Question

Let us consider a Solow growth model in which the aggregate production function

at time t for country i is given by:

Yⁱ_t =Aⁱ(Kⁱ_t)^1-βi(eⁱ Lⁱ_t) ^βi

Where Yⁱ_t is the aggregate real GDP in country i, Kⁱ_t   is the aggregate physical capital in country i, Lⁱ_t     is the aggregate number of workers in country i, eⁱ is the average working time of a worker parameter in country i, Aⁱ >0 is the total factor productivity parameter in country i and βⁱ ∈ (0,1) is the labor share of output parameter in the country i. The equilibrium law of motions of the physical capita per worker from time t to time t+1 in country i can be written as:

                               (1+nⁱ) kⁱ_t+1=yⁱ yⁱ_t +(1- ?ⁱ) Kⁱ_t

where ?ⁱ ∈ (−1, +∞) represents the growth rate of the population of workers parameter in country i, ?ⁱ ∈ (0,1) denotes the investment rate parameter in country i, ?ⁱ ∈ (0,1) is the depreciation rate parameter in country i and ?ⁱ_t denotes the output per worker in country i.

1. Write-down the production function in per worker units at time t for country i and derive the steady-state physical capital per worker and the steady-state real GDP per worker formulas for country i. (please specify if more info needed and what kind of info)

Answer 1

Hope you find the answer useful

please Upvote if you like the answer