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This paper is a revised version of Chapter 3 of my PhD dissertation [Gerson (1993)]. I thank my advisors, M. Ali Khan and Louis J. Maccini, for their assistance. I also thank Stephen Blough, William Carrington, and Se-Jik Kim for their comments on earlier drafts.
Upadhyay (1993) employs a related functional form for the production of education in order to generate increasing returns to scale in that sector.
Implicitly, this functional form assumes an instantaneous depreciation rate of 1 for new knowledge or for networking effects from the newly educated. It may be worth emphasizing that new knowledge in this model effects the physical production process for consumption goods itself, rather than, for example, encouraging the production of consumption goods through a shift in demand.
The assumption of a fixed educated wage is made for analytical convenience. Chapter 2 of Gerson (1993) examines a similar model where the educated wage is endogenous (but long-run educated unemployment persists because firms face a turnover cost when educated workers quit) and obtains results similar to those of this paper. An alternative explanation for the persistence of educated unemployment could, for example, be that firms and workers lack information about supply and demand conditions in specialized markets for educated labor. It may also be worth noting that although the educated wage is fixed, individuals’ decisions in the model depend on the expected lifetime incomes of the educated, which are endogenous because of educated unemployment.
Although human capital-based models of growth are a relatively recent phenomenon, the implications of education and training for economic growth were clear to the classical economists. In fact, the spirit of the equilibrium condition used in this paper can be attributed to Adam Smith, who noted
The wages of labour vary with the easiness and cheapness, or the difficulty and expence of learning the business. When any expensive machine is erected, the extraordinary work to be performed by it before it is worn out, it must be expected, will replace the capital laid out on it, with at least the ordinary profits. A man educated at the expence of much labour and time to any of those employments which require extraordinary dexterity and skill, may be compared to one of those expensive machines. The work which he learns to perform, it must be expected, over and above the usual wages of common labour, will replace to him the whole expence of his education, with at least the ordinary profits of an equally valuable capital.
(Smith (1976), pp.113-114.)
With a positive determinant, the product of the three roots must be positive. With a negative trace, the sum of the roots must be negative. These two conditions imply that model has two negative roots and one positive root, or that the convergent subspace is two-dimensional. If the trace of the matrix is positive, it is not possible to determine whether the model is globally unstable or features a saddle plane.
In fact, it may be the case that since universities usually deduct a fraction of faculty research grants for overhead, government-sponsored faculty research serves as one form of such a transfer.
The effects of alternative tax regimes on the long-run equilibrium of the economy could be an interesting area for additional analysis.
For example, in many African countries the higher education sector is relatively small, with many students studying at government expense in foreign universities. In addition, education in many developing countries may be less capital intensive than in more developed countries because schools are less likely to have large investments in libraries, laboratories, audio-visual equipment, etc.