Question

# The markets are perfectly competitive and the prices are perfectly

flexible, so that the markets are balanced in the economy, that is to say Ldt = Lst = lNt and Tdt = Tst = T on each date t. Firms reinvest a constant part of the value of their output s so that equation fundamental dynamics of Solow (with a general production function) is written: Kt + 1 = sF (Kt, AtLt, T) + (1 - δ) Kt and the investment is written It = ∆Kt + δKt. 1-After having reintroduced the Cobb-Douglas production function in Solow's fundamental dynamic equation, rewrite the latter in variables per worker so as to describe the evolution of capital per worker as a function of the parameters of the economy, but also of land per worker . 2-Deduce the dynamic equation for the rate of growth of per capita capital . 3- ) *Define the notion of regular state. *What is the steady-state equilibrium growth rate of physical capital per worker (depending on the rate of technical progress g and the rate of population growth n which we will assume positive n&gt; 0 for the interpretations)? -Note: follow the same methodological approach as that of the course . 4-) *Deduce the growth rate of per capita GDP at regular state *Interpret precisely the sign of the growth rate as a function of each of the parameters involved  