Assume that the aggregate production function is given by: Y = 3square rootK(EL) 2 ( Raised to the power 2) where Y is aggregate output, K is capital, L is number of workers in the economy and E is the state of technology. Further assume that capital depreciates at a rate of delta, the of technology rate progress is g, the population is growing at a rate of n and the savings rate is s.

i) Determine the scale of production

ii) Suppose capital increased by a factor of 8, while effective labour is held constant. What would be the effect on output? What does this imply about returns to capital.

iii) What is the investment per effective worker in this economy?

iv) What is the investment per effective worker needed to maintain a constant level of capital per effective worker?

v) Solve for the steady state levels of capital per effective worker and output per effective worker.

vi) Analyse what happens to the steady state values of capital if capital's share falls

vii) Analyse what happens to the steady state values of capital if workers exert more effort.