Economics of the Firm

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Economics of the Firm

• Some Introductory Material

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Introducing homo economicus.also known as
Economic Man
Economic man is a RATIONAL being
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Every decision we make involves both incremental
benefits and costsif we are acting rationally,
we will undertake any action where the benefits
outweigh the costs.
Example
Suppose that you have been wandering in the
desert for 5 days when you come across a lemonade
stand. How much would you pay for a glass of
lemonade?
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Suppose that you have been wandering in the
desert for 5 days when you come across a lemonade
stand. How much would you pay for a glass of
lemonade?
Utility is a function of lemonade (among other
things)
A glass of lemonade will raise your utility
A glass of lemonade isnt free..it has a price
You will buy a glass of lemonade as long as the
benefits are greater than the costs
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We can complicate the example by adding an
alternative choicea hot dog stand
Utility is a function of lemonade and hot dogs
(among other things)
A glass of lemonade will raise your utility
Every dollar spent on lemonade is a dollar that
wont be spent on hot dogs
You will buy a glass of lemonade as long as the
benefits are greater than the costs
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In either case, we can say that, given a
representation of individual tastes, price should
have a negative relationship with quantity
purchased
Utility is a function of lemonade and hot dogs
(among other things)
Rational Behavior
(-)
()
Purchases of lemonade are negatively related to
the price of lemonade and positively related to
the price of hot dogs
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We can easily add another variable to our demand
storymost of us are constrained by our
disposable income.
Expenditures on Hot Dogs
Expenditures on Lemonade
Available Income
(Constraint)

