4. Suppose an economy is described by the Solow model and output is produced using a Cobb-Douglas production function: Y, = Kp(AL)'" In per worker terms the production function can be written as: E Et A'Ifa L, Ly : Assume that = 0 and therefore A can be normalized to 1. Suppose the savings behavior is different from what we assumed in class. In particular, below a minimum level of output per Worker,& people cannot save at all because all of the income is used for survival. Above this income level, people are saving a constant fraction of additional income earned beyond%&. (a) Show what this means for the evolution of the capital stock per effective worker if output is below%i. (b) Show graphically that in this economy it is (technically) possible to have one, two or three different steady states. For each of the steady states that you identify (in each of the three cases) briefly discuss if the steady states are (locally) stable