Macreconomics Analysis
Homeowrk #4
Spring 2015
1. (Jones Ch4 Q4) Suppose the production function at the core of out model is given by
Y=AK3/4L1/4 (that is assume the exponents on capital and labor are ¾ and ¼ rather than 1/3 and
2/3) The tables referenced below are included in the slides.
a. Create a new version of Table 4.1 for the new version of this model. What are the five equations
and five unknowns? (Hint: The hiring rules for capital and labor will change in the obvious way)
b. Now solve these equations to get the solution to the model. Put your solution in the same form
as Table 4.2
c. What is the solution for the equilibrium level of output per person?
2. (Jones Ch4 Q5) The table below (next page) reports per capita GDP and capital per person in the
year 2007 for 5 countries (Jones’s table has 10 countries) Your task is to fill in the missing columns
of the table.
a. Given the values in columns 1 and 2, fill in columns 3 and 4. That is, compute per capita GDP
and capital per person relative to the U.S. values.
b. In column 5, use the production model (with a capital exponent of 1/3) to compute predicted
per capital GDP for each country relative to the US, assuming there are no TFP differences.
c. In column 6, compute the level of TFP for each country that is needed to match up the model
and the data.
d. Comment on the general results you found.
3. Assume the country of Freedonia has $500 of capital per worker and has a workforce of 20
million. Also assume that labor and capital split output evenly between themselves.
a. Ignoring total factor productivity. What is output per worker? What is total output?
b. If actual output per worker is $1000 what is total factor productivity? What is the wage rate?
What is the return to capital?
c. Suppose a wizard appears and suddenly makes half of the capital stock disappear. What is output
per worker? What is the wage rate? What is the return to capital? (Assume everything for question
1b holds initially) Do you think that perhaps the wizard owned some of the capital stock left over?
Why?
d. Suppose aliens visit earth and bring with them technological advances that double total factor
productivity. What is output? What is output per worker? What is the wage rate? What is the
return to capital? (assume everything for question 1b holds initially)