Question

Consider an economy where two types of goods are produced: final goods, denoted Y_t, and new ideas, denoted A_t. The total workforce is constant and denoted L, and a share, λ, of all workers are researchers, producing new ideas. All other workers are employed in production under the following linear technology:

Y_t = A_tL_Y,

where L_Y is the number of workers employed in production of the final good. Production of new ideas is governed by

∆A_t+1 =ψA_tL_A,

where ψ is a productivity parameter and LA is the number of workers employed in research.

A. Solve for the growth rates of A and GDP per capita, y ≡ Y/L, in this model.

B. Solve for the level of output per capita as a function of the initial stock of knowledge, A₀.

C. Suppose that λ = 0.08, ψ = 1/4000 and L = 1000. The initial stock of knowledge, A₀, is 1000. Compute GDP per capita at the starting date, i.e. y₀, as well as ten years on, i.e. y₁₀.

Please provide an answer for A, B and C.

Answer 1

Yeo Grod At denoted b犭 At LY

(Aら、 ㄩ Thus

Nou, 거20: A20 (12)L Atti - o.og zo.02.

20=. A20 C 20ワ 6 0 20