2 Problem 2 (25 points) Imagine an economy with a production function Y = KL1. Consumption is equal to C = (1 s)Y and the savings rate is s = 1 4. The rate of population growth is n = 3% and the depreciation rate is = 5%. 1. Write down an expression for output per capita y. 2. Derive the fundamental equation of Solow-Swan starting from the National Income Identity (Y = C + I, where I represents investment). 3. Imagine that = 0.5. In the long run, what is the growth rate of output per capita y? In the long run, what is the growth rate of total output Y ? 4. In the long run, does this economy reach a constant level of capital per capita k, output per person y and consumption per capita c? If so, what are their values? If not, why not? 5. Imagine that the depreciation rate increases from 5% to 10%. If the economy is initially at its steady state, what are the effects on the level and growth rates of k, y and c in the long run?