Suppose the utility function of representative consumer is given by U=∫₀[infinity](c¹⁻σ)/(1-σ)e⁻rhoᵗ , where c is the per capita consumption. Suppose the individuals in this where c is the per capita consumption. Suppose the individuals in this economy is endowed with 1 unit of time. The fraction of time allocated for production is u and (1-u) is the fraction of time allocated for skill accumulation. Also suppose that in this economy entire production is consumed and hence there is no physical capital accumulation.
Construct the optimization problem of competitive economy and command economy clearly explaining the difference between the two. Find out equilibrium and optimal
solution of u and compare the equilibrium and optimal growth rates foro = 1.