Endowment effects on rental rates and supply The differential of 248 249 and

Endowment effects on rental rates and supply the

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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
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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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