Download Suggested Solutions for Problem Set #1

Department of Economics
University of California, Berkeley
Economics 100B Problem Set #1 Solutions
Spring 2017
Professor Olney
Page 1 of 5
Suggested Solutions for Problem Set #1
1. (3 points; 1/4 point each) ) Based on what you learned in your principles course, and in your own words, define each of the
following terms. (It’s important that this is your own words, not copied or paraphrased from a source. If you can’t define these
terms in your own words, reconsider whether this is the course for you.)












gross domestic product: total annual economic output of a nation
unemployment rate: percent of the labor force unemployed (out of work & looking for work)
labor: an input to the production process; people’s work effort
inflation rate: percentage change over time in some average measure of prices
economic growth: more than one definition floats out there. [1] increases over time in the standard of living (real GDP per
capita); [2] increases in real GDP (even if real GDP per capita declines)
aggregate demand: total demand for domestically-produced final goods and services by households, businesses,
government agencies, and the rest of the world
money: anything that is accepted in exchange for goods and services, used as a unit of account, and which has a store of
value. In the U.S. currently, coins, currency, checking balances, denominated in dollars, are money.
capital: an input to the production process, machines and buildings
fiscal policy: changes in G, TA, or TR by the fiscal authorities (in the US, the Congress with the approval of the President).
In some definitions, also add: undertaken with the goal of affecting the macroeconomy.
monetary policy: changes in interest rates and the money supply, by the central bank
government deficit: annual difference between government spending (G + TR) and government revenues (TA)
government debt: accumulation over time of the annual deficits minus the annual surpluses. Total outstanding value of
IOU’s issued by the government
2. (2 points total; 1/2 point for each part)
Use Fred Economic Data at https://fred.stlouisfed.org/to answer the questions.
a. On one graph, graph “constant GDP per capita” for the United States, China, Mexico, and three other countries of your
choice. Time period: 1960 on. Vertical axis: linear scale
Department of Economics
University of California, Berkeley
Economics 100B Problem Set #1 Solutions
Spring 2017
Professor Olney
Page 2 of 5
b. Discuss your graph by addressing at least these questions. Which country has the highest standard of living (real GDP per
capita)? Have living standards increased over time in all of the countries you chose? Has the rank order of the countries you
chose changed over time?
Your answer will vary because it’s unlikely you chose the same 6 countries.
Except for a brief period in the early 1990s, the US has the highest standard of living, 1960-2015. Venezuela was second in the
1960s but its economy has stagnated since then, while standard of living in the US and Japan have increased. The standard of
living in the US and Japan are, on average, far greater than is found in the other four countries: China, Mexico, Venezuela, and
India. India remains, on average, the poorest of these 6 countries.
c. Now change the vertical axis to log scale and reprint the graph. Again, if you don’t have a color printer, write in labels so it
is clear which country corresponds to which line.
d. Discuss this second graph by addressing at least these questions: Which country has the fastest growth rate of living
standards over this period? Are any countries stagnant? Declining? Which?
The rate of growth is the slope of the ln(constant GDP per capita) compared with time. China has the fastest rate of growth
(steepest line) over this 55 year period. The economy of Venezuela has been, at best, stagnant and occasionally in decline.
Compared with India & China, the US and Japanese and Mexican economies have shown relatively slow growth on average
since the 1990s.
3.
Crank through the calculus!
a.
Use the rules of natural logs and calculus to show that the rate of growth over time of a product of two variables, ab, is the
sum of the rates of growth of the variables a and b..
Department of Economics
University of California, Berkeley
Economics 100B Problem Set #1 Solutions
Spring 2017
Professor Olney
Page 3 of 5
d (ln ab )
d (ln a  ln b )
d (ln a ) d (ln b )




dt
dt
dt
dt
da
db
d (ln a ) da d (ln b ) db
1 da 1 db
dt 
dt 



 
 

da
dt
db
dt
a dt b dt
a
b
 a over time  b over time

 growth rate of a  growth rate of b
a
b
growth rate of ab 

b.
 

