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Synthesis
Econ 109 Fall 2002
Looking Back
1
Outline
• Themes: The Big Issues
• Economic Concepts
• Perspectives By Course Section
– What We Learned
– Why We Learned It
– How We Can Use It
2
The Big Issues
• Looking Out for # 1
– answer: save and invest (Course: Part I)
• Can a country (or civilization) generate a
surplus to finance military power and/or the
arts and sciences?
– Answer: Malthus- landowners squeeze the
peasants
– Answer: Marx- capitalists squeeze the workers,
(Course: Part III)
– Answer: Adam Smith- markets lead to
efficiency and general welfare
3
The Big Issues (cont.)
– Answer: Modern economists- population
growth increases the labor force; saving and
investing increases capital; capital deepening
increases worker productivity; research and
development promotes technologival change
(Course: Parts II and III)
– Answer: Monopoly power squeezes consumers
(Course: Part III)
4
Is Globalization & Trade Good or Bad?
• Good
• trade permits
decoupling of
production and
consumption, i.e.
promotes
specialization
• growth in GDP per
capita leads to more
equity
• trade promotes
competition and curbs
monopoly power
• Bad
• growth uses up world
resources
• global warming
• loss of forests
• loss of clean oceans
and rivers (Course:
Part IV)
5
Is Capitalism a Good Economic System
or Not? (Course: Parts II, III, IV)
• Good
• if markets are
competitive, then
economy is efficient
• Bad
• instability, subject to
fear, decreases in
consumption and
investment, capital
flight
• monopoly power
exploits consumers,
wastes resources, and
corrupts democracy
6
Economic Concepts
• Economic Paradigm: A Way of Thinking
– #1 set out your options for choice
– #2 value these options ( using market prices or
personal values or social values)
– #3 optimize, i.e. pick the best choice
• Marginal Principle
– set marginal benefit(revenue) equal to marginal
cost (if marginal revenue is constant then
marginal revenue=average revenue=price)
• Reality Principle
• Scarcity and Opportunity Cost
• Diminishing Returns
7
Concept Applications
• Economic Paradigm
– buying a car; Lecture 2
– supplying your time to the labor market: L.4
– choosing the investments with the average rate
of return-risk tradeoff that is best for you: L5
– crime (pollution)-consumption possibility
frontier, community choice of optimal crim
(pollution) levels L.17
8
Tools Applications
• Keynesian Cross: L. 6, L. 7 & L. 10
• Production Possibility Frontier
– Guns or Butter L. 8, L. 10
– Agricultural goods or manufacturing goods L. 12
– Ag. Or mfg. Goods: a closed economy vs. trade andan
open economy
• Demand and Supply
– demand for mortgage credit: L. 3
– demand & supply of funds in the bond market: L. 4
– demand & supply of banking reserves: L. 9 & L. 10
9
Tools Applications
• Demand and Supply
– demand and supply of world copper L.14
– demand and supply of pesos: capital flight from
peso L. 15
– demand & supply of $, capital flight from the
baht L. 16
– demand and supply of bahts, capital flight from
the baht L. 16
– demand & supply of low-skilled labor
contrasted to demand & supply of high-skilled
labor, the wage differential for skill L 16
10
Tools Applications
• Production Function, wage bill, surplus L. 11
• Marginal product of labor (demand), supply of
labor, surplus L. 12
– demand & supply of labor: minimum wage L. 12
– demand & supply of labor: capital deepening L.13
– demand & supply of labor: technological change L. 13
• Consumer Surplus & Competitive Markets L. 13
– consumer surplus, monopoly profit, and dead-weight
loss L.14
11
Tools Applications
• Lorenz Curve and Gini Coefficient: L.16
12
Perspective
• What we learned
• Why we learned it
• How we can use it
13
Part I: Personal Finance,
Economics of Everyday Life
14
Purchasing the Big Ticket Items:
Cars and Homes
• Why: Need to be well informed about the
important decisions in our lives
• What: cars and houses last a while, and a $
this year is equivalent to a $ next year times
one plus the interest rate $(t) = $(t+1)(1 + r)
• What: cars depreciate physically and most
cars depreciate economically
• What: houses depreciate physically and will
likely appreciate in value in CA
15
Cont.
