Consider the following version of the Ramsey-Cass-Koopmans model with a gov- ernment. The government taxes output at the rate ty taxes labour at the rate TL (a lump-sum tax), provides per capita lump-sum transfers tr and purchases goods and services in the per capita amount g. Production function is Cobb-Douglas (i.e. Y = AK/1-a) with a constant technological progress A. Given this set-up, households maximize utility given by: U = 5 *ucat)eute=at de c(t)- with the utility function u(c(t)) = 1-5 subject to the budget constraint: k = (1 - Ty)Ak TL-C-(n+8)k + tr Assume that actions of government do not affect productivity nor utility. (a) Derive the government's budget constraint (in per capita terms, i.e. g). (b) Derive the first order conditions of households. Assuming that representative household takes ty, TL, tr and g as given. Please, use the current value Hamiltonian (c) Derive an expression characterizing the growth rate of consumption and a steady-state level of capital k. (d) Using a phase diagram explain what happens to k, c (and their steady states) when when government permanently raises TL and g (without changing Ty and tr). a Consider the following version of the Ramsey-Cass-Koopmans model with a gov- ernment. The government taxes output at the rate ty taxes labour at the rate TL (a lump-sum tax), provides per capita lump-sum transfers tr and purchases goods and services in the per capita amount g. Production function is Cobb-Douglas (i.e. Y = AK/1-a) with a constant technological progress A. Given this set-up, households maximize utility given by: U = 5 *ucat)eute=at de c(t)- with the utility function u(c(t)) = 1-5 subject to the budget constraint: k = (1 - Ty)Ak TL-C-(n+8)k + tr Assume that actions of government do not affect productivity nor utility. (a) Derive the government's budget constraint (in per capita terms, i.e. g). (b) Derive the first order conditions of households. Assuming that representative household takes ty, TL, tr and g as given. Please, use the current value Hamiltonian (c) Derive an expression characterizing the growth rate of consumption and a steady-state level of capital k. (d) Using a phase diagram explain what happens to k, c (and their steady states) when when government permanently raises TL and g (without changing Ty and tr). a