Question 1. An economy has the following production function:

Y = K^1/2(LE)^1/2

Some more additional details known about the economy:

The savings rate (s) is equal to 0.3

The population growth rate (n) is equal to 0.02.

The rate of growth of technology (g) is 0.03.

Depreciation rate () is at 0.05.

(a) Does this production function have constant returns to scale? Explain.

(b) Derive the function of output per effective worker in terms of capital per effective worker.

(c) Find the steady state levels of capital per effective worker, output per effective worker and the marginal product of capital.

(d) If the output per effective worker is constant in the steady state, what does it imply about the growth rates of output per worker and the total output? Explain.

(e) Using your answer from part (c), determine whether the steady state capital per effective worker is at Golden Rule level. How do you know?

(f) What are some of the policies governments can enact to increase the nation's savings rate?

(g) Assume that the government successfully brought the savings rate up to 0.4. Would such an increase be enough to take the economy to the Golden Rule level? Explain