• What: mortgage payments on loans are
front loaded with interest, so equity will
build slowly
• What: Need to save for the down payments,
so we need to budget our expenditures
• How to use this info: when the time comes,
tools are available for free on the internet or
at low cost in common software packages
16
Tool: Income-Expense Statement
Income
Amount
own salary
spouse “
insurance
dividends
interest
rent
other
Total
Expenditure Amount
taxes
life insurance
cars
food
clothing
housing
other
Total
Savings Equals Income Minus Expenditure
17
Economic Principles
• A dollar today is not the same as a dollar
tomorrow!
– $10 today @ 6.9% = $10 * 1.069 next year
• The “opportunity cost” of spending your money is
the foregone interest.
• The cost of buying the services of the car,
neglecting operating costs:
– depreciation: owning a new car
– foregone interest
18
Increasing the Length of the Loan
Tradeoffs
•
•
•
•
monthly payment amount decreases
amount of total payments increases
amount of total interest payments increases
total interest as % of total payments
increases
19
Thinking About Problems:
The Economic Paradigm
• describing the alternatives to choose among
• pricing the alternatives
• choosing the best alternative
20
The Economic Paradigm
example: buying a car
• describing the alternatives to choose among
– cash: the opportunity cost of losing interest
– lease: depreciation included in payments
– loan: sell the car to account for depreciation
• pricing the alternatives: valuation
– Oscar Wilde- economists know the price of
everything and the value of nothing
• choosing the best alternative
– best: lowest cost
– possibly subject to a constraint: having the $
21
What to Do with Those Savings
• Why: investments that earn more will let
you buy your cars and house sooner
• What: investments have two attributes,
average rate of return(the reward), a good,
and variability in the rate of return(the risk),
a bad
• What: You want the investment with the
highest average rate of return for a given
level of risk
• What: returns are equal to capital gains
(losses) plus dividends
22
An Example of Two Alternative Investments
Two UC Funds: Monthly Rate of Return, Sept 95 - Aug 01
10
5
Jun-01
Mar-01
Dec-00
Sep-00
Jun-00
Mar-00
Dec-99
Sep-99
Jun-99
Mar-99
Dec-98
Sep-98
Jun-98
Mar-98
Dec-97
Sep-97
Jun-97
Mar-97
Dec-96
Sep-96
Jun-96
Mar-96
Dec-95
Rate
Sep-95
0
-5
-10
Equity Fund
Insurance Contract
-15
Year:Month
23
Tool: Efficient Portfolio- Most Return for Given Risk
Return Versus Risk for Six UC Funds Sept 95-Aug 01
1.20
Equity
Economic paradigm step1
1.00
Average Return
Bond
0.80
0.60
Multi-Asset
Insurance
Savings
0.40
Money Market
0.20
0.00
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
Risk: Volatility
24
Economic Paradigm step 2: Valuation of Mean Return and Risk
Assumption: Mean Return is Good, Risk is Bad: U =U(M,R)
better
Mean
Return,
M
worse
B
C
A
Iso - Preference Curves
Prefer B to A; Prefer B to C
Risk, R
25
Economic Paradigm step 3: Choosing the Best
Investment for You
Optimum for B
UC Funds: Mean Return Vs. Risk (Standard Deviation)
2.00
Investor B: not very risk averse
Equity
1.80
1.60
Mean Return
1.40
1.20
Multi-Asset
Bond
1.00
0.80
0.60
Insurance
Savings
0.40
Money Market
0.20
0.00
0.00
0.50
1.00
1.50
2.00
Standard Deviation
2.50
3.00
3.50
26
Personal Earnings and Human Capital
• Why: Your major source of $ is likely to be
income
• What: Your Earnings will depend upon
– your ability
– your knowledge
– your work experience
• How: Hang in until you get your college
degree
27
Families: Average Income and
Average Net Worth, 1995
Quintile
Lowest 20%
Second 20%
Third 20%
Fourth 20%
Highest 20%
Av. Income
$8,032
$17,916
$28,965
$43,930
$73,058
Av. Net Worth
$3,000
$14,600
$31,185
$51,133
$118,171
Even with wealth of $100, 000, at 5%, you earn only $ 5, 000 of income
so you will need to work
Source: Consumer Federation of America
28
Tool: Earnings Opportunities: Trading Time for Money
Earnings
$480
Opportunities for trading leisure
for earnings (income) at a rate,
$20 per hour, the market wage,
determined by your stock of human
capital(step one of the paradigm:
describing the alternatives for choice)
Economic Paradigm step 1
$0
0 hours
24 hours
Leisure
(learning)
29
Tool: Your preferences (tastes) for 2 goods, income & leisure
Earnings
$480
Depicting your tastes graphically
low value
high
Iso-Preference Curves:
You value all points on
a curve equally
Economic paradigm step 2
high value
$0
0 hours
Leisure
24 hours (learning)
30
Putting the 2 tools together: explaining your supply of labor
Earnings
$480
low value
high Individual’s Supply of Labor
Economic paradigm step 3
$180
for 9 hrs
of work
Optimum
high value
Leisure
(learning)
$0
0 hours
15 hours
of
24 hours
31
Part Five: Economic Welfare and
Public Policy
• Why: we need to consider the welfare of
fellow citizens, not just me-me-me
• What: most folks that are poor are poor
because they do not work
• What: most folks that do not work have a
low level of human capital, i. e. the labor
market places a low value on their time
• What: persistent pockets of poverty among
female heads of households and their kids
32
Cont.
