Stochastic Capital Theory I. Comparative Statics

William A. Brock, Michael Rothschild, Joseph E. Stiglitz

NBER Technical Working Paper No. 23
Issued in May 1982
NBER Program(s):   ME

Introductory lectures on capital theory often begin by analyzing the following problem: I have a tree which will be worth X(t) if cut down at time t. If the discount rate is r, when should the tree be cut down? What is the present value of such a tree? The answers to these questions are straightforward. Since at time t a tree which I plan to cut down at time T is worth e[to the power of rt]e[to the power of ?rT]X(T), I should choose the cutting date T* to maximize e[to the power of -rT]X(T); at t < T* a tree is worth e[to the power of rt]e[to the power of -rT*]X(T*). In this paper we analyze how the answers to these questions of timing and evaluation change when the tree's growth is stochastic rather than deterministic. Suppose a tree will be worth X(t,w) if cut down at time t when X(t,w) is a stochastic process. When should it be cut down? What is its present value? We study these questions for trees which grow according to both discrete and continuous stochastic processes. The approach to continuous time stochastic processes contrasts with much of the finance literature in two respects. First, we obtain sharp aomparative statics results without restricting ourselves to particu,ar stochastic specifications. Second, while the option pricing literature seems to imply that increases in variance always increase value, we show that an increase in the variance of a Tree's growth has ambiguous effects on its value.

download in pdf format
   (1568 K)

email paper

Machine-readable bibliographic record - MARC, RIS, BibTeX

Document Object Identifier (DOI): 10.3386/t0023

Published: pp. 591-622, 1989. MacMillan Press: LOndon. Joan Robinson and Modern Aconomic Theory

Users who downloaded this paper also downloaded these:
Brock and LeBaron Liquidity Constraints in Production-Based Asset-Pricing Models
Stiglitz w0632 Self-Selection and Pareto Efficient Taxation
Stiglitz w0678 Information and Capital Markets
Stiglitz w1442 Theories of Wage Rigidity
NBER Videos

National Bureau of Economic Research, 1050 Massachusetts Ave., Cambridge, MA 02138; 617-868-3900; email:

Contact Us