1. Some Introductory Material
Economics of the Firm
Some Introductory Material

2. Introducing homo economicus….also known as “Economic Man”
Economic man is a RATIONAL being

3. Every decision we make involves both incremental benefits and costs…if 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?

4. 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 isn’t free..it has a price
You will buy a glass of lemonade as long as the benefits are greater than the costs

5. We can complicate the example by adding an alternative choice…a 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 won’t be spent on hot dogs
You will buy a glass of lemonade as long as the benefits are greater than the costs

6. 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

7. We can easily add another variable to our demand story…most 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

8. We have a similar situation on the supply side…with 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 decisions…how do we align their incentives?

9. 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

10. While it is not necessary, it is sufficient to say that maximizing each year’s 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 firm’s decisions are made at the margin!!!

11. For each sale that is made, it must be profitable at the margin
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 firm’s decisions are made at the margin!!!

12. In either case, we can say that, given a representation of a firm’s 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

13. 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.

14. 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

15. 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 4 5

16. 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 4 5

17. 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.

18. 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

19. 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 it’s lemonade sales to 250 cups per week
Price
$3.00
$2.00
Quantity
200
250

20. 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

21. Suppose that the overall market consists of 5,000 identical lemonade drinkers and 100 lemonade suppliers
Price
$2.75
At a price of $2.50, each of the 5,000 lemonade drinkers buys 5 glasses per week.
$2.50
Quantity
20,000
25,000
Price
At a price of $3.00, each of the 100 lemonade suppliers is willing to sell 250 glasses per week.
$3.00
$2.00
Quantity
20,000
25,000

22. Given the behavior of suppliers and consumers, the market price would need to settle in between $2.50 and $2.75
Price
$2.00
At a price of $2.00, total supply is 20,000, but demand is at least 25,000
Quantity
20,000
Q>25,000

23. 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
Q<20,000
25,000

24. We would call the $2.60 price the equilibrium price
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

25. Suppose that average income in the area rose to $75,000
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

26. Suppose that average income in the area rose to $75,000
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

27. At the wage level of $10, $2.60 can no longer be the equilibrium price
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
18,000
22,500
At the wage level of $10, $2.60 can no longer be the equilibrium price

28. Higher wages cause a rise in market price and a drop in sales
Suppose that lemonade store wages rose to $10/hr. Higher wages should lower supply at any market price
Price
$2.75
$2.60
Quantity
20,000
22,500
Higher wages cause a rise in market price and a drop in sales

29. + 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
(+)
(+)

30. If we truly believe in competitive markets, we can sleep well at nigh knowing several things…goods 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

31. 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)

32. 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
$50K
$23M
$15K
Quantity
3,000,000
Quantity 1

33. Microsoft’s new Xbox 360 gaming console was released in North America on November 22 at a retail price of $ Available supply sold out almost immediately as Christmas shoppers stood in line for this year’s hot item. (Microsoft has increased its sales target from 3M units to 6M units).
What’s odd about this??

34. Why didn’t Microsoft raise their price?
???
$299.99
Quantity 3M
Clearly, $ is not an equilibrium price !

35. 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

36. And now for something completely different….

37. 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 tomorrow’s temperature is 95 degrees?

38. The answer to all these questions come from a probability distribution
1/2
Head
Tail
A probability distribution is a collection of probabilities describing the odds of any particular event
Probability
1/6 1 2 3 4 5 6

39. 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)

40. Without some math, we can’t find the probability of a specific outcome, but we can easily divide up the distribution
Probability
Temperature
Mean-2SD
Mean -1SD
Mean
Mean+1SD
Mean+2SD
2.5%
13.5%
34%
34%
13.5%
2.5%

41. Can’t we do a little better than this?
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 23 41 59 77 95
Can’t we do a little better than this?

42. Conditioning on month gives us a more accurate forecast!
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 70 77 84 91 95 98
Conditioning on month gives us a more accurate forecast!

43. 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!

44. The Truth Temperature ~
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.

45. The Truth Conditional Distributions Temp (Summer) ~ Temp (Winter) ~
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

46. = 3 X Some useful properties of probability distributions
Probability distributions are scalable =
3 X
Mean = 1
Variance = 4
Std. Dev. = 2
Mean = 3
Variance = 36 (3*3*4)
Std. Dev. = 6

47. = + Probability distributions are additive COV = 2 Mean = 1
Variance = 1
Std. Dev. = 1
Mean = 2
Variance = 9
Std. Dev. = 3
Mean = 3
Variance = 14 ( *2)
Std. Dev. = 3.7
COV = 2

48. 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

49. The Truth How much should a six year old car be worth?
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.

50. Searching for the truth….
You believe that there is a relationship between age and value, but you don’t know what it is….
Collect data on values and age
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!!

51. Value = a + b * (Age) + error
Slope = b a
Value = a + b * (Age) + error
We want to choose ‘a’ and ‘b’ to minimize the error!

52. We have our estimate of “the truth”
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

53. Regression Statistics
R Squared
0.36
Standard Error
2250
Percentage of value variance explained by age
Error Term
Mean = 0
Std, Dev = $2,250

54. We can now forecast the value of a 6 year old car
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)

55. 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

56. What are the odds that Pat Buchanan received 3,407 votes from Palm Beach County in 2000?

57. The Strategy: Estimate a conditional distribution for Pat Buchanan’s votes using every county EXCEPT Palm Beach
Using Palm Beach data, forecast Pat Buchanan’s vote total for Palm Beach

58. 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

59. P = Buchanan’s Vote Percentage B = Percentage Black
Side note: Why logs?
P = Buchanan’s 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 Buchanan’s vote percentage by 5% (Say, from 1% to 6%)
A 10% increase in the black percentage (say, from 30% to 40%) increases Pat Buchanan’s 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 Buchanan’s vote percentage by 5% (Say, from 1(1.05) = 1.05%)

60. The Results:
Variable
Coefficient
Standard Error
t - statistic
Intercept
2.146
.396
5.48
Black (%)
-.0132
.0057
-2.88
Age 65 (%)
-.0415
-5.93
Hispanic (%)
-.0349
.0050
-6.08
College (%)
-.0193
.0068
-1.99
Income (000s)
-.0658
.00113
-4.58
Now, we can make a forecast!

61. 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 Buchanan’s vote total!

62. We know that the log of Buchanan’s vote percentage is distributed normally with a mean of and with a standard deviation of .2556
Probability
LN(%Votes)
– 2*(.2556)
*(.2556) = =
There is a 95% chance that the log of Buchanan’s vote percentage lies in this range

63. Next, lets convert the Logs to vote percentages
Probability
% of Votes
There is a 95% chance that Buchanan’s vote percentage lies in this range

64. Finally, we can convert to actual votes
Probability
Votes
There is a 95% chance that Buchanan’s total vote lies in this range