a). Suppose that Y=AK^{∝}L^{1-∝ }where A is a measure of the level of technology called "total factor productivity." Assume that capital's share 40%, output grows at 3%, capital grows at 2.5% and labour grows at 2%.

i. Calculate the growth of total factor productivity.

ii. What is another name for the growth rate of total factor productivity?

b). Would a policy maker choose a steady state with more capital than in the golden rule steady sate? With less capital than in the golden rule steady sate? Explain your answers.

c). In the Solow model, how does the saving rate affect the steady-state level of income? How does it affect the steady-state rate of growth?

d). Assume that the aggregate production is given by:

Y=∜(K(EL)^3)

where Y is aggregate output, K is capital, L is the number of workers in the economy and E is the state of technology. Further assume that capital depreciates at a rate of *δ*, the rate of technological progress is g, the population is growing at a rate of n and the saving rate is s.

i. Determine the scale of production?

ii. Suppose capital is increased by a factor of 16, 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 level of 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.