2 Endogenous Growth Model (Public Goods) Consider the growth model where firms have the linear production function y = Ak, where A > 0, k is capital per capita and y is output per capita. There is no population of growth and the size of the population is equal to one. Assume that government expenditures are g, a fixed fraction of output, which are enjoyed by the citizens. Assume that capital doesn't depreciate. Infinitely lived households maximizes the following utility: with > 0. a) Assuming a perfect competition framework in the market for production factors, derive the expression for the interest rate and the wage rate. b) Set up the representative household's optimization problem. What is the Hamiltonian? c) Derive the Euler equation. d) What is the growth rate of consumption, capital, and output at the steady state? e) Would the household optimization problem change if the tax was on capital gains? Write the new budget constraint and explain if this tax would be distortionary or not. No need to derive the model again, just briefly explain. f) In which cases will solving for the social planner problem lead to a different result than solving for an individual