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Copyright © The Author 2007. Published by Oxford University Press.
The 1956 contribution to economic growth theory by Robert Solow: a major landmark and some of its undiscovered riches
* University of Geneva, e-mail: olivier.delagrandville{at}ecopo.unige.ch
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Abstract |
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The famous ‘1956’ contribution by Robert Solow was always thought to be central to positive, or descriptive, economic growth theory. We show that it is also at the core of optimal growth, because the Fisher equation of competitive equilibrium is nothing short of an Euler equation; it corresponds to the maximization of the sum of discounted consumption flows. From this equation an optimal savings rate results with reasonable, very reachable values. We also show the importance of the elasticity of substitution: there is a threshold value of this parameter leading to a permanent growth rate of income per person that is above the labour-augmenting rate of technical progress, and that rate does depend upon the investment–saving ratio.
Key Words: economic growth • competitive equilibrium • Euler equation • optimal economic growth • elasticity of substitution
1 On this see Hardy et al. (1952). The fact that the harmonic, the geometric, and the arithmetic means are in increasing order is just a particular illustration of the property (their orders are –1, 0, and 1, respectively).
2 See La Grandville (1989) and Klump and La Grandville (2000).
3 The complexity of the second derivative of the general mean does not seem to allow for an analytical proof.
4 This conjecture was successfully tested by Yuhn (1991).
5 See La Grandville and Solow (2006).
6 This result is not limited to the case of analysis in real terms in a risk-free world, but is perfectly general: if p(t) is the time path of the price level, and if 
(z) is the economy's risk premium, maximizing the functional 
leads to an integrand 
which is also affine in 
, and thus to an Euler equation which yields, after simplifications, the Fisher–Solow equation 
, where i(t) is augmented by the risk premium (t).
7 Supposing that i, n, and g are constants, it can be shown that 
is equal to
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| (8) |
1, and
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| (9) |
= 1.
The result mentioned in the text is obtained by computing the ratio 
(see La Grandville, 2007).
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