A changing land share. 12 In Section 8.3.3 we mentioned the role of structural transformation in contributing to sustained growth. Consider an economy that produces two goods, an agricultural good and a manufacturing good. An amount YA of the agricultural good can be produced using land and labor according to YA = Xb(ALA)1-b, (1) where b 6 1. An amount Ym of the manufacturing good can be produced using labor only; no land is required: YM = ALM. (2) Assume that both these production functions benefi t from the same technological progress, A. Finally, the economy faces a resource constraint for labor, LA + LM = L. For simplicity, assume that the price of the agricultural good in terms of the manufacturing good is one, so that total GDP in the economy is Y = YA + YM.

(a) Defi ne s = LA>L as the fraction of the economy’s labor force that works in agriculture. Assume that A and L are constants. What is total GDP in the economy, as a function of the allocation variable s and the exogenous parameters

b, X, A, L?

(b) Find the allocation s* that maximizes total GDP.

(c) What happens to s* if A and L increase over time?

(d) Let the price of land Px be given by the value of its marginal product. What happens to land’s share of GDP, Px X>Y, if A and L increase over time?