ECON 302: Problem Set #1
Lecturer: Santiago Acosta Ormaechea, Social Science 6460
Due on Monday, September 29, 2008 (4pm CDT).
You may work in groups of 2,3 or 4 students. You must submit you work individually. You must
also indicate the name/s of your collaborators.
1. GDP Accounting
Imagine a world with only two countries: Alpha and Beta. Alpha produced 5 cars and 100
gallons of milk in 2006 and 2007:Both countries produce only these two goods (i.e., cars and
milk) and can freely trade without any cost. Further assume that prices are exactly the same
in both countries. In 2006 Alpha sold 2 cars and 40 gallons of milk to Beta. Each car was
sold at $80. In 2007 the price of each car was $100 while that of each gallon of milk was $10:
Assume that there is neither investment nor government consumption.
(a) Noting that the GDP deator in 2007 (with 2006 as its base year) is 120;calculate the
nominal GDP of Alpha in 2006:
(b) Obtain the growth rates of nominal and real GDP of Alpha in 2007:
(c) Construct a CPI index for Alpha taking 2006 as the base year. How will you choose the
units of cars and milk to construct this index? Obtain the ination rates between 2006
and 2007 with the GDP deator and the CPI index. Interpret the dierences in results.
(d) Imagine that you are giving advice to a very smart Senator of Alpha, on the best way to
preserve the real value of pensions. Based on the same information that you have here,
he suggests that pensions should be indexed to the CPI instead of the GDP deator.
Would you agree with him? Why?
2. Constant Returns to Scale
Consider the following production function:
F(K; L; H ) = KLH;;;>0:
(a) Under which conditions F() is a constant returns to scale (henceforth CRS) production func-
tion?
(b) Obtain the MPK, MPL and MPH (marginal productivity of human capital). Assume that
F() is linearly homogeneous (i.e., CRS). Show that F() exhibits diminishing MPK, MPL
and MPH.
(c) Assume that all markets are perfectly competitive and that rms maximize prots. Let w;
rkand rhdenote the real wage, the real rental price of capital and the real rental price of
human capital, respectively. Show that a prot maximizer rm will set w=MPL, rk=MPK
and rh=MPH. What are the shares of capital, labor and human capital in total output?
(d) Prove that Y=F(K; L; H) = wL +rkK+rhH: Which is the mathematical theorem that
allows you to know that this must be the case whenever F() is linearly homogeneous, rms
maximize prots and markets are competitive?
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