Consider the Solow growth model. Suppose that the production function is constant returns to scale and it is explicitly given by: Y = K^(a)*L^(1-a)

a. What is the level of output per capita, y, where y = Y/L?

b. Individuals in this economy save s fraction of their income. If there is population growth, denoted by n, and capital depreciates at the rate of over time, write down an equation for the evolution of capital per capita, k, k = K/L over time, denoted by k

c. On a Solow diagram show the steady state levels of k, y, c and i.

d. Assume that the country is in its steady state. Explain what happens if half the population dies due to a contagion. Illustrate your answer on a Solow diagram