(Preferences)
Rational Behavior
(-)
()
()
Purchases of lemonade are negatively related to
the price of lemonade and positively related to
income and the price of hot dogs
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We have a similar situation on the supply
sidewith one complication.
Managers provide effort to the firm
Stockholders/Bondholders provide capital for the
firm
Managers receive compensation from the firm
Stockholders/Bondholders receive payments from
the firm
Stockholders own the company, but managers make
the decisionshow do we align their incentives?
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If we assume that the institutional details have
been worked out, then the job of the decision
maker is to maximize firm value
Profits one year in the future
Profits two years in the future
Current Profits
Risk adjusted rate of return
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While it is not necessary, it is sufficient to
say that maximizing each years profits will
maximize firm value
Variable costs are influenced by sales decisions
Price times quantity equals current revenues
Fixed costs (overhead) is not affected by the
level of sales and, hence, has no impact on sales
decisions
As with the average consumer, a firms decisions
are made at the margin!!!
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For each sale that is made, it must be profitable
at the margin. For now, lets assume that the
firm has no control over the price it charges
How does an additional sale affect revenues?
How does an additional sale affect costs?
A sale will be made as long as it has a bigger
impact on revenues than costs.
As with the average consumer, a firms decisions
are made at the margin!!!
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In either case, we can say that, given a
representation of a firms cost structure, price
should have a positive relationship with sales
(higher price raises profit margin) while
anything that influences costs at the margin
should have a negative relationship with sales
Costs are a function of wages, material prices,
etc.
Rational Behavior
(-)
()
Sales of lemonade are positively related to the
price of lemonade and negatively related to
marginal costs
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A Demand Function represents the rational
decisions made by a representative consumer(s)
Is a function of
Quantity Purchased
Market Price (-)
Income ()
For example, suppose that at a market price of
2.50, an individual with an annual income of
50,000 chooses to buy 5 glasses of lemonade per
week.
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A Demand Curve is simply a graphical
representation of a demand function
For example, suppose that at a market price of
2.50, an individual with an annual income of
50,000 chooses to buy 5 glasses of lemonade per
week.
Price
2.50
Quantity
5
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A Demand Curve is simply a graphical
representation of a demand function
Suppose that an increase in the market price from
2.50 to 2.75 causes this individual to reduce
his/her lemonade purchases to 4 glasses per week
Price
2.75
2.50
Quantity
5
4
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Demand curves slope downwards this reflects the
negative relationship between price and quantity.
Elasticity of Demand measures this effect
quantitatively
Price
2.75
2.50
Quantity
5
4
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A Supply Function represents the rational
decisions made by a representative firm(s)
Is a function of
Quantity Supplied
Market Price ()
Marginal Costs (-)
For example, suppose that at a market price of
2.00, a firm facing a wage rate of 6/hr will
supply 200 glasses per week.
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A Supply Curve is simply a graphical
representation of a supply function
For example, suppose that at a market price of
3.00, a firm facing a wage rate of 6/hr will
supply 200 glasses of lemonade per week.
Price
2.00
Quantity
200
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A Supply Curve is simply a graphical
representation of a supply function
Suppose that an increase in the market price from
3.00 to 3.90 causes this firm to increase its
lemonade sales to 250 cups per week
Price
3.00
2.00
Quantity
200
250
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Supply curves slope upwards this reflects the
positive relationship between price and quantity.
Elasticity of Supply measures this effect
quantitatively
Price
3.00
2.00
Quantity
200
250
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Suppose that the overall market consists of 5,000
identical lemonade drinkers and 100 lemonade
suppliers
Price
2.75
2.50
At a price of 2.50, each of the 5,000 lemonade
drinkers buys 5 glasses per week.
Quantity
25,000
20,000
Price
3.00
At a price of 3.00, each of the 100 lemonade
suppliers is willing to sell 250 glasses per week.
2.00
Quantity
20,000
25,000
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Given the behavior of suppliers and consumers,
the market price would need to settle in between
2.50 and 2.75
Price
2.00
Quantity
At a price of 2.00, total supply is 20,000, but
demand is at least 25,000
20,000
Qgt25,000
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Given the behavior of suppliers and consumers,
the market price would need to settle in between
2.50 and 2.75
Price
3.00
At a price of 3.00, total supply is 25,000, but
demand is less than 20,000
Quantity
Qlt20,000
25,000
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Given the behavior of suppliers and consumers,
the market price would need to settle in between
2.50 and 2.75
Price
2.60
Quantity
22,500
We would call the 2.60 price the equilibrium
price
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Suppose that average income in the area rose to
75,000. Higher income levels should raise
demand at any market price
Price
At the current 2.60 market price, supply is
still 22,500, but with a higher level of income,
demand has risen to 28,000
2.60
Quantity
22,500
28,000
At the new income level of 75,000, 2.60 can no
longer be the equilibrium price
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Suppose that average income in the area rose to
75,000. Higher income levels should raise
demand at any market price
Price
3.00
2.60
Quantity
22,500
25,000
The increase in income causes a rise in sales and
a rise in market price
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Suppose that lemonade store wages rose to 10/hr.
Higher wages should lower supply at any market
price
Price
At the current 2.60 market price, supply has
fallen to 18,000, but demand is still at 22,500
2.60
Quantity
22,500
18,000
At the wage level of 10, 2.60 can no longer be
the equilibrium price
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Suppose that lemonade store wages rose to 10/hr.
Higher wages should lower supply at any market
price
Price
2.75
2.60
Quantity
22,500
20,000
Higher wages cause a rise in market price and a
drop in sales
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Supply, Demand, and equilibrium prices/sales
(Constraint)

