UC Davis Economics 101 - Intermediate Macro Theory

Economics 101
Intermediate Macro Theory
Problem Set #1 -- Due Thursday, July 2

Department of Economics
UC Davis
1.

 

Exogenous and Endogenous Variables

2.

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Recall the production possibilities frontier (PPF) model from introductory
economics (for a review see
http://en.wikipedia.org/wiki/Production_possibility_frontier). What are the
exogenous variables in this model and what are the endogenous variables?
Briefly explain.

The Definition of GDP

Are the following included or not included when estimating GDP? Provide a
brief (one sentence) explanation in each case below.
A.
Flour sold to a bakery at a local grocery store.
B.
Sale of an existing home.
C.
Rental value of owner-occupied housing.
D.
Interest payments on the national debt.
E.
Household production (laundry, cooking, childcare, etc.)
F.
A purchase of a Wal-Mart stock in the stock market.
G.
Flour sold to a customer at the grocery store.

3.

Equivalent Methods of Computing GDP

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Consider a simple economy consisting of only four firms. Firm A, a mining
enterprise, extracts iron ore. Firm B, a steelmaker, produces steel sheets. Firm C,
a carmaker, makes automobiles while Firm D produces automobile tires.
In 2009, Firm A extracts 50,000 tons of ore, valued at $200 per ton, using
previously existing machinery. Firm B produces 10,000 tons of steel sheets,
valued at $3,000 per ton, having bought and used all of the ore produced by Firm
A. Firm C manufactured 5,000 vehicles and sold them all to households for
$20,000 each, having purchased 8,000 tons of steel sheets from Firm B. In
addition, Firm C imported 5,000 engines from a foreign subsidiary, each valued at
$5,000, and purchased 20,000 tires from Firm D for $100 each. Firm D produced
100,000 tires valued at $100 each, but only sold 60,000 tires during 2009. Firm D
purchased 2,000 tons of steel sheets from Firm B since all of their tires are steel
belted radials.



1

Calculate GDP in 2009 for this economy using the value added approach. Also,
calculate GDP in 2009 using the expenditure approach. You need to show all of
your work for full credit.

4.

Chain-Weighted Index Numbers
Consider a hypothetical economy that produces only two goods, cars and
computers.

A.
B.

C.

D.

5.

Quantity Produced
Cars
Computers
10
100
9
120
8
140

Cars
$17,000
$20,000
$22,000

Prices
Computers
$1,000
$800
$700

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Year
2008
2009
2010

Calculate a chain-weighted (Fisher) price index for this economy for the
years 2008, 2009, and 2010. Let
= 100.
Based on the price index you constructed in Part A above, what is the
average annual inflation rate between 2008 and 2010?
Calculate a chain-weighted real GDP (
for this economy for the years
2008, 2009, and 2010. Let real GDP in 2008 = nominal GDP in 2008.
Visit the U.S. Bureau of Economic Analysis webpage (www.bea.gov).
What is U.S. real GDP for 2008, measured in billions of chained 2000
dollars?

Saving for Retirement

Suppose that your child is born this year, and that you’d like to set aside enough
money now so that your child will have $3,000,000 at retirement in 65 years.

Th

A.

B.

6.

If the rate of return on your money averages 7 percent per year over the
next 65 years, how much do you have to invest today so that your child
will have $3,000,000 in 65 years.
Suppose that your child decides to retire at the age of 50 instead, how
much money will there be based on the assumptions and answers from
Part A above.

Long-Run Economic Growth in the G-7 Countries
Angus Maddison has spent almost his entire career measuring and estimating
historical real GDP and real GDP per capita from 1 A.D. to the present. This



2

problem asks you to calculate long-run growth rates of real GDP per capita for the
G-7 countries (Canada, France, Germany, Italy, Japan, the United Kingdom, and
the United States). Maddison’s data can be found at:
http://www.ggdc.net/maddison/. Scroll down until you see a hyperlink to “World
Population, GDP and Per Capita GDP, 1-2006 AD” under “Historical Statistics.”
This is an Excel file that you can copy and paste from to answer the questions
below.
A.

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B.

C.

7.

Report real per capita GDP for each of the G-7 countries for the years 1
AD, 1000, 1500, 1700, 1850, 1900, 1950, and 2006. You may find it
easier to use Excel or Calc (www.openoffice.org) for this problem.
Using the data from Part A, compute and report in a similarly formatted
Excel table the average annual growth rates of real GDP per capita in each
country for the following periods: 1 AD – 1000, 1000 – 1500, 1500 –
1700, 1700 – 1850, 1850 – 1900, 1900 – 1950, and 1950 – 2006.
Remember that you can copy and paste formulas, so once you do this for
one country, you can copy the same formula for all the other countries as
well. Also, format the cells as a “percentage” to more easily interpret the
growth rates.
Based upon the results from Part B above, what general conclusions can
you make about the changing rate of economic growth over time? Would
Thomas Malthus be surprised by the results from Part B? Why or why
not?

The Production Model

Assume that an economy has the following Cobb-Douglas production function:
?

?

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where Y is real GDP, K is the stock of physical capital, and L is labor. The
parameter A is equal to 10. Assume also that capital is 64 and labor is 16, and
that markets are competitive so that both capital and labor are paid their marginal
products.
A.
B.
C.
D.
E.
F.

What is Y?
What is the real wage of labor?
What is the real rental price of capital?
What is labor’s share of income?
Does the production function above exhibit decreasing returns to scale,
constant returns to scale, or increasing returns to scale? Briefly explain.
Does the production function above exhibit the property of diminishing
marginal product of each factor of production? Briefly explain.