Endowment effects on rental rates and supply The differential of (2.48), (2.49), and (2.50) with respect to en- dowments, can be shown to yield the following expressions: ˜ w = ε w p s ε P L ˜ L + ε P K ˜ K + ε P H ˜ H ˜ r = ε r p s ε P L ˜ L + ε P K ˜ K + ε P H ˜ H ˜ Y j = ε Y j p s ε P L ˜ L + ε P K ˜ K + ε P H ˜ H + ε Y j L ˜ L + ε Y j K ˜ K, j = m, s ˜ Y a = ε Y a w ˜ w + ε Y a r ˜ r each of which show the indirect effects of changes in endowments on factor rental rates and supply. Here, we utilize the endowment components of the home-good price equation (2.44). Consider the case where manufacturing is the most capital intensive sector while the home-good sector is the most labor intensive. Then ε Y m K , ε Y s L > 0 , and ε Y m L , ε Y s K < 0. For this case, as stated above, the elasticity ε P K is positive, and ε P L is nega- tive. Now, for purpose of the growth models presented in future chapters, consider the additional condition that growth in the capital stock exceeds the growth in labor, ˜ K > ˜ L. In this en- vironment, the net effect of labor and capital accumulation on growth in the price of the home-good is positive, ˜ p s > 0. Under these circumstances, w increases and r falls. This result implies an increase in the productivity of labor as the capital to
40 2. The Preliminaries labor ratio increases over time, while the productivity of capital falls. Manufacturing output is affected negatively by the indirect effect of an increase in the home-good price, as determined by ε Y m p s ε P L ˜ L + ε P K ˜ K . Output is affected by Rybczynski effects, one of which is negative, ε Y m L ˜ L, and other positive ε Y m K ˜ K. Since manufacturing is capital intensive, it is possible for the capital effects to dominate. The home-good sector output is affected in almost the oppo- site way. The home-good price effect ε Y s p s ε P L ˜ L + ε P K ˜ K is pos- itive, while the net factor accumulation effect, as determined by ε Y j L ˜ L + ε Y j K ˜ K can be negative. However, the net price effect can dominate the factor accumulation effect so that growth in disposable income leads to increased consumption of the home- good, albeit at a higher price of the home-good. In this way, the home-good is competing for resources allocated to the pro- duction of traded goods so that the price ratio of traded to home-goods falls. The effect on agricultural output once again depends on not only the magnitude of changes in w and r, but also on the sec- tor’s relative factor intensity. Changes in agricultural output, and the employment of labor and capital need not be mono- tonic as the labor and capital variables evolve over time. Although most of the comparative static results in this sec- tion are ambiguous, all of the effects discussed above can be measured when a structural model is fit to data. Knowledge of these effects is crucial to explaining the evolution of a modeled economy.
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