question archive The economy has two sectors, manufacturing firms and research universities

The economy has two sectors, manufacturing firms and research universities

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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).

-Write the equation of motion of capital, K = sY - K, in intensive form.
-Write down the steady state condition and find the steady state  level of capital per effective worker.
-Write down the Golden Rule and find the saving rate required to reach the Golden Rule steady state.
-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)?

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