The economy has two sectors, manufacturing firms and research universities. The two sectors are described by the production functions

Y = K power 1/2 [(1-u)LE] Power 1/2

E = u E

where u is the fraction of labour force in universities (assume u is exogenous).

1. Write the equation of motion of capital, K = sY - K, in intensive form.
2. Write down the steady state condition and find the steady state level of capital per effective worker.
3. Write down the Golden Rule and find the saving rate required to reach the Golden Rule steady state.
4. Suppose the economy is in a steady state and, due to government policies, the value of u increases. What happens to the steady state consumption per worker (compared to the old steady state consumption per worker)?