• In the US, the rich are getting richer and the
poor are getting poorer
• In the US economy, there is a growing
earnings premium on ability, on education,
and on experience, i.e. on human capital
• In the US, we can’t seem to get the poverty
rate below 10%
• How to use this info: on public policy issues
when you vote
33
Life does not offer very good options for the uneducated
Earnings
$480
low value
slope of the iso-preference
curve through the 24 hour
high
endowment is the lowest
wage at which you are
willing to work
$96
$0
0 hours
24 hours
Leisure
(learning)
dropout is unwilling to work for $4/hr
34
Poverty and Female Heads of Households
Lab10: Children, Poverty, and Politics:
US Census Bureau: Poverty in the United States: 2000
35
One Difficulty in Reducing Poverty: Adverse Social Trends
Percentage of Births Occuring Out of Wedlock, .
White Women by Age Group, US
.
35
30
Percent
25
15-19
20-24
25-29
20
15
10
5
0
1955
1960
1965
1970
Year
1975
1980
36
Poverty and Youth
Lab 10: Children, Poverty, and Politics
37
In the US, the Rich Get Richer and the Poor get Poorer
T rends in Shares of US Family Income .
60
Top 5 %
Top 20 %
Bottom 40%
50
30
20
10
Year
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
0
1970
Percent
40
38
Ratio of Median Earnings, Males: College Grad to High School Grad
Source: Economic Report of the President, 1997
39
Growing Wage Differentials Between the Less Skilled and More Skilled:
Less Demand for Less Skilled and More Demand for the More Skilled
Source: Economic Report of the President, 1997
40
Cont.
• What: In the world, developed countries
have a more equitable distribution of
income than undeveloped countries, one of
the positive consequences of growth
• What: In the world, political systems and
history also count. Socialist countries and
countries with mixed economies tend to be
more equitable. However, their tax burden
is also greater
41
The Distribution of Income and Growth
0.7
Jamaica
0.6
Brazil
Honduras
Mexico
Hong Kong
Gini Coefficient
0.5
Malaysia
0.4
Singapore
0.3
0.2
0.1
0
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
GDP Per Capita, 1990
42
Tool: Lorenz Curves for Hungary and Brazil
43
Income Inequality Across the World
Lab 7, Ch. 23, Internet Exercises, World Bank Links
http://www.worldbank.org/depweb/
44
Higher Tax Burden in
France than in the US
Lab 7, Ch. 23, Internet Exercises,
“Taking a Look at the Level of
Economic Development and
Well-Being in Countries
Around the World”
Link to Handbook of International
Economic Statistics
45
Part Two: Macroeconomics and the
US Economy
• Why: because the economy affects your
prospects for finding and keeping a job, the
interest rate you pay on loans, and the return
you get on your investments
• What: There are two ways to measure the
size of an economy, National Income and
National Expenditure or GDP (circular
flow). They have to be the same, i.e. in
equilibrium
46
Cont.
