1. Assume an output production function Y(t) = A(t)(1 — aL)L(t) and a production function of new ideas A(t) = B[atL”t’AB. Also, assume population grows at rate n. For the simple endogenous growth model, this setup implies gA(t) = 7n9A(t) + (0 — 1)gAW2, where gA(t) is growth rate of knowledge. (a) Why is either 0 < 1 and n > 0 or 0 = 1 and n = 0? Explain. (b) What is the equilibrium growth rate of output (per capita) if 0 = 1 and n = 0? (c) If 0 < 1 and n > 0, steady-state growth of knowledge is =gn. Why, in economic terms, does the steady-state knowledge growth rate increase in -y, n, and 0 (hint: discuss’ in terms of the production functions)? (d) What is the equilibrium growth rate of output per capita if 0 < 1 and n > 0? Explain why.
2. Consider the role of different frictions in explaining why monetary policy shocks have real effects.
(a) In the imperfect competition/menu cost model of nominal rigidity, the flex-price equi-librium relative price is Pa P = where n > 1 is the elasticity of elasticity of demand for good i and 1/(y — 1) is the elasticity of labour supply with 7 > 1. Noting that Yi = Y and = Pin equilibrium, derive an expression for yi in terms of pi – Ebt -y, and q.