Graphs
Economists are very fond of graphs.
What information is displayed in a graph?
In all cases, a comparison is given.
Graphs display "covariation."
They always suggests a relationship.
Simple Bar Graph
Compares men to women: Covariation by sex
Compares 1990 to 1995: Covariation by year
Plot of a Variable over Time
Compares values at one point in time with
those at another.
Suggests changes over time
Plot of one Variable Against Another
Compares values of two variables, usage and
Income - suggests that they move in the same
direction, over time.
"Positive" covariation.
Linear Relationships
Enumeration
NewspapersProduction Cost
0 $50,000 (setup costs)
100,000 $55,000
200,000 $60,000
500,000 $75,000
and so on (not very efficient).
Functional Relationship
Cost = $50,000 + $0.05 Newspapers
In a Graph
Linear Relationships
Fahrenheit and Centigrade Temperatures
Fahrenheit = Centigrade + 32
‘
Centigrade = Fahrenheit - 32
Slope of a Function
Definition: Dependent Variable: The variable on the left of the equals sign in a linear function.
Independent variable: The variable on the right.
Dep.Var. = a + b Indep.Var.
Definition: Slope of a function: The ratio of the change in the dependent variable to a change in the independent variable. This is often written
Slope = =
.
For example, .
Nonlinear Relationships
Slope changes as independent variable changes
Example: Progressive Income Tax
Independent Dependent
Income($1000s) Tax(Amount)
0 to 25 20%
25 to 50 5 + 50% amount over $25
50 to 500 17.5 + 80% amount over 50
Over 500 A very large number.
A Function of More than One Variable
Functional Relationship: Familiar, one variable
relates to another. Y = a + bX.
A variable may depend on more than one other
variable. Taxes = a + bRooms + cLotSize
To graph, hold one constant, vary the other.
Holding Other Things Constant
Most economic relationship involve many
variables
To study a relationship, we isolate an effect of
interest by “holding other things constant.”
The U.S. gasoline market, 1960-1995.
Doesn’t quantity sold when price rises?
Income is not held constant – it is rising.
Income also exerts a significant effect.
Solving a Set of Equations
“Circular Systems” – Pairs of Equations
Lottery Tickets Sold = a + b $Jackpot Prize
$Jackpot Prize= c + d Tickets Sold
How to “solve?”T= -10 + ½ P (Tickets)
P= 5 + 3 T (Prize)
Graphically: T = -10 + ½ PP = 20 + 2T
Algebraic Solution
(1) If necessary, invert one of the equations, so
that the same variable is on the left hand
side of both equations.
P= 20 + 2T
P= 5 + 3T
(2) Equate the two results. P = P. So,
20 + 2T = 5 + 3T.
(3) Solve the resulting one equation for the
one variable.
20 - 5 = 3T - 2T
15 = T
(4) Use either of the equations in Step 1 to solve
for the other variable.
P = 20 + 2(15) = 50.
Break Even Analysis
Newspaper production costs
$50,000 + .05 N
where N is the number of newspapers sold.
Revenue is $5,000 in advertising revenue plus
50 cents ($.50) per newspaper.
How many newspapers must be sold in order
to have revenues equal (or exceed) costs?
Find N for which revenues is greater than or
equal to cost.
$5,000 + .50 N $50,000 + .05 N
The break-even point is
N = 100,000 newspapers.
Marginals, Averages and Totals
Total = The quantity of Interest
Average = .
Marginal =
= Change in Total Per Unit Change in Items
Airborne Advertising, Inc., N = Flights
Total Revenue = R = $2,000 + $50 N
Average Revenue =
Marginal Revenue = Additional Revenue Per
Additional Flight
= $50
Compound Interest
Interest, then interest on interest, and so on.
Per $: Now: $1
1 Yr.:$1 (1 + r)
2 Yrs:$1 (1 + r) (1 + r)
T Yrs:$1 (1 + r)T
The Rule of 72. How long to become $2?
Years = T 72 / (100 r)
At 10%, T 7.2 years.
Discounting
How much is a promise to pay $1 sometime in
the future worth right now?
Discounting accounts for the fact that interest
can be earned if you have the money now, but
not if you must wait for it.
Discounted Present Value. How much is
the $1 million sweepstakes (lottery) worth?
Depends on the appropriate r and the number
of years. Suppose first payment is after
one year, $25,000 per year.
DPV = $25,000/(1+r) + $25,000/(1+r)2
+ ... + ($25,000)/(1+r)40.
Assuming r = 10%, DPV = $244,476.
“Funding” the $1 million lottery requires
only $244,476!
Rates of Change
Percentages and Absolutes
Change over Time: Index Numbers
What is the CPI?
