Turnpike theory refers to a set of
economic theories about the optimal path of accumulation (often
capital accumulation
Capital accumulation is the dynamic that motivates the pursuit of profit, involving the investment of money or any financial asset with the goal of increasing the initial monetary value of said asset as a financial return whether in the form o ...
) in a system, depending on the initial and final levels. In the context of a
macroeconomic exogenous growth model
In a variety of contexts, exogeny or exogeneity () is the fact of an action or object originating externally. It contrasts with endogeneity or endogeny, the fact of being influenced within a system.
Economics
In an economic model, an exogeno ...
, for example, it says that if an infinite optimal path is calculated, and an economic planner wishes to move an economy from one level of capital to another, as long as the planner has sufficient time, the most efficient path is to quickly move the level of capital stock to a level close to the infinite optimal path, and to allow
capital
Capital may refer to:
Common uses
* Capital city, a municipality of primary status
** List of national capital cities
* Capital letter, an upper-case letter Economics and social sciences
* Capital (economics), the durable produced goods used fo ...
to develop along that path until it is nearly the end of the desired term and the planner must move the capital stock to the desired final level. The name of the theory refers to the idea that a
turnpike
Turnpike often refers to:
* A type of gate, another word for a turnstile
* In the United States, a toll road
Turnpike may also refer to:
Roads United Kingdom
* A turnpike road, a principal road maintained by a turnpike trust, a body with powe ...
is the fastest route between two points which are far apart, even if it is not the most direct route.
Origins
Although the idea can be traced back to
John von Neumann in 1945,
Lionel W. McKenzie traces the term to
Robert Dorfman
Robert Dorfman (27 October 1916 – 24 June 2002) was professor of political economy at Harvard University. Dorfman made great contributions to the fields of economics, statistics, group testing and in the process of coding theory.
His pape ...
,
Paul Samuelson, and
Robert Solow's ''Linear Programming and Economic Analysis'' in 1958, referring to an American English word for a Highway:
Variations
McKenzie in 1976 published a review of the idea up to that point. He saw three general variations of turnpike theories.
*In a system with a set initial and terminal capital stock where the objective of the economic planner is to maximize the sum of utilities over the finite accumulation period, then so long as the accumulation period is long enough, most of the optimal path will be within some small neighborhood of an infinite path that is optimal. This often implies that
** If a finite optimal path starts on (or near) the infinite path, it hugs that path for most of the time, regardless of the desired capital stock at the end.
** The theorem also generalizes for infinite paths, where the basic result is that optimal paths converge to each other, regardless of initial capital stocks.
Applications
The theorem has many applications in
optimal control
Optimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering an ...
and in a
general equilibrium
In economics, general equilibrium theory attempts to explain the behavior of supply, demand, and prices in a whole economy with several or many interacting markets, by seeking to prove that the interaction of demand and supply will result in an o ...
context. In general equilibrium, the variation which involves infinite capital accumulation paths can be applied. In a system with many infinitely lived agents with the same (small) discount rates on the future, regardless of initial endowments, the equilibrium allocations of all agents converge.
References
{{Reflist
Economic growth
Macroeconomic theories