Consider the Malthusian Growth Model. The production function is Y = LaN 1-a, where L is fixed stock of land, N is current population, and 0 < a < 1 . The population follows the following dynamics N=Ncb , where N is next period population, c is current consumption per capita, and 0 < b < 1.

(a) Find the size of population in steady state.

(b) Suppose a natural disaster kills half of the steady state population. What happens to population and per capita consumption in the short run? In the long run?