Distinguish between “high” and “rising.”
What do index numbers tell you?
Useful Math for Rates of Growth
Product: Growth Rate of XY = Growth
Rate for X + Growth Rate for Y
Revenue = Units Sold Price per Unit
Growth in revenue is from increased sales
and from increase in price.
Ratio: Growth Rate of X/Y = Growth Rate
for X – Growth Rate for Y
Growth in Per Capita Computers = Growth
rate in number of computers minus growth
rate of population.
Microeconomics
Topics
Some Basic Principles
Supply (Sellers) and Demand (Buyers)
Demand in a Market (Consumers)
Supply in a Market (Business Decisions)
Market Equilibrium (Price Determination)
Changes in Market Equilibrium
Describing a Market Using Elasticities
Some Basic Principles of Microeconomics
Scarcity in the economy
Resources: space, materials, wealth
Time
Opportunity cost
A consequence of scarcity
The implication of an economic decision
The cost benefit “test”
People do this naturally
A natural form of economic behavior
Application of the cost benefit test “at the
margin”
Economic incentives
Their implication for behavior
As an explanation for economic decisions
Demand and Supply
What is a market?
Physical characteristics
Essential characteristics – buyers and sellers
What takes place in a market?
Demanders: Individual buyers converge to
purchase
Suppliers: Individual sellers converge to
sell
What is the outcome?
Collective actions of buyers and sellers
lead to a price and a quantity that together
are the market “outcome” or “equilibrium.”
Both buyers and sellers are necessary for
the outcome.
The equilibrium results from the interplay
of “demand” and “supply.”
Demand in a Market
Individual demanders have preferences given
prices and their incomes. Individuals have
different opinions and preferences
Market demand is the sum of all individuals’
demands.
Application: The market for gasoline
Illustrates the general result: As a price rises,
consumers generally demand less of a good.
Conditions that Affect Demand
Demand depends on economic conditions
Mainly:Consumers’ incomes
Prices of other goods
Consumer preferences (they change)
When these things change, demand changes
Example: Sales of electric cars (a change in
preferences) will reduce demand for gasoline;
rising incomes which lead consumers to buy
more and bigger cars will increase demand.
Supply in a Market
Individual suppliers (sometimes) differ in
their costs to produce (some farmers have
better land – some producers have patents and
trade “secrets”).
Costs of production (sometimes) change when
producers try to expand.
Application: Natural gas (similar to other
resource markets).
Market Supply
Depends on “technology”
Depends on prices for labor, materials, etc.
Market supply is the sum of individual
supplies
Application: The market for gasoline
Slopes upward: Increased output is expensive
Higher prices attract high cost producers
Conditions that Affect Supply
Changes in technology generally make
production less expensive, increasing supply
Changes in prices for things needed for
production change costs of production, and
change supply – can go in either direction.
Application: Rapid technological advance
is making it cheaper to find and extract oil;
this leads to lower costs to produce and sell
gasoline.
Equilibrium in a Market
What is the equilibrium?
A price at which the amount buyers wish to
buy matches the amount which sellers wish
to sell.
We place buyers and sellers together in the
market. Their interaction produces the
equilibrium.
There is a single equilibrium price.
Computing the Equilibrium
Using the gasoline market:
QD = quantity demanded = 31.525 - 1.25P
QS = quantity supplied = 23.9125 + 2.375P
Equilibrium is defined by QD = QS.
31.525 - 1.25P = 23.9125 + 2.375P
P = (31.525 - 23.9125) / (2.375 + 1.25) = 2.1.
Q = 31.525-1.25(2.1) = 28.9.
See previous page for this solution in a
graph.
Shortages and Surpluses
The Law of One Price: In a market, absent
any impediments, a commodity will trade at a single price. Where more than one price exists for a commodity, forces will be set in motion that have the tendency to erase the difference(s).
Shortage: When quantity demanded exceeds
quantity supplied. The price is below the
equilibrium
Ticket scalping
Milk shortages at the advent of a storm
Consumers compete by bidding prices up.
Surplus: When quantity supplied exceeds
quantity demanded. The price is above the
market equilibrium
After Christmas toy sales
Producers compete with each other by
offering lower prices – pushing prices down.
The Law of One Price acts to eliminate
shortages and surpluses
Factors that Change the Equilibrium
Equilibrium (the price) depends on both
supply and demand.
If either supply or demand changes, the
equilibrium price will change also.
When an economic factor changes, we can
predict how price will change based on what
we know about changes in supply and/or
demand.
A Change in Demand
Factors that change demand:
Rising income higher (lower) demand
means a normal (inferior) good
Change in the price of another good
Increasing price of another good higher
(lower) demand means they are
substitutes (complements)
Changes in consumer preferences can increase
or decrease demand.
