1. (20 percent) Consider the following production function:

Y = K^0.5(AN)^0.5

where both the population and the pool of labour are growing at a rate n = 0.07, the capital stock is depreciating at a rate d = 0.03, and total factor productivity A is normalized to 1.

1. Find the elasticity of output with respect to labour and the elasticity of output with respect to capital.
2. Rewrite the production function in per worker form (i.e. y = f(k) ).
3. Find the steady-state values of k and y when the saving rate s = 0.20.
4. At what rate is per capita output growing at the steady-state? At what rate is total output growing?