1 Proving there is a BGP in the Solow Model with technology and population growth Consider the Solow Model with technology and population growth in continuous time. The production function is given by: Y, = A, (K )% (L)' and the law of motion of capital is given by K, = sY, 6K,. The growth rate of technology is given by g4 = %'L =~ and the growth rate of population is given i by g = 7+ =n. 1. 2, =1 What are the endogenous and exogenous variables in the model? Define ky = %+ Find the growth rate of k, as a function of k. AT Ly Draw the growth rate of k; as a function k; and use the graph to prove that k; converges to a steady state (you can follow similar steps as slides 12-13 of the static Solow model lecture) Compute the steady state level of k. Compute income per capita y; = L% as a function of k. Is there a steady state level of output per capita y;? Define g = 1}1/_' A= L, Does ; have a steady state? Does it imply that the economy converges to a Balanced Growth Path (BGP)? . Solve for the growth rate of income per capita on the BGP based on this question. Solve for the level of income per capita on the BGP as a function of parameters and exogenous variables