Named by the American economists ROBERT DORFMAN (1916-2002), Paul Samuelson (1915- ) and Robert Solow (1924- ); turnpike theory asserts that it is sometimes better to adopt a maximum or near maximum possibility balanced growth-path to allow an economy to move to a more satisfactory state quickly, even if consumption is lower in the interim than at the beginning or end.

An optimal growth theory, turnpike theory was named after the American term for motorway.

Also see: Harrod-Domar growth model, Solow economic growth

Source:

R Dorfman, P A Samuelson, and R Solow, Linear Programming and Economic Analysis (New York, 1958)

## Origins

Although the idea can be traced back to John von Neumann in 1945,^{[1]} Lionel W. McKenzie traces the term to Robert Dorfman, Paul Samuelson, and Robert Solow’s *Linear Programming and Economic Analysis* in 1958, referring to an American English word for a Highway:

Thus in this unexpected way, we have found a real normative significance for steady growth—not steady growth in general, but maximal von Neumann growth. It is, in a sense, the single most effective way for the system to grow, so that if we are planning long-run growth, no matter where we start, and where we desire to end up, it will pay in the intermediate stages to get into a growth phase of this kind. It is exactly like a turnpike paralleled by a network of minor roads. There is a fastest route between any two points; and if the origin and destination are close together and far from the turnpike, the best route may not touch the turnpike. But if the origin and destination are far enough apart, it will always pay to get on to the turnpike and cover distance at the best rate of travel, even if this means adding a little mileage at either end. The best intermediate capital configuration is one which will grow most rapidly, even if it is not the desired one, it is temporarily optimal.

^{[2]}

## Variations

McKenzie in 1976 published a review of the idea up to that point. He saw three general variations of turnpike theories.^{[3]}

- 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.
^{[4]}

## Applications

The theorem has many applications in optimal control and in a general equilibrium 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.^{[5]}^{[6]}

## References

**^**Neumann, J. V. (1945–46). “A Model of General Economic Equilibrium”.*Review of Economic Studies*.**13**(1): 1–9. doi:10.2307/2296111. JSTOR 2296111.**^**Dorfman; Samuelson; Solow (1958). “Efficient Programs of Capital Accumulation”.*Linear Programming and Economic Analysis*. New York: McGraw Hill. p. 331.**^**McKenzie, Lionel (1976). “Turnpike Theory”.*Econometrica*.**44**(5): 841–865. doi:10.2307/1911532. JSTOR 1911532.**^**A review of different variations in the theory can be found in McKenzie, Lionel (1976). “Turnpike Theory”.*Econometrica*.**44**(5): 841–865. doi:10.2307/1911532. JSTOR 1911532.**^**Bewley, Truman (1982). “An Integration of Equilibrium Theory and Turnpike Theory” (PDF).*Journal of Mathematical Economics*.**10**(2–3): 233–267. doi:10.1016/0304-4068(82)90039-8.**^**Yano, Makoto (1984). “The Turnpike of Dynamic General Equilibrium Paths in Its Insensitivity to Initial Conditions”.*Journal of Mathematical Economics*.**13**(3): 235–254. CiteSeerX 10.1.1.295.3005. doi:10.1016/0304-4068(84)90032-6