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An economy has constant returns to scale production function given by ????????= ????????????????????????????????1−????????, where Y is total output, K measures total capital in the economy, L is the total amount of labor, and A>0.

a) Derive a mathematical expression for the steady-state capital-labor ratio.

b) Derive a mathematical expression for the steady-state level of output per capita.

c) Derive a mathematical expression for the steady-state level of replacement investment

d) Draw the steady-state for the above economy on a diagram clearly labeling the quantities you have derived in parts (a)-(c).

e) Assume ???????? = 0.5. Using the growth accounting method discussed in class, calculate the change in the steady-state output per capita if the savings rate increases by 50% and the total factor productivity parameter decrease by 10%. Assume all else remains unchanged.

f) Assume ???????? = 0.5. Using the growth accounting method discussed in class, calculate the change in the steady-state capital-labor ratio if the savings rate increases by 50% and the population growth rate decreases by 10%. Assume all else remains unchanged.

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