Cnsider the following production functiony fk l

Question

Consider the following production functionY = F(K, L) = A[αKρ + (1 - α)Lρ]1ρ ,where K stands for capital and L for labor.

(b) Find and expression for output per capita in terms of capital per capita.

(c) If α = 0.3, ρ = 0.5, A = 2 and capital per capita is equal to 1.5, what is output percapita?

(d) Suppose capital per capita increases 20%, how much will increase output per capita?

(e) If the government wants to achieve a 10% increase in output per capita, how much wouldhave to increase total factor productivity (A) given the capital increase in part 3d