Professor Xavier Presents...
Problem
Set 1
Pinocchio 
(1) When You Wish Upon a Star (The Blue Fairy)
(a) Get the excel file with GDP per capita data for a cross section of
countries in 1960 and 2007 (some countries are missing because the data are not
available).
Click Here to Get the Excel File
(i) In 2007, what are the 5 richest countries in the world?
(ii) In 2007, what are the 5 poorest countries in the world?
(iii) In 2007, how many times richer is the average person of the richest country than the average person of the poorest country in the world?
(b) For the countries that have data for 1960, compute the average ANNUAL growth rate of per capita GDP between 1960 and 2007 (Hint: If Y2007 is GDP per capita in 2007 and Y1960 is the corresponding number in 1960, the average annual growth rate is given by: growth=[1/47]*[Y2007-Y1960]/Y1960.
(i) What 5 countries have grown the MOST over this period?
(ii) What 5 countries have grown the LEAST over this period?
(c) Go to the internet and find a blank POLITICAL map of the world.
(d) Paint in RED all countries with a 2007 GDP per capita of MORE than 5,000 dollars.
(e) Paint in BLUE all countries with a 2007 GDP per capita of LESS than
5,000 dollars.
(f) Hang the map on your wall.
(g) Lay down in bed and look at the map while think about WHY some countries are rich and some countries are poor.
(h) Write down some of your thoughts from (g).
(2) Figaro and Cleo
(a) Define the concept of poverty (use your own words; no need to go to a book or encyclopedia).
(b) Why do you think growth is important for poverty reduction?
(c) Why do you think growth is important for poverty inequality reduction? Do you think growth ALWAYS reduces income inequality?
(3) 
Jiminy Cricket
(a) Define the concepts of constant returns to scale and diminishing returns to capital.
(b) Why is it sensible to assume that the production function exhibits constant returns to scale and diminishing returns to capital?
(c) Show that the Cobb Douglas production function with coefficient
α=0.3 (that is 
) exhibits constant returns to scale and diminishing
returns to capital.
(d) Show that the Cobb Douglas production function in general (that is 
) exhibits constant returns to scale and
diminishing returns to capital.
(4) Stromboli
(a) Recall the fundamental equation of the Solow-Swan model: 
. Describe with words this equation. What is the
meaning of the term δ+n? Why is it subtracting from the first term?
(b) Why is the growth rate in the long run equal to zero (in the absence of
technological progress)?
(5) Monstro
Consider the Solow-Swan model of growth. Imagine that the production
function is 
.
Furthermore, imagine that the savings, depreciation, and population growth
rates take the values s=0.11, δ=0.1 and n=0.01.
(a) Use the production function to compute output per capita, y=Y/L, as a
function of capital per person, k=K/L.
(b) Use the fundamental equation of the Solow-Swan model to compute the growth
rate of capital per person as a function of k.
(c) In the steady-state, the growth rate of capital is zero. Using the
parameters assumed above, find the steady-state level of the capital
stock, k*.
(d) Imagine that this country is in its steady state so its capital stock is k*.
Imagine that the country receives a gift of one unit of capital from the world
bank (so, suddenly, the capital stock is k*+1). Can you say what is
going to happen to the growth rate immediately after the donation? Why? What
will the capital stock be in the long run? Explain.