Elasticity and Revenue
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1.docxII. Price Elasticity of Demand
(A) Definitions:
1. The PRICE ELASTICITY OF DEMAND measures the responsiveness, or sensitivity, of the quantity demanded by consumers as prices change.
Note the negative sign in the formula. This is to keep the Elasticity of Demand greater or equal to zero. Because of the Law of demand, when price goes down, the quantity demanded goes up (and vice versa).
2. If the percentage change in quantity is greater than the percentage change in price, then the price elasticity of demand is greater than one and the demand for the good is said to be ELASTIC.
% change in Qd > % change in P then
Ed > 1 ==> ELASTIC DEMAND
For example the elasticity of demand for restaurant meals is greater than two (2.3), so demand for restaurant meals is elastic.
3. If the percentage change in quantity is less than the percentage change in price, then the price elasticity of demand is less than one and the demand for the good is said to be INELASTIC.
% change in Qd < % change in P then
Ed < 1 ==> INELASTIC DEMAND
For example the elasticity of demand for salt is about .1, so demand for salt is very inelastic.
4. Elasticity is calculated in terms of percentages so the units used do not affect the measure.
Since quantity demanded moves in the opposite direction as price, the measure should be negative, but elasticity of demand is always expressed in positive numbers, thus the negative sign in the equation.
Elasticities are calculated using statistical analysis of quantity demanded for different goods and services, holding other variables such as household income constant.
One way to practically think about elasticity of demand is: Does the price of the good or service make you think about whether to buy it or not? The more elastic the demand, the more you think about it and the more the price influences your decision.
For example the elasticity of demand for restaurants is fairly elastic (2.3), so that price almost always comes into play in deciding whether to go out, where to go, and what to order. This is not the case with salt (Ed = 0.1), if you are out of salt, then you buy it. Also, if the price of salt falls, you are not going to buy a lot more (unlike restaurants...).
Or another example, an estimated price elasticity of demand for rice is about 0.265, so the demand for rice is quite inelastic. (Note: this is from the Philippines, and is corrected for the income effect. In the Philippines, a rise in the price of rice, which is a staple, causes household real income, or purchasing power, to fall, driving down their ability to buy in general, and rice in particular. But here in the U.S., this income effect is smaller because of the higher incomes here and because rice is a small part of household budgets - almost none for many).
(B) Determinants of Elasticity of Demand:
1. SUBSTITUTES:
The greater the number of substitute goods, the greater the elasticity of demand. Consumers will be responsive to changes in price by switching to or from substitute goods.
Thus elasticity for a nationally known brand of sliced cheese was 3-3.5, where there are many close substitutes, will be greater than the elasticity for store brand of sliced cheese (Ed = 1.8 to 1.9), where there are not many close substitutes.
Note that these results are affected by the product and income of the buyers - for some types of products like snack cheese, and also higher income consumers, the elasticity affect is much less as people seem to see the nationally known brand as not having substitutes.
2. PROPORTION OF INCOME:
The more a good costs with respect to a person's income, the more its elasticity.
Thus the elasticity of demand is higher for automobiles (Ed = 1.1) than gasoline (Ed = 0.2 in the short run).
We can see this in that when gasoline prices rose in 2005 15% or more as compared to 2004, but there was only a small decline in sales of gasoline. But in 2005 GM had the “employee price” sale, so prices in 2006 were up without this sale, and GM sales fell 20% or more.
3. LUXURIES VS. NECESSITIES:
Luxuries tend to be more price elastic than necessities. Thus restaurant meals (Ed = 2.3) is much more price elastic than foods such as salt, bread, rice, sugar, coffee, eggs, or milk (Ed = 0.1 to 0.63).
4. TIME:
The elasticity of demand for products is greater over a longer period of time when consumers have more ability to adjust. Thus the short run elasticity for gasoline (.2) is much less than the long-run (.7), as consumers have a chance to buy smaller cars, adjust to public transport, telecommute more, or even move to minimize their commutes.
