Turnpike theory refers to a set of
economic
An economy is an area of the production, distribution and trade, as well as consumption of goods and services. In general, it is defined as a social domain that emphasize the practices, discourses, and material expressions associated with the ...
theories about the optimal path of accumulation (often
capital accumulation) in a system, depending on the initial and final levels. In the context of a
macroeconomic
Macroeconomics (from the Greek prefix ''makro-'' meaning "large" + ''economics'') is a branch of economics dealing with performance, structure, behavior, and decision-making of an economy as a whole.
For example, using interest rates, taxes, and ...
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 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 powers ...
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
John von Neumann (; hu, Neumann János Lajos, ; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was regarded as having perhaps the widest cove ...
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 paper†...
,
Paul Samuelson
Paul Anthony Samuelson (May 15, 1915 – December 13, 2009) was an American economist who was the first American to win the Nobel Memorial Prize in Economic Sciences. When awarding the prize in 1970, the Swedish Royal Academies stated that he " ...
, and
Robert Solow
Robert Merton Solow, GCIH (; born August 23, 1924) is an American economist whose work on the theory of economic growth culminated in the exogenous growth model named after him. He is currently Emeritus Institute Professor of Economics at the ...
'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 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 ov ...
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