due Dec 2 2009...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online