Physical Capital in Dual Economies

Abstract

In this chapter we shift attention to industrialization and economic growth in dual economies. We focus again on the consequence of missing land markets, a common characteristic of developing economies that was documented in the previous chapter. Here we examine the connections between land ownership, saving, and physical capital formation.

Appendix

Here are a few notes about solving for the dynamic path of the model from Sect. 8.2. The transition equation given by (8.23) can be written out in terms of wages and capital intensity,

$$ {\displaystyle \begin{array}{ll}& {\widehat{k}}_{t+1}\\ {}& =\frac{\beta {w}_t}{\left(1+\beta \right)\left(1+d\right)n}\left[\frac{\frac{{\overline{N}}_t+{\tilde{N}}_t}{N_t^{\ast }}+\frac{1-\overline{\alpha}-\alpha }{\overline{\alpha}}{\left(\frac{\overline{\alpha}{\widehat{k}}_t^{\alpha }}{w_t}\right)}^{\frac{1}{1-\overline{\alpha}}}}{1+\frac{1}{1+\beta}\frac{\overline{\alpha}}{1-\alpha}\frac{{\left(\frac{\left(1-\alpha \right){p}_{t+1}}{w_{t+1}}\right)}^{1/\alpha}\left(\mathrm{L}/{D}_{t+1}\right)}{{\overline{N}}_{t+1}+{\tilde{N}}_{t+1}\kern0.5em -\kern0.5em {\left(\frac{\left(1-\alpha \right){p}_{t+1}}{w_{t+1}}\right)}^{1/\alpha}\left(\mathrm{L}/{D}_{t+1}\right)}}\right].\end{array}} $$

(8.23)

Given an initial value for ${\widehat{k}}_t$, one can use (8.21) to solve for w_t. Next, given the values for ${\widehat{k}}_t$ and w_t, use (8.21), updated one period, and (8.23) to solve simultaneously for ${\widehat{k}}_{t+1}$ and w_t+1.

It is important to note from (8.21) and (8.23), that the split of the population across migrant workers and farmers does not affect the equilibrium determination of the capital stock or wages (${\overline{N}}_t$ and ${\tilde{N}}_t$ only appear together as a sum). In the numerator of (8.23), the farmers and migrants can be aggregated because they receive the same wage. In the denominator, the supply of farmers and migrants minus the farm demand for labor determines the equilibrium employment of unskilled labor in the urban sector (see 8.21). More unskilled labor in the urban sector lowers the capital to unskilled labor ratio and the wage-interest rate ratio (see 8.17a, 8.17b, 8.17c). A lower wage-interest rate ratio lowers the present value of land rents relative to wages, thereby increasing the saving of farmers and capital formation (see Problem 7 for more details).

The fact that ${\overline{N}}_t$ and ${\tilde{N}}_t$ only appear together as a sum is important because ownership claims on land in the early stages of development are unclear and it is difficult to determine what fraction of the population were migrant workers and what fraction earned some land rent. In addition, note that the capital stock and factor prices can be determined independently of the composition of output between manufacturing and agricultural goods (i.e. 8.21, 8.22, and 8.23) are independent of χ).