Consider the market for roses on Valentine’s
Day. Preferences suddenly increase. Price
Rises from $15 to $50 per dozen.
A Change in Supply
Factors that change supply
Rising prices of inputs to production (labor)
Changes in technology
Example: A shortage of college teachers.
(Rising cost of labor to universities)
Rising labor cost causes supply for education
to shift upward (decreased supply).
Rising cost of labor (faculty) forces
universities to raise prices.
Elasticity
A definition: Elasticity =
.
Economists prefer percentage changes to
describe covariation. Consider the demand on
page 20. Looks like a very strong relationship
between price and quantity. Is it? Not at all!
This is (will be called) an “inelastic” demand.
Computing an Elasticity
Various ways, depending on information
available. Simplest:
E =
Application: Roses on Valentine’s Day
Change from price = 20 to price = 8.
Quantities change from 5 to 20. Elasticity is
Ed = .
Demand Elasticity
Ed = Absolute value of
.
Gasoline market demand equation is
QD = 31.525 - 1.25P
equilibrium is P = 2.1 and Q = 28.9
Ed(Gasoline) = Abs[-1.25 (2.1/28.9)] = .091.
ED < 1 Inelastic demand,
ED > 1 Elastic demand,
ED = 1 Unit elastic demand.
Gasoline demand is extremely inelastic.
Other elasticities: Income elasticity
Cross price elasticity
Elasticity effects are larger in the long run
than in the short run.
Other Elasticities
Revenue = Price Quantity
As price rises, quantity falls. Since they move
in opposite directions, the product could rise
or fall. Some businesses (theaters) worry
more about revenue than about quantity.
Revenue elasticity = 1 + Demand Elasticity
(Demand elasticity keeps minus sign here.)
If demand is inelastic, revenue rises when
Price rises. If not, revenue falls.
Supply elasticity
ES = .
QS = 23.9125 + 2.375P. P = 2.1, Q = 28.9
ES = 2.375(2.1/28.9) = 0.1725.
Also quite inelastic.
Macroeconomics and
Money in the Economy
Topics
Interesting Economic Variables
Views of Macroeconomic Policy
Measuring the Economy
Prices and Interest Rates
Fiscal Policy and the Deficit
Monetary Policy, Interest Rates and Inflation
The Money Stock and Money in the Economy
Interesting Economic Variables
Variables that policy makers are interested in
Unemployment and economic activity
Inflation
Interest rates and investment
Exchange rates and world trade
Distribution of income and wealth
Overall well being of the society
Policy
What tools are available?
How do they work?
Do they work?
Policy Tools
Fiscal Policy: Taxes and Spending
Monetary Policy: Money Supply (Interest
Rates)
Are the policies complementary?
Conflicting?
Do the Policy Tools Work?
The Policy “Debate”
Keynesian: Fiscal policy is powerful
Monetarism: Monetary policy is (too)
strong. Fiscal policy is weak and imprecise.
Rational Expectations: Long run
equilibrium; neither policy works in the
long run.
Contemporary view: Long run growth
equilibrium with short run fluctuations
Measuring Economic Activity
Stocks and Flows
Stock = An amount at a point in time
Flow = A change in an amount over time
Application: Is Microsoft, capitalized value
$500 billion as large as Spain, GDP = $500
billion? (New York Times, July 17, 1999)
No (!) Compare MS revenue $20b (flow) to
Spain GDP, $500b. Or, Spain’s capital stock,
several trillion $ to MS $500b.
Compare stocks to stocks or flows to flows.
Flows are the economic activity. Stocks are
the accumulated result of economic activity.
Application: The debt vs. the deficit.
A Measure of Economic Activity
Gross Domestic Product: GDP is the total
value of goods and services produced in the economy during a particular period, valued at current market prices in that period.
GDP for the U.S. in 1998: $8.5 trillion.
To avoid double counting, GDP includes only
final goods and services, not intermediate goods used as inputs in the production of other goods.
Current market prices. If prices change from
one year to the next, this makes comparison of GDP in different years difficult. Does it increase, because more was produced or because the same amount was sold for higher prices?
GDP includes only things that are made or
produced in the current year. Sale values of used cars counted as new before 1999, existing homes, antiques, do not count in 1999 GDP, but the salaries of salespeople who sell them do.
Computing GDP to Measure
Economic Activity
Final Demands: Add up final purchases of
goods and services.
Factor payments: Purchases of goods and
services are ultimately paid to factors of
production, labor (wages and salaries) and
capital (everything else, by definition).
Value added: Add up values added at each
stage of production.
Value added? Approximately total revenue
minus costs of purchased intermediate
products.