Use the rules of natural logs and calculus to show that the rate of growth over time of a quotient of two variables, a/b, is the
difference between the rates of growth of the variables a and b.
 a
d  ln 
d (ln a  ln b )
d (ln a ) d (ln b )
b
 a
growth rate of    




dt
dt
dt
dt
 b
da
db
d (ln a ) da d (ln b ) db
1 da 1 db
dt
dt 





 


da
dt
db
dt
a dt b dt
a
b
 a over time  b over time

 growth rate of a  growth rate of b
a
b

c.
  
Use the rules of natural logs and calculus to show that the rate of growth over time of a variable b raised to a constant power,
ba, is the constant a times the rate of growth of the variable b.


d ( a  ln b )
d (ln b )
 a

dt
dt
db
d (ln b ) db
1 db
dt 
a

 a 
 a
db
dt
b dt
b
b over time
a
 a  growth rate of b
b
growth rate of b a 
d ln b a
dt

 
Department of Economics
University of California, Berkeley
Economics 100B Problem Set #1 Solutions
Spring 2017
Professor Olney
Page 4 of 5
4. Cobb-Douglas production function.
Assume the production function is Cobb-Douglas.
Assuming the production function is Cobb-Douglas means to assume that we have a multiplicative function, with
each factor of production raised to a power. The sum of the powers must equal 1, which is what gives a CobbDouglas production function the property of constant returns to scale.


Y  K  1
Y  K  1
   E . For part b, use the formula    (E )
For part a, use the formula
L L
L Y 
a.
What is the value of output per worker when K = 1,000,000; L = 500; E = 100; and α = 0.25?
 1,000,000 
a. Y/L = 

 500 
0.25
(100 ) 0.75 = (2,000)0.251000.75 = 211.5
b.
What is the value of output per worker when the capital intensity is 4, labor efficiency is 1,000, and α = 1/3?
b.
Y/L =  4 2 / 3 (1,000 )   4 2 (1,000 ) = 2(1,000) = 2,000
c.
Excel graph (first version of PS solutions had an error in calculations here; this is corrected graph as of 2/3/2017)



1/ 3






1



Department of Economics
University of California, Berkeley
Economics 100B Problem Set #1 Solutions
Spring 2017
Professor Olney
Page 5 of 5
5.
For each activity listed below, indicate where the activity would be recorded on the expenditure side of U.S. GDP
accounting. Your choices are C, I, G, GX (exports), IM (Imports), and NR (not recorded). Give a brief explanation for
each answer; one sentence should suffice.
a. A family from Sweden, visiting Berkeley, buys jewelry from a vendor on Telegraph Avenue.
EX. Export of a good (jewelry) that was produced domestically (in Berkeley) and purchased by someone who is
not a resident of the United States (a Swede). Where the purchase takes place is irrelevant.
b. A California-resident Cal student purchases a new textbook that was published in Singapore.
C and IM. Purchase of a good (a book) by a U.S. resident, thus C. But the item was produced abroad, so also IM.
It is recorded in both places. The addition to US GDP is any difference between C & IM, which would be the value
added domestically. If the book was purchased in Singapore, the $ value nets out to zero, but because the sources
of information for C and IM are different, the transaction gets recorded in both places.
c. Bancroft Clothing buys Cal sweatshirts that were manufactured in Vietnam. The sweatshirts do not sell.
I and IM. When Bancroft Clothing buys the sweatshirt, it’s an intermediate good. Normally we don’t record
intermediate goods but in this case we do because the good didn’t sell in the current period. It was instead added
to the inventory of Bancroft Clothing, which is recorded in I (investment). The sweatshirt was manufactured in
Vietnam, so it is also recorded in IM. So far, there is no value added in the US.
f. The local school district pays its teachers their monthly salaries.
G. People don’t pay to go to public K-12 school, so there is no “purchase” of public education. Instead we record
the value of the government-paid inputs to the production of education. Salaries paid teachers in public schools
are recorded in G.