(Preferences)
Rational Behavior
Rational Behavior
(-)
()
(-)
()
With the additional assumption that prices adjust
and that markets clear (equilibrium), we have the
following
()
(-)
Sales are related to average income and marginal
costs
Prices are related to average income and marginal
costs
()
()
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If we truly believe in competitive markets, we
can sleep well at nigh knowing several
thingsgoods are being produced by the most
efficient producers (i.e. those with the lowest
costs) and given to individuals with the highest
values.
Somebody who bought a glass of lemonade paid
2.60 when they actually valued it at much
higher. We call this consumer surplus
Price
Somebody who sold this glass of lemonade
collected 2.60 when the marginal production cost
was much lower. We call this producer surplus
(a.k.a Profit)
Quantity
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We also can rest assured that we are producing
exactly the right goods and services
Price
Price
Quantity
Quantity
Lemonade
Hot Dogs
If consumer preferences suddenly shifted away
from lemonade and towards hot dogs, the lemonade
market would shrink (as the price of lemonade
falls) while the hot dog market expands (and the
price rises)
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Can we use our market model to explain
differences in salaries?
Kobe Bryant Salary 23,000,000,000
High School Teacher Salary 50,000
Price
Price
23M
50K
15K
Quantity
3,000,000
Quantity
1
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Microsofts new Xbox 360 gaming console was
released in North America on November 22 at a
retail price of 299.99. Available supply sold
out almost immediately as Christmas shoppers
stood in line for this years hot item.
(Microsoft has increased its sales target from 3M
units to 6M units).
Whats odd about this??
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Why didnt Microsoft raise their price?
Price
???
299.99
Quantity
3M
Clearly, 299.99 is not an equilibrium price !
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When do our rationality assumptions begin to
break down?
Situations involving interactions among small
groups of people Example How to split 20.
Situations involving the immediate present vs.
the future Example Instant gratification and
the time value of money
Situations involving uncertainty Example The
Monty Hall Problem
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And now for something completely different.
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What are the odds that a fair coin flip results
in a head?
What are the odds that the toss of a fair die
results in a 5?
What are the odds that tomorrows temperature is
95 degrees?
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The answer to all these questions come from a
probability distribution
Probability
1/2
Head
Tail
A probability distribution is a collection of
probabilities describing the odds of any
particular event
Probability
1/6
1
6
2
3
4
5
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The distribution for temperature in south bend is
a bit more complicated because there are so many
possible outcomes, but the concept is the same
Probability
Standard Deviation
Temperature
Mean
We generally assume a Normal Distribution which
can be characterized by a mean (average) and
standard deviation (measure of dispersion)
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Without some math, we cant find the probability
of a specific outcome, but we can easily divide
up the distribution
Probability
Temperature
Mean
Mean1SD
Mean2SD
Mean -1SD
Mean-2SD
2.5
2.5
13.5
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13.5
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Annual Temperature in South Bend has a mean of 59
degrees and a standard deviation of 18 degrees.
Probability
95 degrees is 2 standard deviations to the right
there is a 2.5 chance the temperature is 95 or
greater (97.5 chance it is cooler than 95)
Temperature
59
77
95
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Cant we do a little better than this?
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Conditional distributions give us probabilities
conditional on some observable information the
temperature in South Bend conditional on the
month of July has a mean of 84 with a standard
deviation of 7.
Probability
95 degrees falls a little more than one standard
deviation away (there approximately a 16 chance
that the temperature is 95 or greater)
Temperature
84
91
98
77
70
95
Conditioning on month gives us a more accurate
forecast!
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We know that there should be a true probability
distribution that governs the outcome of a coin
toss (assuming a fair coin)
The Truth
Suppose that we were to flip a coin over and over
again and after each flip, we calculate the
percentage of heads tails
(Sample Statistic)
(True Probability)
That is, if we collect enough data, we can
eventually learn the truth!
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We can follow the same process for the
temperature in South Bend
The Truth
Temperature
We could find this distribution by collecting
temperature data for south bend
Sample Mean (Average)
Sample Variance
Note Standard Deviation is the square root of
the variance.
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Conditional Distributions
Obviously, the temperature in South Bend is
different in the winter and the summer. That is,
temperature has a conditional distribution
Temp (Summer)
The Truth
Temp (Winter)
Regression is based on the estimation of
conditional distributions
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Some useful properties of probability
distributions
Probability distributions are scalable

3 X
Mean 1 Variance 4 Std. Dev. 2
Mean 3 Variance 36 (334) Std. Dev. 6
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Probability distributions are additive


Mean 1 Variance 1 Std. Dev. 1
Mean 2 Variance 9 Std. Dev. 3
Mean 3 Variance 14 (1 9 22) Std. Dev.
3.7
COV 2
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Suppose we know that the value of a car is
determined by its age
The Truth
Value 20,000 - 1,000 (Age)
Value
Car Age
Mean 8 Variance 4 Std. Dev. 2
Mean 12,000 Variance 4,000,000 Std. Dev.
2,000
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We could also use this to forecast
The Truth
Value 20,000 - 1,000 (Age)
How much should a six year old car be worth?
Value 20,000 - 1,000 (6) 14,000
Note There is NO uncertainty in this prediction.
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Searching for the truth.
You believe that there is a relationship between
age and value, but you dont know what it is.

