Economics of the Firm

1. Economics of the Firm Consumer Demand Analysis

2. Demand relationships are based off of the theory of consumer choice. We can characterize the average consumer by their utility function. “Utility” is a function of lemonade and hot dogs Consumers make choices on what to buy that satisfy two criteria: Their decision on what to buy generates maximum utility Their decision on what to buy generates is affordable These decisions can be represented by a demand curve

3. Example: Suppose that you have $10 to spend. Hot Dogs cost $4 apiece and glasses of lemonade cost $2 apiece. This point satisfies both conditions and, hence, is one point of the demand curve

4. Now, suppose that the price of hot dogs rises to $6 (Lemonade still costs $2 and you still have $10 to spend) You can’t afford what you used to be able to afford – you need to buy less of something! (Income effect) Your decision at the margin has been affected. You need to buy less hot dogs and more lemonade (Substitution effect)

5. Now, suppose that the price of hot dogs rises to $6 (Lemonade still costs $2 and you still have $10 to spend) This point satisfies both conditions and, hence, is one point of the demand curve

6. Demand curves slope downwards – this reflects the negative relationship between price and quantity. Elasticity of Demand measures this effect quantitatively Price $6.00 $4.00 Quantity 1 2

7. Arc Elasticity vs. Price Elasticity At the heart of this issue is this: “How do you calculate a percentage change? Suppose that a variable changes from 100 to 125. What is the percentage increase? - OR - Note: This discrepancy wouldn’t be a big deal if these two points weren’t so far apart!

8. Consider the following demand curve: Price $12.00 $10.00 Quantity 32 40 Arc Elasticity

9. Consider the following demand curve: Price $12.00 $10.00 Quantity 32 40 Point Elasticity

10. If demand is linear, the slope is a constant, but the elasticity is not!! Price $18.00 $10.00 $2.00 Quantity 8 40 72

11. If demand is linear, the slope is a constant, but the elasticity is not!! High prices = High Elasticities Price Unit Elasticity $18.00 Low prices = Low Elasticities $10.00 $2.00 Quantity 8 40 72

12. If you are interested in maximizing revenues, you are looking for the spot on the demand curve where elasticity equals 1. Revenues Price

13. Now, suppose that the price of a hot dog is $4, Lemonade costs $2, but you have $20 to spend. Your decision at the margin is unaffected, but you have some income left over (this is a pure income effect)

14. Now, suppose that the price of a hot dog is $4, Lemonade costs $2, but you have $20 to spend. This point satisfies both conditions and, hence, is one point of the demand curve

15. For any fixed price, demand (typically) responds positively to increases in income. Income Elasticity measures this effect quantitatively Price $4.00 Quantity 2 4

16. Cross price elasticity refers to the impact on demand of another price changing Note: These numbers aren’t coming from the previous example!! Price $4.00 Quantity 2 6 A positive cross price elasticity refers to a substitute while a negative cross price elasticity refers to a compliment

17. Cross Sectional estimation holds the time period constant and estimates the variation in demand resulting from variation in the demand factors Demand Factors Time t-1 t+1 t For example: can we predict demand for Pepsi in South Bend by looking at selected statistics for South bend

18. Estimating Cross Sectional Demand Curves Lets begin by estimating a basic demand curve – quantity demanded is a function of price. Next, we need to assume a functional form. For simplicity, lets start with a linear model

19. Next, Collect Data on Prices and Sales Price Quantity

20. That is, we have estimated the following equation

21. (3.004) (0.774) (10.02) Our forecast of demand is normally distributed with a mean of 23 and a standard deviation of 9.90.

22. If we want to calculate the elasticity of our estimated demand curve, we need to specify a specific point. $2.50 23

23. Given our model of demand as a function of income, and prices, we could specify a variety of functional forms Linear Demand Curves Here, quantity demanded responds to dollar changes in price (i.e. a $1 increase in price lowers demand by 4 units.

24. Given our model of demand as a function of income, and prices, we could specify a variety of functional forms Semi Log Demand Curves Here, quantity demanded responds to percentage changes in price (i.e. a 1% increase in price lowers demand by 4 units.

25. Given our model of demand as a function of income, and prices, we could specify a variety of functional forms Semi Log Demand Curves Here, percentage change in quantity demanded responds to a dollar change in price (i.e. a $1 increase in price lowers demand by 4%.

26. Given our model of demand as a function of income, and prices, we could specify a variety of functional forms Log Demand Curves Here, percentage change in quantity demanded responds to a percentage change in price (i.e. a 1% increase in price lowers demand by 4%. Log Linear demands have constant elasticities!!

27. One Problem Suppose you observed the following data points. Could you estimate a demand curve? D

28. Estimating demand curves A problem with estimating demand curves is the simultaneity problem. S Market prices are the result of the interaction between demand and supply!! D

29. Estimating demand curves Case #1: Both supply and demand shifts!! Case #2: All the points are due to supply shifts S S S’ S’ S’’ S’’ D D’ D’’ D

30. An example… Suppose you get a random shock to demand Demand The shock effects quantity demanded which (due to the equilibrium condition influences price! Supply Therefore, price and the error term are correlated! A big problem !! Equilibrium

31. Suppose we solved for price and quantity by using the equilibrium condition

32. We could estimate the following equations The original parameters are related as follows: We can solve for the supply parameters, but not demand. Why?

33. By including a demand shifter (Income), we are able to identify demand shifts and, hence, trace out the supply curve!! S D D D

34. Time Series estimation holds the demand factors constant and estimates the variation in demand over time Demand Factors Time t-1 t+1 t For example: can we predict demand for Pepsi in South Bend next year by looking at how demand varies across time

35. Time series estimation leaves the demand factors constant and looks at variations in demand over time. Essentially, we want to separate demand changes into various frequencies Trend: Long term movements in demand (i.e. demand for movie tickets grows by an average of 6% per year) Business Cycle: Movements in demand related to the state of the economy (i.e. demand for movie tickets grows by more than 6% during economic expansions and less than 6% during recessions) Seasonal: Movements in demand related to time of year. (i.e. demand for movie tickets is highest in the summer and around Christmas

36. Suppose that you work for a local power company. You have been asked to forecast energy demand for the upcoming year. You have data over the previous 4 years:

37. First, let’s plot the data…what do you see? This data seems to have a linear trend

38. A linear trend takes the following form: Estimated value for time zero Estimated quarterly growth (in kilowatt hours) Forecasted value at time t(note: time periods are quarters and time zero is 2003:1) Time period: t = 0 is 2003:1 and periods are quarters

39. Lets forecast electricity usage at the mean time period (t = 8)

40. Here’s a plot of our regression line with our error bands…again, note that the forecast error will be lowest at the mean time period T = 8

41. We can use this linear trend model to predict as far out as we want, but note that the error involved gets worse! Sample

42. One method of evaluating a forecast is to calculate the root mean squared error Sum of squared forecast errors Number of Observations

43. Lets take another look at the data…it seems that there is a regular pattern… Q2 Q2 Q2 Q2 We are systematically under predicting usage in the second quarter

44. Average Ratios • Q1 = .87 • Q2 = 1.16 • Q3 = .91 • Q4 = 1.04 We can adjust for this seasonal component…

45. Now, we have a pretty good fit!!

46. Recall our prediction for period 76 ( Year 2022 Q4)

47. We could also account for seasonal variation by using dummy variables Note: we only need three quarter dummies. If the observation is from quarter 4, then

48. Note the much better fit!!

49. Ratio Method Dummy Variables

50. A plot confirms the similarity of the methods