Question

1. (The AK Model) Consider an economy with an aggregate production function given by Y=F(K) = AK of capital. The law of motion for capital is just as in the neoclassical model where s and δ are the savings rate and depreciation rate, respectively. a) Show whether F(K) exhibits constant, decreasing or increasing returns to scale. Com pute the marginal product of capital. Does this function satisly the neoclassical assumptions?

Answer 1

Y = F(K) = AK K = SY - SK F(K) = A K F(lambda K) = A(lambda K) F(lambda K) = A lambda K = 0 lambda (A K) It exhibit constant return to scale dy/dk = A = > marginal product of capital is constant Neoclassical = > Diminishing return of capital But the key property of AK endogenous-growth model is the absence of diminishing return of capital. If uses Linear model so it does not satisfy the Neo-classical assumption