1. Collect data on values and age
2. Estimate the relationship between them

Note that while the true distribution of age is
N(8,4), our collected sample will not be N(8,4).
This sampling error will create errors in our
estimates!!
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Slope b
a
Value a b (Age) error
We want to choose a and b to minimize the
error!
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Regression Results Regression Results Regression Results Regression Results
Variable Coefficients Standard Error t Stat
Intercept 12,354 653 18.9
Age - 854 80 -10.60
We have our estimate of the truth
T-Stats bigger than 2 in absolute value are
considered statistically significant!
Value 12,354 - 854 (Age) error
Intercept (a) Mean 12,354 Std. Dev. 653
Age (b) Mean -854 Std. Dev. 80
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Regression Statistics Regression Statistics
R Squared 0.36
Standard Error 2250
Percentage of value variance explained by age
Error Term Mean 0 Std, Dev 2,250
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We can now forecast the value of a 6 year old car
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Salary 12,354 - 854 (Age) error
Mean 12,354 Std. Dev. 653
Mean 854 Std. Dev. 80
Mean 0 Std. Dev. 2,250
(Recall, Shoe size has a mean of 6)
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Value
95
Forecast Interval
-95
Age
Note that your forecast error will always be
smallest at the sample mean! Also, your forecast
gets worse at an increasing rate as you depart
from the mean
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What are the odds that Pat Buchanan received
3,407 votes from Palm Beach County in 2000?
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The Strategy Estimate a conditional
distribution for Pat Buchanans votes using every
county EXCEPT Palm Beach
Using Palm Beach data, forecast Pat Buchanans
vote total for Palm Beach
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The Data Demographic Data By County
County Black () Age 65 () Hispanic () College () Income (000s) Buchanan Votes Total Votes
Alachua 21.8 9.4 4.7 34.6 26.5 262 84,966
Baker 16.8 7.7 1.5 5.7 27.6 73 8,128
Error term
Buchanan Votes
100
Total Votes
Parameters to be estimated
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Side note Why logs?
P Buchanans Vote Percentage B Percentage
Black
Option 3 Log Linear
Option 1 Linear
Option 2 Semi Log Linear
A 10 increase in the black percentage (say, from
30 to 40) increases Pat Buchanans vote
percentage by 5 (Say, from 1 to 6)
A 10 increase in the black percentage (say, from
30 to 40) increases Pat Buchanans vote
percentage by 5 (Say, from 1 to 1(1.05) 1.05)
A 10 increase in the black percentage (say, from
30 30(1.10) 33 increases Pat Buchanans vote
percentage by 5 (Say, from 1(1.05) 1.05)
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The Results
Variable Coefficient Standard Error t - statistic
Intercept 2.146 .396 5.48
Black () -.0132 .0057 -2.88
Age 65 () -.0415 .0057 -5.93
Hispanic () -.0349 .0050 -6.08
College () -.0193 .0068 -1.99
Income (000s) -.0658 .00113 -4.58
Now, we can make a forecast!
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County Black () Age 65 () Hispanic () College () Income (000s) Buchanan Votes Total Votes
Palm Beach 21.8 23.6 9.8 22.1 33.5 3,407 431,621
This would be our prediction for Pat Buchanans
vote total!
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We know that the log of Buchanans vote
percentage is distributed normally with a mean of
-2.004 and with a standard deviation of .2556
Probability
LN(Votes)
-2.004 2(.2556)
-2.004 2(.2556)
-2.5152
-1.4928
There is a 95 chance that the log of Buchanans
vote percentage lies in this range
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Next, lets convert the Logs to vote percentages
Probability
of Votes
There is a 95 chance that Buchanans vote
percentage lies in this range
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Finally, we can convert to actual votes
Probability
Votes
There is a 95 chance that Buchanans total vote
lies in this range