Question 4 Endogenous Growth Model The production function for a representative rm i is Yi = Ki\"(ALi)1_\". A represents the level of knowledge in the economy and is perfectly linked to the level of capital in the economy, K. Markets are competitive and there is no depreciation of capital. Households maximize their utility, resulting in the following consumption growth: c'/c = 1/ B[r - p] and accumulate assets according to their budget constraint: 3' = w + ra i c. a) [5pts] Write down the representative firm's prot maximization problem rewriting the production function in terms of the level of capital in the economy K and in per-capita terms. Determine r and w. b) [5pts] Assuming that all the firms are the same, what is the equilibrium K? Rewrite to show that this is an AK model and describe any implications on growth rates. c) [5pts] Continue assuming all the rms are the same, obtain the equilibrium r. What would be the equilibrium consumption growth rate and the capital law of motion? (1) [5pts] Intuitively, is this consumption growth optimal? Explain why it is or why not