Consider a hypothetical economy that has the production function Y = F(K, LE) = K^1/3(LE)^2/3, where Y is output, K is capital, and LE is the number of effective workers. Suppose the saving rate is 20%, the capital depreciates by 3%, the population grows at the rate of 1%, and the rate of labor-augmenting technological change is 1%.

a. Solve for the per-effective-worker production function. 

b. At what rate (%) do the following grow in the steady state? 

i. Total output 

ii. Output per worker 

iii. Output per effective worker 

iv. Real rental price 

v. Real wage 

c. Find the steady-state level of capital per effective worker, output per effective worker, and consumption per effective worker.