• What: GDP is equal to consumption by
consumers plus investment by firms, plus
spending by government plus net exports (
exports minus imports)
• GDP = C + I + G + X - M
47
: Chapter Twenty
• Conceptual Framework: Circular Flow
Firms
Income
Firms
Labor
Supply
Goods
Demand
Goods
Households
Households
Income Perspective
Expenditure Perspective
Y
=
GDP
48
Expenditure Perspective: Open
Firms
Exports
(Sales)
Supply
Goods
Demand
Goods
Imports
(puchases)
Households
Government
Households: Consumption of Goods and Services
Firms: Investment in Plant and Equipment
Government: Purchase of Goods and Services
All Three: Exports - Imports = Net Exports
49
Bust
Consumption, C
Investment, I
GDP
Aggregate
Expenditure
45
Income = expenditure
I.e. Y = GDP
GDP = C + I +G
Total
Expenditure
GDP Line
Unemployment
Rate Oct. 2000
= 3.9%
0
GDP = Y
National
Unemployment Rate
Income, Y
Sept 2001 = 4.9 %
Graphical Tool: The Keynesian Cross
50
US Postwar Expansions
Trough - Peak
Duration, Months
Oct. ‘45 - Nov. ‘48
37
Oct. ‘49 - July ‘53
45
May ‘54 - Aug. ‘57
39
April ‘58 - April ‘60
24
Feb. ‘61 - Dec. ‘69
106
Nov. 70 - Nov. ‘73
36
March ‘75 - Jan. ‘80
58
July’80 - July ‘81
12
Nov. ‘82 - July ‘90
92
March ‘91 – March ‘01
121
51
Cont.
• What: In addition to fiscal policy, I.e
taxation policy and government spending,
the US central bank, the Federal Reserve,
engages in monetary policy
• What: the Fed can buy government
securities on the secondary bond market
(open market operations) and if it buys from
a private bank, for example, credits this
bank with reserves. This private bank can
use any excess reserves over those required
by the Fed to make loans to consumers and
businesses. In turn these groups can spend.
52
Cont.
• What: the federal funds rate is the rate of
interest banks pay to borrow from one
another. If the Fed increases the supply of
reserves through open market operations,
this results in a decrease in the federal funds
rate.
• What: The central bank acts as a bank of
last resort, lending money to private banks
at the discount window, charging them
interest at the discount rate.
53
Impact of the Supply of Reserves
on the Federal Funds Rate
FFR,
price of
reserves
Demand for Reserves by Banks
Supply of Reserves: Fed
quantity of reserves
54
Fighting Recession, the Fed Cuts the Federal Funds Rate
from 6.5% in Dec. 2000 to 2.5% in Oct 2001
During the Same Period, the Fed Cut the Discount
Rate from 6% to 2 %
55
56
Part Three: Competition, Monopoly,
and Public Policy
• Why: Growth in GDP per capita increases
the standard of living for people and means
that we can avoid the Malthusian trap and
avoid Marx’s prediction of the increasing
immiseration of the working class
• What: Growth depends on increasing
worker productivity, i.e. output per worker
or average product. Output per worker
increases as capital per worker rises (capital
deepening), including social infrastructure,
and as technology improves
57
Cont.
• What: Malthus believed that population
increases would devour any surplus in
output, keeping peasants at a subsistence
wage.
• What: Marx believed that capitalists would
seek more profit by introducing labor
saving machines, displacing workers and
creating an army of the unemployed. This
surplus of workers would keep wages at the
subsistence level. Neither Malthus nor Marx
foresaw capital accumulation and
technological change saving the day.
58
Cont.
• What: Because economic growth leads to
prosperity, more and more countries are
embracing free markets, capitalism, and
international trade.
• How to use this info: You can stay up at
night worrying whether science,
engineering and technology will bail us out
in the coming century, as it did in the past
two, or whether Malthus and Marx will
ultimately be right.
59
GNP Per Capita, Growth Rates Around the World
60
Output per
Worker
Average,
Marginal
Product
Things Improve with capital deepening:
Output per worker
increase, shifting APL
Labor Supply1874
Labor Supply1954
Real Wage1954
MPL1874
APL
Real Wage1874
MPL1954
L1874 L1954
Input, # of workers
61
Capital Formation
National
Savings
Gross
Investment
+
-
Net
Investment
Capital Stock
Depreciation
62
Table 23.2
Source of Real GDP Growth, 1929-1982 (average annual
percentage rates)
Due to capital growth
0.56
19 %
Due to labor growth
1.34
46 %
+ technological progress
1.02
35 %
Output growth
2.92
100 %
Source: Edward F. Denison, Trends in Economic Growth 1929-82
(Washington, DC: The Brookings Institution, 1985).