(C) Calculating Elasticity:
1.
Note that elasticity is actually a point concept, and best done using derivatives (calculus). But most students don’t know this, and I forgot almost all my calculus so no calculus!
2. To calculate elasticity of demand (without calculus), we use the MIDPOINT METHOD, where the changes are based on the midpoint of the two quantities and prices.
By using the midpoint method, we avoid the problem of the percentage change being affected by the starting and ending points. For example, what is the percentage change between one and two? Going from one to two is a 100% change, but from going from two to one is only a 50% change.
To calculate the elasticity of demand for a price change from p1 to p2, causing a change in the quantity demanded from q1 to q2, we have:
Numerical example (Table 6.1 page 118)
Total Quantity Price per Unit Elasticity
1 $8
2 $7
3 $6
4 $5
5 $4
6 $3
7 $2
8 $1
Numerical Example of the midpoint method:
(D) Graphical Analysis:
1. First of all need to realize that ELASTICITY CHANGES ALONG A LINEAR (STRAIGHT) LINE. This means that a straight line, with constant slope, has different elasticities, depending on where you are.
(optional) For example for the graph of the table above:
Around the midpoint of the line, where the quantity and price are changing at the same rate, there is unitary elasticity. But at higher prices and lower quantities, where the % change in quantity is greater and the % change is price is less than at the midpoint, then elasticity is greater than one and demand is elastic. In the same way, at lower prices and greater quantities, the % change in quantity is less and the % change in price is more than at the midpoint, so that the elasticity is less than one and demand is inelastic.
A demand curve with unitary elasticity throughout would actually be a curve which is steeper as the quantity approaches zero and almost flat as the price approaches zero. Ed = 1 for all P & Q
Note that constant Ed means - (dQ/Q)/(dP/P) = k for all P, Q
then (dQ/Q) = - k(dP/P)
integrating ==> integral (dQ/Q) = integral - k(dP/P) = - k integral (dP/P)
then ln(Q) + c = - k[ln(P) + b] = - kln(P) - kb
let (- kb – c) = g, then ln(Q) = - k(ln(P)) + g
exponentiating Q = e(-k(ln(p)) + g) = e(-kln(p))X(e(g))
let e(g) = h, then Q = hp(- k)
if k = 1 (unit elasticity), Q = hP(-1) = h/P, or P = h/Q,
which is a rectangular hyperbola as seen in the graph above.
2. But given the same price and quantity, curves with steeper slopes will have smaller elasticities.
This can be seen in terms of the extremes of zero and perfect elasticity.
When a good is totally inelastic, or price elasticity equal zero, then there is no change in quantity demanded no matter what the price, so the curve is a straight line. An example is demand for medicine such as insulin or Epipen.
What is an example of very inelastic? Demand for tobacco...
On the other hand, when demand is totally elastic, so that even a very small change in price will produce a large change in the quantity demanded, then the Ed = ∞ and the demand curve will be virtually flat.
An example for this might be demand for one farmer's rice -- if it is at all above the market equilibrium, no one will want to buy.
What is an example of very elastic? Demand for yachts…
Thus the demand curves for goods with inelastic demand will be very steep, while the demand curves for goods with elastic demand are relatively flat.
III. Elasticity and Total Revenue
(A) TOTAL REVENUE equals price times quantity, so
TR = P x Q
(B) Examples
1. IF DEMAND IS ELASTIC then the % change in Q is greater than the % change in P, then a decrease in price will increase quantity more, so that total revenue will rise.
% CHANGE IN Q > % CHANGE IN P
SO IF P DOWN AND Q UP, THEN TR UP
Example: demand for restaurant food is elastic, so if a restaurant lowers its prices then it could gain so many customers that it would make more money. This can explain some of the success of fast food restaurants that have been able to gain market share through lower prices.
Note here the importance of ceteris paribus, everything else being equal. This is assuming the demand for their food is constant, other restaurants haven’t raised their prices, etc. etc.
