Suppose the production function is given by Y = K ^1 2 N ^1 2 where Y is the aggregate income, N the workforce and K is the capital stock. The workforce is constant and the capital stock evolve as Kt+1 Kt = sYt Kt where s is the savings rate and the depreciation rate. a. Define the steady state allocation. Find the steady-state capital stock per effective worker and output per effective worker as a function of s, and . b. Assume that = 2% . Find the output per worker and consumption worker in the steady state for s = 10%. c. Assume the economy is at the steady state. Following an earthquake, half of the capital is lost. Is the economy at the steady state right after the shock? is the steady state altered by the shock? d. Assume the economy is at the steady state. Due to an increasing level of uncertainty, people start to save more, such that s = 50% . Is the economy at the steady state right after the shock? is the steady state altered by the shock?