63
Research and Development as a Percentage of GDP
Chapter 23, Figure 23.5
64
Optimal Size of Plant with Variable Returns to Scale
LMC
LATC
LATC
SMCIV
D
SATCIV
SMCIII
pM
SATCIII
Quantity
Reference: Lecture 14
S
Market
(different
scale for
output)
The Social Cost of Monopoly: Example, Constant Returns to Scale
Competition
Monopoly
Market Demand
Market Demand
Consumer Surplus
Dead Weight Loss
PM
Profit
LATC = LMC
PM
LATC = LMC
MR
QCOMP
QMONOP
Under monopoly, some consumer surplus is redistributed to the
monopolist as profit, and some is lost to society
66
The Ghost of Malthus
67
Population Growth Rates Around the World
68
Part Five(again): Economic
Welfare and Public Policy
• Why: Economic growth and prosperity may
not be unambiguously good. Growth may
bring pollution as a byproduct. Free markets
and free societies may have more deviant
behavior.
• What: Societies must choose through their
political system how much GDP to allocate
to cleaning up the environment and how
much GDP to allocate to fighting crime and
keeping citizens and their property safe
69
Tool: Crime (pollution) - Consumption Possibility Frontier
Offenses (pollution): bad
Minimum possible
Opportunity cost of
less crime
Consumption: good
The first step of the paradigm: the options for choice
70
Community Values Confront Reality:
Crime (pollution) - Consumption Possibility Frontier
Offenses (pollution): bad
optimum
Community preferences
Community wish
list
Consumption: good
The second step of the paradigm: pricing the options
71
The Developed Countries Are
Increasing the Risk of Global Climate
Change
72
The Developed Countries Are Also the
Ones That Can Afford To Clean Up
Central Government Expenditure as a % of GDP, 1995
http://www.worldbank.org/depweb
Llad Ph illips
76
73
Part Four: Trade, the Balance of
Payments and the Global Economy
• Why: Globalization characterizes our times.
World trade is stimulating economic
growth, breaking down the barriers that
protect inefficient domestic industries.
• What: Trade, or voluntary exchange,
benefits both parties. Trade allows them to
specialize on what they do best, rather than
be self-sufficient, and specialization
increases productivity. Trade permits the
decoupling of production from
consumption.
74
Cont.
• What: Trade of goods and services may not
always be in balance however. Imports may
exceed exports and countries, like people,
may borrow to live a little higher on the
hog. For people, this is often reflected by
credit card debt. In the case of countries, we
call them debtor nations.
• What: The danger in being a debtor nation
is the possibility of capital flight. Foreigners
who own a country’s bonds may sell them
and then sell this country’s currency to buy
their own, i.e. cash out and go home.
75
Cont.
• What: If the target country’s central bank
does not have sufficient reserves of foreign
currencies to permit them to buy their own
currency, and offset the effect of capital
flight on the exchange rate, they will have
to devalue their currency.
• What: A stable exchange rate means trade
and economic activity is less risky.
• What: Currently, the only mechanism to
offset capital flight and avoid international
monetary crises is cooperation among
central banks, arranging loans for the target.
76
Growth in World Trade
Source: Economic Report of the President, 1997
http://www.gpo.ucop.edu/catalog/erp97.html
77
Around the World, Trade is
Growing Faster Than GNP
78
Trade Allows the West to Decouple Production & Consumption
Production Possibility Frontier, PPF
Eastern Prices: Ag/ Mf = PMf/PAg
Agriculture
QAg
Exports
Regional Tastes:
B
C
CAg
A
Imports
QMf
CMf
Manufactures
79
Capital Flight
1. foreigners sell their Thai investments
2. foreigners exchange their Baht proceeds for say dollars
3. Demand for dollars shifts and price of the dollar in Bahts rises
demand for dollars
supply of dollars
Bahts per US $
quantity of dollars
80
Part III. (45 points) Answer all three questions.
