Assume a production function that takes a CobbDouglas form in capital K, labour L, and land C:
Yt = AtKtαLβ t Cλ,
where technology grows at a constant rate, γA > 0, α > 0, β > 0, λ > 0, L > 0, and α+β +λ = 1. The amount of land, C, is xed. Labour grows at the constant rate n > 0, capital depreciates at rate δ > 0, and the saving rate is exogenously given at the level of s. Answer these questions:
(a) Write the law of motion for capital dynamics.
(b) Determine the steady state.
(c) What is the long-run growth rate of capital, capital per unit of labour and capital per eective labour? Are corresponding growth rates for labour the same?
(d) How do these results compare to those of Solow-Swan model without land?