1 show using equations that the cobb douglas production

Question

1. Show using equations that the Cobb Douglas production function has...

• Constant returns to scale
• Positive but declining marginal products of capital and labor
• That α and (1-α) are the share of output going to capital and labor

2. A Solow economy has a production function y = 4 k^1/3.  If k = 27

a. What is output (y) per worker?

b. If  s = saving and investment rate = .20, d  = depreciation rate = .05, and labor force growth n = 0, what are steady state k*, y*, and consumption c*?

c. If labor force growth rises from 0 to .05 a year, what are steady state k*, y*, and c*?

d. If labor force growth = .05 but s rises to .5, what are steady state k*, y*, and c*?

e. If d = n = .05, what saving rate s maximizes steady state consumption?  What are steady state k*, y*, and c* for this golden rule s?

3. Draw a diagram with y on the vertical axis and k on the horizontal axis to show your answers to 2 a, b, c, and d.  You can use a 2^nd diagram if the 1^st one gets too crowded.  Explain everything, either in this question or in 2.

4. What does the Solow model say about the following?  Explain why.

a. The importance of improving technology on long term economic growth?

b. The effect of labor force growth on growth in GDP and per capita GDP?

c. The effect of increasing the saving rate on per capita GDP in the short term and long term for a country not at its steady state?

d. Use a diagram with y and k on the axes to explain your answers.

5. Inequality

a. Draw and explain a Lorenz curve.  Label both axes.

b. What is a Gini coefficient?

c. What is the Gini coefficient for the US?

d. Draw a diagram showing the US Gini coefficient since about 1920.

e. Which continent is the most unequal?

f. Which countries are the most equal?

6. Draw a diagram showing changes in the world's Gini coefficient since 1750.  What explains the increases and decreases?

7. How does the World Bank define poverty?  How are its poverty lines adjusted over time?

8. Which region had the highest rate of extreme poverty in 1980? 1990?  2010?  Will there be any people in China in extreme poverty in 2030?

9. Does economic growth reduce poverty (draw diagram)?

10. Does economic growth reduce inequality?  Explain.

11. Does high inequality reduce economic growth?  Explain.