Chapter 6: Simple Pricing
I. Introduction
Hi, this is Luke Froeb of Vanderbilt University’s Owen School of Management. I am the author of Managerial Economics: A Problem Solving Approach, along with Brian McCann. This lecture is designed to supplement Chapter 6: Simple Pricing.
(Pause to create separation.)
II. Opening Anecdote:
From early 2007 to the middle of 2008, the average price of a gallon of gas in the United States rose from under $2 to over $4. This was, of course, bad news for drivers of gas-guzzling SUVs. However, it was very good news for two McMinnville, TN, workers named Dolly and Molly—or perhaps bad news, depending on how you look at it. You see, Dolly and Molly are mules, and when the price of gas rose, the cost of running a tractor rose, meaning it now made sense for their owner to switch back to use mules.
Similarly, farmers in India reacted to higher gas prices by increasing their use of camels. This increased demand for camels caused a tripling of prices for camels over a two-year period.
By contrast, NNS, a U.S. company producing potash fertilizer, failed to adjust the price of their branded fertilizer in response to market signals, and thus lost out on $13 million in earnings. You see, petroleum is a key ingredient of fertilizer, so when the cost of oil, and thus fertilizer inputs, rose, NNS’s price of “generic” fertilizer doubled. Historically, NNS had priced their branded fertilizer at a 35% premium above the generic price. However, they failed to adjust the price in accordance to rising input costs and ended up pricing their branded fertilizer at 25% below the generic price. If the premium had simply been maintained, they would have sold the same volume at a higher price and thus would have earned an additional $13 million.
This is not a unique case. Despite the power of pricing, it is an oft-neglected tool. We all know that profit equals price times quantity minus cost times quantity, but business seem to focus on selling more and reducing costs and forget about raising price.
III. Background: Consumer Surplus and Demand Curves
Let’s consider a simplified relationship between price and quantity purchased by a single customer at a hot dog stand. The table shows how many hot dogs the customer will buy at various prices. As you can see, as price falls, the customer buys more hot dogs, providing a fine illustration of the first law of demand, which says that consumers demand more as price falls, assuming other factors are held constant. This makes intuitive sense. We’ve all been there. That first hot dog is amazing and extremely satisfying. The second might still be pretty good. By the time you’re on your fifth hot dog, you might not be enjoying yourself too much. In economic speak, you are experiencing diminishing marginal returns.
Now we can construct a chart with marginal values for various quantities—he values the first hot dog at $5, the second at $4, and so on—as well as the total values, which is the sum of the preceding marginal values.
The key here is to think in marginal terms. Looking at the chart, the total value of 5 hot dogs is $15, so you might be tempted to price the hot dogs at $3. However, the marginal value of the fourth hot dog is only $2, so at a price of $3, the consumer will only purchase 3.
When consumers behave optimally, they try to maximize the surplus they get from consuming hot dogs, which is equal to the difference between their total value and the price they pay. So if the consumer is charged a price of $3 and buys 3 hot dogs, his surplus is the $12 total value minus the $9 cost, so $3. If he were to purchase more or less than 3 hot dogs, his surplus will decrease.
To describe how consumers respond to price, economists use demand curves, which tell us how much a consumer or group of consumers will consume as a function of price. The demand curve slopes downward because, as we’ve learned, consumers purchase more as prices fall.
This is true for both a single consumer and for groups of consumers. To describe the buying power of a group of consumers, we add up all the individual demand curves to get an aggregate, or market demand curve.
This aggregate demand curve is the relationship between the price and the number of purchases made by this group of consumers. You can see that at a price of $7, 1 person is willing to buy; at $6, 2 people are willing to buy; and so on.
You can see on the graph that price, which is the independent variable, is on the wrong axis. For now, you can just attribute that to economists being weird. Also, when moving up and down the demand curve, we say that “the quantity demanded” changes. When the demand curve itself moves, we say demand changes.
IV. Marginal Analysis of Pricing
Looking at the demand curve, you can see there is an implicit trade-off. The seller can either raise the price, thereby earning more on each unit sold but selling fewer, or reduce the price, thereby earning less on each unity sold but selling more. To resolve the dilemma, we once again turn to marginal analysis and find ourselves a great rule-of-thumb: If marginal revenue is greater than marginal cost, you can increase profit by reducing the price and thus selling more. If marginal revenue is less than marginal cost, then you should increase the price and thus sell less.
In order to see how to use marginal analysis to maximize profit, let’s take a look at a table listing price, quantity, revenue, marginal revenue, marginal cost, and total profit for our demand curve.
Remember, in order to entice new consumers into the marketplace, a firm has to reduce the price for all customers, not just the additional customers attracted by the lower price.
Okay, at a price of $7, one customer would purchase a hot dog, so revenue would be $7. Cost would be $1.50, so profit would be $5.50. If we reduce the price to $6, two customers purchase hot dogs, revenue goes up to $12, which makes marginal revenue $5, which we get by subtracting the $7 from $12. In order to maximize profit, the seller should continue lowering the price until the marginal revenue is equal to the marginal cost of $1.50, or just higher if that is impossible. Here, we can see that the seller should lower the price to $5, where marginal revenue is $3 and the marginal cost is $1.50.
V. Price Elasticity and Marginal Revenue
Unfortunately, it’ll never be this easy in the real world. You’ll never see a demand curve like the one we just looked at. In reality, it is very difficult to predict consumer response to a price change. The best one can do is make an educated guess as to what demand looks like away from current prices.