1. Suppose, in the future, countries in the European Monetary Union (EMU) lose
confidence in the attractiveness of the United States as a haven for their investments,
perhaps in part because US interest rates decline dramatically. Suppose this causes a
repatriation of money to EMU countries, and fewer Euros are supplied to the US and to
the foreign exchange
Demand for Euros
$ price of the
Euro
Demand for Euros
$ price of the
Euro
$/Euro
$/Euro
Supply of Euros
Quantity of Euros
Figure 1A: Before Capital Flight
Quantity of Euros
Figure1B: After Capital Flight
a. After capital flight, show the shift in the supply curve of Euros in Figure 1B.
b. Does the equilibrium quantity of Euros increase or
decrease?__decrease____________
c. Does the Euro appreciate or depreciate? __appreciate_______________
d. Illustrate the new exchange rate in Figure 1B.
e. If the U S Federal Reserve intervenes in the foreign exchange market using its
reserves of foreign exchange, which curve will shift, the demand curve for Euros
or the supply curve for Euros? __supply____________
2. Currently, for the third quarter of 2000, the economy is at full employment at $10.05
trillion(T) for GDP. Net exports, X-M, are in deficit at $-0.39 T and government
expenditures, G, are $1.75 T. So together, government expenditures and net exports are $
1.36 T. Note that the government is in surplus, i.e. expenditures exceed receipts from
taxes etc., so the government is absorbing purchasing power rather than generating it.
For the sake of simplicity, assume government expenditures and net exports do not vary with national
income, as illustrated in Figure 2.
In thinking about the prospects about a recession in 2001, the expenditure
emphasis is on the private domestic economy: consumers and business firms.
GDP,
Expenditure
Components
In $ Trillions
$10.05 T
Total GDP
Line
Total GDP Line if C + I fall
G + (X-M) = $ 1.36 T
G + (X-M) < $ 1.36 T
450
National Income
Full Employment
National Income, $10.05T
Figure 2: The Keynesian Cross and GDP Expenditure = National Income
a. Together, how many trillions must consumption and investment total at the full
employment level of national income? _____$8.69 T______________
b. Draw in the total expenditure (or GDP) line in Fig. 2, which increases with
national income, since consumption increases with national income, showing
its intersection with the GDP= National Income line at $10.05 T.
c. Suppose consumer confidence continues to weaken, and consumption and
investment expenditure fall. Illustrate the consequent shift in the total
expenditure (or GDP) line in Figure 2.
d.
If the balance of trade deficit grows worse, and fiscal policy and government expenditure do not
change, illustrate the effect on the G + (X-M) line in Figure 2.
e.
If all of these unfortunate things come to pass, what will happen to the unemployment rate? __it ___
___will_______
___rise_____________.
3. The technology for electricity generation has increasing returns to scale and therefore a downward sloping longrun average total cost (LATC) curve, as illustrated in Figure 3. These are the conditions for a natural monopoly.
Price per
Kilowatt Hour
Market Demand
pM
LATC
pR
Long Run Marginal Cost
qM
Marginal Revenue
qR
Billions of Kilowatt Hours,q
Figure 3: Market Demand and Long Run costs per Kilowatt Hour for Electricity
a. If the government deregulates electricity, as has happened in California, and
the monopolist is free to determine output and price, show in Fig. 3 the price,
pM, and the output, qM, the monopolist will choose.
b. Under government control of electricity, an efficient use of resources would
result from setting price equal to long run marginal cost (LMC) where LMC
crosses the demand curve. Why isn’t this a feasible price for the government
to set? The low price would benefit the consumer. _monopolist_________
_makes_____
_a_ __loss___________.
c. With government regulation of the electricity market, using average cost
pricing, the government could set long-run average total cost to price where
LATC crosses the demand curve. Illustrate this regulated price, pR, and
corresponding quantity, qR, in Fig. 3. Comparing, deregulation, with the
monopolist free to maximize profits, to regulation, is the consumer better off
or worse off? _better________ ___off_________( with regulation).
Course Grading
Quiz
Midterm
Final
Course
40
80
169
289
If you complete over 70 % of both the text Problems and Lab
Exercises, then your course grade is increased by 1/3 grade point
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Thursday, Dec. 12, 4:00-7:00
PM, Final, You will need a
scantron sheet and #2 pencil.
• Good Luck
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