# Foundation Series: Price Elasticity

When prices go up, demand goes down.  But how much does it go down?  Price elasticity of demand is the term economists use for the math that describes this behavior.

## Cause and Effect

Prices go up and sales go down.  Prices go down, and sales go up.  There is definitely a correlation – and economists will argue that it is cause and effect.  I think they’re right – and here’s the rationale.

Imagine an apple, a group of people who are interested in buying that apple.  Each person would be willing to pay a different amount for that apple, because each person assigns a different value, or utility, to having that apple.   Even two identical twins who normally would value the apple the same might value it differently right now.  Imagine that one of our twins has not eaten in a couple days, and the other just finished a very large meal.  They would realize different amounts of utility right now from that same apple.  Or imagine a millionaire and a pauper, who value apples equally, but place less importance on a small amount of money.  Or imagine someone with a bushel of apples, and someone with none – to whom is “one more apple” worth more?

Because different people are willing to pay different amounts (for different reasons) to buy an apple, we have the effect of demand (a proxy for eventual sales) that varies with price.

At price X, half of this group of people would be willing to buy the apple.  Some people might see it as a great bargain, while others are only just barely willing to pay the price of X.  There are also some people who are almost willing, but the price is just a bit too high.  And finally, some people for whom a price of X is just unreasonable.

If you lower the price, all of the people who were previously willing to buy the apple are still willing.  The people who were almost willing before will now buy the apple.  If, on the other hand, you had raised the price, the people who were just barely willing to buy will instead not buy.

The graph above shows price on the vertical axis, and quantity on the horizontal.  When you lower the price from P0 to P1, the quantity that will be sold increases from Q0 to Q1.

## Price Elasticity of Demand

When you’re talking about pricing impacts on demand, you’ll usually just say “price elasticity” but it is worth remembering the “of demand” part.  For example – there’s also Price Elasticity of Supply.  Think of the apple example above.  Imagine that the group of people are all selling apples, and there’s a single buyer.  Depending on the price the buyer sets, some people would be willing to sell, and others unwilling.  Change that market price, and the number of available apples for sale will change.  For now, we’ll focus on the impact of changing prices on demand.

The reason price elasticity is interesting is because it gives us some insight into how much the quantity will change when prices change.

Economists have a couple formulas for price elasticity (of demand), including e = % change in quantity / % change in price.

When the relative quantity changes by exactly the same amount as the relative price, you have e=-1, referred to as unitary elasticity.  If you reduce your price by 10%, you increase the quantity sold by 10%.

As a numerical example, you price bags of apples at \$10 each, and are able to sell 20 bags of apples for \$200.  With e=-1, unitary elasticity, if you lowered the price to \$9, you would then sell 22 bags for \$198.  If you had raised the price to \$11 per bag, you would have sold 18 bags for \$198.  If you dropped the price to \$5 per bag, you would have sold 40 bags for \$200.  Ignoring rounding errors, you would always have the same revenue.

The areas of the two rectangles formed by matching price and quantity are identical.  This leads to the conclusion that you will get the same revenue (assuming you can meet demand) regardless of the price you set for your product.  However, don’t worry about this too much – as far as I know, no real-world products have unitary elasticity.

## Changes, More or Less

Elasticity is still useful for understanding the magnitude of change in demand that results from changes in price.  Does demand change by more than your change in price, or by less?

An inelastic demand curve has an elasticity value between 0 and -1.

The resultant relative changes in quantity from a given change in price are smaller than the change in prices.  You can see from the steepness of the cuve in the inelastic demand curve above that a large drop in price (from P0 to P1) results in a small increase in quantity sold (from Q0 to Q1).  However, the converse is also true – a relatively large increase in price will cause a proportionally smaller decrease in demand.

This tends to be the case with products that people “must have.”  In other words, people don’t have good alternatives (substitute goods, or doing without).  When the price of gas doubled, did you reduce the amount of gas you purchase by half, or by less than half?  On the whole, demand for gas dropped by less than 50% when the price doubled.  Another example is anti-biotics.

An elastic demand curve is one where the quantity is very sensitive to changes in price, and has elasticity values below -1.

Small changes in price result in large changes in quantity with an elastic demand curve.  This tends to happen when there are reasonable alternatives to purchasing the product.  For example, when mass-scale production of chicken started and poultry prices dropped in the US, demand increased faster than prices dropped.  This happened at the expense of beef and pork purchases.

## Conclusion

In Predictably Irrational, the authors identify several pricing concepts, like anchoring where people are psychologically influenced to believe one product is more valuable than another.  They look at some very interesting experiments that appear to highlight things that influence people’s perception of utility – making them willing to pay different prices.  An interesting extension of their ideas is that you can influence the price elasticity of demand for your product through positioning and marketing actions.

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