But hold on—don’t quit the class just yet. You might not see an entire demand curve, but you don’t need to see an entire demand curve to know how to price—all you need is information on marginal revenue and marginal cost. Remember, if marginal revenue is greater than marginal cost, reduce price. If marginal revenue is less than marginal cost, increase price.
So how do we estimate marginal revenue? Basically, you can either measure quantity responses to past price changes, “experiment” with price changes, or run market surveys to see how quantity would change in response to a price change. If you can find any information on how consumers will respond to a price change, it’s likely to be information on the price elasticity of demand, which is denoted by a small e.
The price elasticity of demand is equal to the percent change in quantity demanded divided by the percent change in price. It measures the sensitivity of quantity demanded to price changes.
If quantity changes more than price, the demand curve is elastic, which means it is sensitive to price. If quantity changes less than price, the demand curve is inelastic. Note that, since price and quantity move in opposite directions, meaning as price goes up quantity goes down, price elasticity is negative. To keep things clear, we use the absolute value of price elasticity.
Let’s consider what happened when MidSouth, a grocery store, decreased the price of Coke from $1.79 to $1.50 in order to match the price offered at a nearby Wal-Mart. In response to the price drop, the quantity sold doubled from 210 to 420 units per week.
To get the most accurate estimate, we need to divide the midpoint of price (P1 plus P2) divided by 2 and the midpoint of quantity (Q1 plus Q2 divided by 2). Note that since 2 divides by both denominator and numerator the two two’s cancel each other out.
So we end up with Q1 minus Q2 over Q1 plus Q2 divided by P1 minus P2 over P1 plus P2. Plugging in the numbers gives us an estimated price elasticity of -3.8, indicating that a 1% decrease in price of Coke leads to a 3.8% increase in quantity. Revenue increases by $254.10, and, in general, the percent change in revenue is equal to the percent change in price plus the percent change in quantity. Since price and quantity move in opposite directions, one will be positive and one will be negative. So whichever change is bigger—price or quantity—determines whether revenue goes up or down.
Elasticity tells you which change is bigger. With elastic demand, the change in quantity will, as we learned, be greater than the change in price. So if you increase the price, the revenue will decrease. If you decrease the price, revenue will increase.
When demand is inelastic, the relationship is reversed, meaning that price increases raise revenue because the price increase is bigger than the corresponding quantity increase. Conversely, price decreases reduce revenue because the price reduction is bigger than the quantity increase.
In order to test your understanding of the relationship between price changes, elasticity, and revenue, you can turn to page 73 in order to derive the relationships between elasticity, price changes, and revenue changes. (Note: Luke, this derivation section had a lot of formulas, and it seemed like it’d be a little awkward and confusing to go through it verbally. You might disagree, however.)
VI. What makes demand more elastic?
We know now that the more elastic demand is, the lower the profit-maximizing price is. Given the clear importance of elasticity to pricing, it’s worthwhile to sharpen our intuitive feel for what would make demand more or less elastic. There are four factors here, and we’ll go through them one by one.
First, products with close substitutes have elastic demand. Obviously, if the next-best alternative is largely indistinguishable from a product you purchase, if the price of the product goes up even a little bit, you will switch to the alternative.
Second, demand for an individual brand is more elastic than industry aggregate demand. This makes sense because individual brands within a product category have close substitutes in each other; product categories do not. As a general rule of thumb, we can say that brand price elasticity is approximately equal to industry price elasticity divided by the brand share. For example, if the elasticity of demand for all running shoes is -.4, and the market share of Nike running shoes is 20%, price elasticity of demand for Nike running shoes is -.4 divided by .2 which equals -2. Using our optimal pricing formula, we can see that Nike has a desired markup of about 50%.
Also, products with many complements have less elastic demand. Products that are consumed as part of a larger bundle, say shoelaces with shoes, have less elastic demand. If the price of shoelaces increases, you’re not going to just stop buying shoelaces because you need them to wear with your shoes.
Third, there is the factor of time. Given more time, consumers are more responsive to price changes because they have more time to find substitutes when price goes up. In the long run, demand curves become more elastic, meaning the absolute value of e increases. Also, as time passes, information about a new price becomes more widely known and people react to that change.
Finally, as price increases, demand becomes more elastic as consumers find more alternatives to the good whose price has gone up. And as they find more substitutes, we can look back to maxim one to see that demand becomes more elastic. For example, high fructose corn syrup and sugar are perfect substitutes for use in soft drinks. However, due to various reasons, sugar costs about twice as much as high fructose corn syrup in the U.S. As a result, all soft drink bottlers use high fructose corn syrup because they have no close substitutes to the low-priced corn syrup; its demand is relatively inelastic. But if the price of high fructose corn syrup rose, then sugar would be a good substitute and demand for high-priced corn syrup would become very elastic.
VII. Forecasting demand using elasticity
We can also use elasticity as a forecasting tool. With an elasticity and a percent change in price, you can predict the corresponding change in quantity by multiplying the elasticity by percent change in price. For example, if price elasticity of demand is -2, and price goes up by 10%, then quantity is expected to go down by 20%.
Price is not the only factor affecting demand, though. To measure the effects of other factors, such as income or advertising, we define factor elasticity of demand as percent change in quantity divided by percent change in the factor. For example, demand for iced tea is strongly influenced by temperature. If the temperature elasticity of demand for iced tea is .25, then a 1% increase in temperature will lead to a .25% increase in quantity demanded.
Income elasticity of demand measures the affect of changing income on demand. If demand increases with income, the good is normal. If demand declines as income increases, the good is inferior.