1. Consider a modied version of the Solow Growth Model in which there is a represen- tative Laborer (L), a representative nancier (F), and a representative rm. The total population of the economy evolves according to NtH = {1 +93le1 where as: is the population growth rate. The laborer represents an exogenously given fraction 3; E (0, l) of the total population N c at date it. She supplies her labor inelastically to the representative rm each period, but is not allowed to invest in capital. Her budget constraint is Cf\" = 10,6,N, where w, is the real wage and CE is her consumption at date if. The nancier represents the remaining fraction (1 9;) of the total population N; at date t. She owns the capital stock and invest a fraction 5: E [0,1] of her income each period in new productive capital, but is not allowed to work. Her budget constraint is 03F 'i- I: = '1"er and her capital accumulation equation is Kt+1= 1: +Kt{1 5:)- where r, is the rental rate, 5, E (0, 1) is the depreciation rate, K1 is the capital stock, and Cf is her consumption at date t. The representative rm is competitive and has access to the production technology Y: = z=(K:')\"{N:')1'\" where Kf' and Nf' are capital and labor employed in the production process, respec- tively, z: > G is total factor productivity, and a E (0,1). (a) What is the policy rule of the laborer? (b) What are the policy rules of the nancier? (c) Use the problem of the representative rm to derive expressions for the rental rate, rt, and the wage rate, wt. (d) What are the market clearing conditions? (e) Prove that, in a competitive equilibrium, the change in capital per capita is gov- erned by the following equation: 1 55'; Akt,t+l E k+1 kg : 1 sgazgkfra (112'; + 6Jk}, where k: E Kg/Ng. Explain each step in your proof. (f) Derive an equation for the steady state level of capital per capita, it", and one for the steady state level of real GDP per capita, y'. (g) In recent years, the concentration of wealth in developed, market economies has increased dramatically. Through the lens of our model, we can think about an increase in the concentration of wealth as an increase in the fraction of laborers relative to nanciers (i.e. 6 T). Analyze the implications of this exogenous shock on the steady state levels of capital per capita, real GDP per capita, consumption per laborer, and consumption per nancier. Assume all exogenous variables are constant in steady state. Is an increase in 6 \"good\" for nanciers? Is an increase in 0 \"good\" for laborers? Explain your reasoning