1. 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. “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 Lemonade Expenditures on Hot Dogs 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 receive compensation from the firm Managers provide effort to the firm Stockholders/Bondholders provide capital for 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 Current Profits Profits one year in the future Risk adjusted rate of return Profits two years in the future

10. While it is not necessary, it is sufficient to say that maximizing each year’s profits will maximize firm value 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 Variable costs are influenced by 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 now, lets assume that the firm has no control over the price it charges As with the average consumer, a firm’s decisions are made at the margin!!! 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.

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 Rational Behavior (-) Sales of lemonade are positively related to the price of lemonade and negatively related to marginal costs Costs are a function of wages, material prices, etc. (+)

13. A Demand Function represents the rational decisions made by a representative consumer(s) Quantity Purchased “Is a function of” 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. Quantity Price $2.50 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 Quantity Price $2.50 5 $2.75 4

16. Demand curves slope downwards – this reflects the negative relationship between price and quantity. Elasticity of Demand measures this effect quantitatively Quantity Price $2.50 5 $2.75 4

17. A Supply Function represents the rational decisions made by a representative firm(s) Quantity Supplied “Is a function of” 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 Quantity Price $2.00 200 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.

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 Quantity Price $2.00 200 $3.00 250

20. Supply curves slope upwards – this reflects the positive relationship between price and quantity. Elasticity of Supply measures this effect quantitatively Quantity Price $2.00 200 $3.00 250

21. Quantity Price $2.00 $3.00 Quantity Price 25,000 20,00025,000 $2.50 $2.75 20,000 Suppose that the overall market consists of 5,000 identical lemonade drinkers and 100 lemonade suppliers At a price of $2.50, each of the 5,000 lemonade drinkers buys 5 glasses per week. At a price of $3.00, each of the 100 lemonade suppliers is willing to sell 250 glasses per week.

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

23. Quantity Price Given the behavior of suppliers and consumers, the market price would need to settle in between $2.50 and $2.75 $3.00 Q<20,00025,000 At a price of $3.00, total supply is 25,000, but demand is less than 20,000

24. Quantity Price Given the behavior of suppliers and consumers, the market price would need to settle in between $2.50 and $2.75 $2.60 22,500 We would call the $2.60 price the equilibrium price

25. Quantity Price Suppose that average income in the area rose to $75,000. Higher income levels should raise demand at any market price $2.60 22,50028,000 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 At the new income level of $75,000, $2.60 can no longer be the equilibrium price

26. Quantity Price Suppose that average income in the area rose to $75,000. Higher income levels should raise demand at any market price $2.60 22,50025,000 The increase in income causes a rise in sales and a rise in market price $3.00

27. Quantity Price Suppose that lemonade store wages rose to $10/hr. Higher wages should lower supply at any market price $2.60 22,50018,000 At the current $2.60 market price, supply has fallen to 18,000, but demand is still at 22,500 At the wage level of $10, $2.60 can no longer be the equilibrium price

28. Quantity Price Suppose that lemonade store wages rose to $10/hr. Higher wages should lower supply at any market price $2.60 22,50020,000 Higher wages cause a rise in market price and a drop in sales $2.75

29. Supply, Demand, and equilibrium prices/sales (Preferences) Rational Behavior (-)(+) + (Constraint) (-)(+) 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. Quantity Price 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 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)

31. Quantity Price We also can rest assured that we are producing exactly the right goods and services Quantity Price Hot Dogs Lemonade 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. High School Teacher: Salary = $50,000 Kobe Bryant: Salary = $23,000,000,000 Can we use our market model to explain differences in salaries? Quantity Price $23M 1 Quantity Price $50K 3,000,000 $15K

33. Microsoft’s 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 year’s hot item. (Microsoft has increased its sales target from 3M units to 6M units). What’s odd about this??

34. Quantity Price 3M Clearly, $299.99 is not an equilibrium price ! ??? $299.99 Why didn’t Microsoft raise their 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 Head Tail 1/2 Probability 16 1/6 Probability 2345 A probability distribution is a collection of probabilities describing the odds of any particular event

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 Temperature We generally assume a Normal Distribution which can be characterized by a mean (average) and standard deviation (measure of dispersion) Mean Standard Deviation

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

41. Annual Temperature in South Bend has a mean of 59 degrees and a standard deviation of 18 degrees. Probability Temperature 5977954123 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) Can’t we do a little better than this?

42. 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 Temperature 8491987770 95 degrees falls a little more than one standard deviation away (there approximately a 16% chance that the temperature is 95 or greater) 95 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) Suppose that we were to flip a coin over and over again and after each flip, we calculate the percentage of heads & tails That is, if we collect “enough” data, we can eventually learn the truth! (Sample Statistic)(True Probability)

44. We can follow the same process for the temperature in South Bend 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. 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) ~ Temp (Winter) ~ Regression is based on the estimation of conditional distributions

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

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

48. Mean = 8 Variance = 4 Std. Dev. = 2 Mean = $ 12,000 Variance = 4,000,000 Std. Dev. = $ 2,000 Suppose we know that the value of a car is determined by its age Value = $20,000 - $1,000 (Age) Car Age Value

49. We could also use this to forecast: 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…. 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!!

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

52. Regression Results VariableCoefficientsStandard Errort Stat Intercept12,35465318.9 Age- 85480-10.60 Value = $12,354 - $854 * (Age) + error We have our estimate of “the truth” Intercept (a) Mean = $12,354 Std. Dev. = $653 Age (b) Mean = -$854 Std. Dev. = $80 T-Stats bigger than 2 in absolute value are considered statistically significant!

53. Regression Statistics R Squared0.36 Standard Error2250 Error Term Mean = 0 Std, Dev = $2,250 Percentage of value variance explained by age

54. We can now forecast the value of a 6 year old car Salary = $12,354 - $854 * (Age) + error 6 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. +95% -95% Age Value 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 Forecast Interval

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 CountyBlack (%) Age 65 (%) Hispanic (%) College (%) Income (000s) Buchanan Votes Total Votes Alachua21.89.44.734.626.526284,966 Baker16.87.71.55.727.6738,128 Parameters to be estimated Error term Buchanan Votes Total Votes *100

59. Side note: Why logs? P = Buchanan’s Vote Percentage B = Percentage Black Option #1: LinearOption #2: Semi –Log Linear Option #3: 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: VariableCoefficientStandard Errort - statistic Intercept2.146.3965.48 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!

61. CountyBlack (%) Age 65 (%) Hispanic (%) College (%) Income (000s) Buchanan Votes Total Votes Palm Beach21.823.69.822.133.53,407431,621 This would be our prediction for Pat Buchanan’s vote total!

62. Probability LN(%Votes) There is a 95% chance that the log of Buchanan’s vote percentage lies in this range -2.004 – 2*(.2556)-2.004 + 2*(.2556) = -2.5152= -1.4928 We know that the log of Buchanan’s vote percentage is distributed normally with a mean of -2.004 and with a standard deviation of.2556

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

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