2. IF DEMAND IS INELASTIC so that the percent change in Q is less than the percent change in P, then an increase in price will decrease quantity less, so that total revenue will rise.
% CHANGE IN Q < % CHANGE IN P
SO IF P DOWN AND Q UP, THEN TR DOWN
Example: demand for farm goods is inelastic. So if farmers if farmers all have good harvests due to good weather, then Q is up, but prices will fall. Since D is inelastic, P falls more (in percentage terms), so that total revenue or farm income can fall. Thus a bumper crop can actually be bad for farmers.
(generally can skip the following as there are no real life examples:)
3. IF DEMAND IS UNIT ELASTIC then a change in price would have no impact on total revenue, since the percent change in price would be exactly offset by an equal and opposite percent change in quantity.
% CHANGE IN Q == % CHANGE IN P
SO IF P UP AND Q DOWN, THEN TR UNCHANGED
Note that total revenue and profits are not the same. If one increases quantity by lowering the price, total revenue may increase, but not profits, as the profit margin falls too. This has happened to auto companies with the record sales due to rebates and low-interest financing.
(C) Summary and Example
1. Summary: If businesses want to raise revenue:
if demand is elastic, need to have lower prices.
if demand is inelastic, need to cut quantity
2. Elasticity of Demand and Lobbying:
Demand for farm products is inelastic. So farmers want higher prices, which requires less output, but increases total revenue. Since output is less, expenses must be the same or less, so profits rise. But farming is competitive, with thousands of farmers, so this is difficult to do.
So farmers organize to have the government enforce less output through farm subsidy programs. Farmers lobby for farm supports to raise farm prices – this will increase the revenue, income, and profits for farmers.
On the other hand, demand for restaurants is elastic. So to increase total revenue restaurants need lower prices. But to maintain profits, restaurants have to keep costs down. Restaurants use a lot of labor, so they want to keep labor costs down.
Restaurants lobby against raising the minimum wage. This would held to keep restaurant costs low, so that they can keep prices low, and this will increase revenues and maintain their profits.
Some of you may of heard of nationwide protests a few years ago targeting fast food restaurants and demanding $15 an hour in pay.
3. Elasticity of Demand and Legalization of Drugs
Elasticity of Demand also comes into play when debating the legalization of drugs. If demand for drugs were inelastic, then legalization would increase supply, which would cause only a small increase in use and a large drop in price. Thus the total revenue (=total expenditures) on the drug falls. Then the savings in terms of less crime to support drug users habits and also in terms of prisons (half to two-thirds of prisoners in California are for drug-related crimes), and ability of police and courts to focus on other crimes.
Graph of inelastic demand: Supply increases with legalization. The quantity of drugs rises, but much less than price falls.
The drop in spending on prisons and drug enforcement could be used to fund more drug rehabilitation and education campaigns to reduce the demand for drugs.
On the other hand, if the demand for drugs was relatively elastic, then legalization would lead to a large increase in drug use as supply increased. While you would still get the same savings in terms of prison costs and drug enforcement, you would not get the savings from a reduction in crime to support the drug use.
However the main drug that I think has more elastic demand in marijuana, which does not have much secondary crime.
Graph of elastic demand: Supply increases with legalization. Quantity of drugs rises more than price falls:
A question here is how much taxes could be collected? I thought that the tax benefits are overstated by supporters of legalization, and initially tax revenues were significantly lower than estimated. However, this was probably because the industry supply grew slower than estimated as after a few years revenues are more than estimates. This probably means that demand for marijuana is not that elastic, and indeed I don’t see that much increase in use.
Another possibility is that supply didn't increase that much with legalization, since pot was pretty widespread even before legalization.
Note that there are some unexpected overdosing because of eating too much pot. There also is an unexpected benefit in that studies show a DROP in teenage use of pot. An unanticipated downside was a sizable increase in THC (active ingredient in pot) vaping, which seems to be the most dangerous kind (associated with a spate of lung disease and even death).