Application: VAR in the computer business
is a “value added reseller.” Buys computers,
adds some software and parts, resells. Value
added is the revenue minus the cost of the
original computer
All 3 methods give the same answer.
GDP vs. GNP
The International Economy
GDP is the total value of goods and services
produced inthe domestic economy
GNP is the total value of goods and services
produced by the domestic economy. (Some
payments to U.S. labor may be made in
foreign countries
Difference is net payments to foreign capital
and labor.
Application for 1998: $billion
Gross domestic product..... 8,511.0
Plus: Receipts of factor income from
the rest of the world..... 269.2
Less: Payments of factor income to
the rest of the world..... 289.6
Gross national product..... 8,490.5
Small for the U.S. Large for most countries.
Thinking About Economic Activity
Where does GDP go? Y
=
Private consumption C
Consumption by the government + G
Net purchases by foreigners + X-M
Investment (real, e.g., factories) + I
Society’s choices: Consumption (now) vs.
Investment (consumption later)
Y - T - C= “disposable income” minus
consumption. (T-Taxes)
= savings by individuals
+ T - G = savings by government
= the “deficit”
+ X – M= “savings” by export sector
=I= Investment. Savings is how
we pay for investment.
Private savings. Low by world and historical
standards? Stock market gains may be a form
of wealth accumulation. (High risk if so.)
Price Indexes
Measure how prices of “all goods” have
changed, on average.
Price Index = Sum over goods in the index
100 weight of good i
100
Implicit Price Deflator for GDP
1992=100, Seasonally Adjusted Annual
Rate Source: U.S. Department of
Commerce, BEA, Quarterly
Year Deflator Real GDP Nominal GDP
1998.1 112.32 7749.0 8384.2
1999.1 113.47 ------8807.9
(Note, 8384.2/1.11232 = 7537.6. There
is a “seasonal adjustment.”)
Consumer Price Index (CPI) does the same
computation for the goods consumed by
“consumers.”
Inflation
Rate of inflation = percentage change in the
price index.
Application: Depends on who you are and
where you are. The CPI for 1999. 1984=100
Consumer Price Index % Change to April
Jan. Feb. Mar. Apr. Jan. Feb. Mar.
U.S. city average
161.1 161.2 161.6 162.8 1.1 1.0 0.7
Northeast Urban
168.5 168.4 168.7 169.7 0.7 0.8 0.6
Midwest Urban
156.6 156.6 157.1 158.3 1.1 1.1 0.8
South Urban
158.0 158.1 158.5 159.5 0.9 0.9 0.6
West Urban
162.5 162.8 163.3 165.0 1.5 1.4 1.0
From 1984 to 1999, prices rose fastest in the
Northeast
From January to April, 1999, prices rose
fastest in the West
Where are prices “highest?” Cannot tell.
Inflation in the U.S.
The CPI: Lines show the base year, 1984.
The rate of inflation. Note how low for 90s.
Real Output (Activity)
Nominal GDP and Growth Rates:
Year Deflator Real GDP Nominal GDP
1998.1 112.32 7749.0 8384.2
1999.1 113.47 ------8807.9
From 1998.1 to 1999.1, nominal GDP rose
5.05%. The GDP deflator rose 1.01%. Using
our result for growth rates of products, Real
GDP rose 4.04%. (“Robust growth.”)
How fast is the economy growing?
Recession = Negative growth. 6 appear above
Real Interest Rates
Nominal Interest Rate = “stated” or face
value.
Real Interest Rate = nominal - inflation
Ex-post vs. Ex-ante
Ex-post: Looking backward
Accounting for inflation, return
on asset was …
Ex-ante: Looking forward
Nominal interest rates include
a factor for anticipated inflation.
When lenders lend money, or investors
put money in assets, they look forwardto
their returns.
Investors care about “real returns” which
are typically 3% to 7% in the U.S. economy.
Macroeconomic Policy
Policy Objectives
Real economic activity
Employment
Output
Investment in productive capacity
Prices, the rate of inflation
Policy Tools and Mechanisms
Fiscal Policy: Tax and Spending Policy
Affects demand for goods and services
Taxes affect markets through prices
Monetary Policy: Money Stock,
Interest Rates
Interest rates affect investment and
credit demand.
Monetary policy affects inflation
Fiscal Policy
Taxes and spending directly affect demand
for goods and services
The debt and the deficit:
National Debt =
Sum of the yearly deficits over all years we
have been a country
When tax receipts exceed spending, a surplus
results, and the debt declines.
What is “debt reduction?” (1999-2000 budget)
Can the government change spending or
taxes enough to affect total demand?
More than 75% of the federal budget is
not changeable – interest obligations and
entitlements. Taxes change only slightly.
Probably not.