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## Economics of the Firm

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**Economics of the Firm**Consumer Demand Analysis**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**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**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)**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**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**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!**Consider the following demand curve:**Price $12.00 $10.00 Quantity 32 40 Arc Elasticity**Consider the following demand curve:**Price $12.00 $10.00 Quantity 32 40 Point Elasticity**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**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**If you are interested in maximizing revenues, you are**looking for the spot on the demand curve where elasticity equals 1. Revenues Price**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)**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**For any fixed price, demand (typically) responds positively**to increases in income. Income Elasticity measures this effect quantitatively Price $4.00 Quantity 2 4**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**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**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**Next, Collect Data on Prices and Sales**Price Quantity**(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.**If we want to calculate the elasticity of our estimated**demand curve, we need to specify a specific point. $2.50 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.**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.**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%.**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!!**One Problem**Suppose you observed the following data points. Could you estimate a demand curve? D**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**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**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**Suppose we solved for price and quantity by using the**equilibrium condition**We could estimate the following equations**The original parameters are related as follows: We can solve for the supply parameters, but not demand. Why?**By including a demand shifter (Income), we are able to**identify demand shifts and, hence, trace out the supply curve!! S D D D**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**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**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:**First, let’s plot the data…what do you see?**This data seems to have a linear trend**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**Lets forecast electricity usage at the mean time period (t =**8)**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**We can use this linear trend model to predict as far out as**we want, but note that the error involved gets worse! Sample**One method of evaluating a forecast is to calculate the root**mean squared error Sum of squared forecast errors Number of Observations**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**Average Ratios**• Q1 = .87 • Q2 = 1.16 • Q3 = .91 • Q4 = 1.04 We can adjust for this seasonal component…**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**Ratio Method**Dummy Variables