1.  Derive the Harrod-Domar equation with population growth. Please show all intermediate
steps leading to the final equation.  

2.  Ray, Development Economics. Chapter 3, Exercise 3 on Xanadu.

3.  This is an exercise to understand the Solow Model. Assume an economy has the following
production function: Y = F(K, L) = K^0.4 L^0.6


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

b.  What is the per-worker production function?

c.  If the savings rate is 0.2, population growth rate is 0.03 and the depreciation rate is 0.05,
calculate the steady-state capital stock per-worker, output per-worker, and consumption
per-worker. What is the growth rate of output per-worker in the steady state?

d.  Now suppose the government increases spending, reducing the country’s savings rate to
0.1. Redo the calculations in (c) based upon this change. What is the effect of
government spending on output per-worker and consumption per-worker?

e.  Now suppose the population growth rate increases to 0.04 and the economy was in a
steady state before the population increase. What effect will the increase in the
population growth rate have on the steady state level of capital per-worker? Explain how
the transition to the new steady state will take place. Is the growth rate of output per-
worker in the economy positive or negative during the transition? What about the
growth rate of total output? Once the economy reaches the new steady state, what is the
growth rate of output per-worker?

4. We now introduce labor augmenting technical progress to the Solow Model. Assume an
economy has the following production function, where E is labor augmenting technical
progress: Y = F(K, L) = K^0.4EL^0.6


a.  What is the per-effective worker production function?  
b.  For this economy, the savings rate is 25 percent, the depreciation rate is 5 percent,
the population growth rate is 2 percent, and the technical progress growth rate is 3
percent. Calculate the steady-state capital stock per-effective worker, output per-
effective worker, and consumption per-effective worker.  
c.  What is the growth rate of output per-effective worker, output per-worker and total
output in the steady state?

5.  Ray, Development Economics. Chapter 4, Exercise 1, parts b, c and e.

能解答多少都行，万分感谢：）我在此就不翻译了：）