Demand Elasticity - Who pays?

In high school, through university and even in the CFA, economics is an important field of study. One of my favourite topics is the concept of elasticity.

Elasticity is literally defined as the percentage change in quantity over the percentage change in price and has several flavours (negative elasticity, positive elasticity for substitutes, negative cross elasticity for complements etc)

Elasticity = %ΔPrice / %ΔQuantity
%ΔPrice = ΔPrice / Pavg = P1 - P2 / Pavg
%ΔQuantity = ΔQuantity / Qavg = Q2 - Q1 / Qavg

Mathematically, note that as you move up and down the curve, the elasticity changes because percentage is affected by the absolute value of the average price. If the average price falls, the elasticity increases because the change becomes larger relative to the average to which it is compared for percentage purposes.

Another way of looking at elasticity is flexibility or bargaining power. If you review Michael Porter's five forces, you can see that elasticity for suppliers or customers increases their bargaining power. That is to say, the more competition and choices available means more options.

Let's look at a good which exhibits perfect inelasticity. This means that regardless of the price, consumers will always consume a constant amount (they set the quantity demanded). This manifests in a horizontal demand curve as shown below:

Note that the determining factor of the price is the supply curve. If there are more suppliers, the supply curve shifts right and the price drops. If there are less suppliers, the supply curve shifts left and the price rises. This is similar to what happens with oil and the "prisoner's dilemma" in OPEC's oligopoly.

Next, look at a perfectly elastic curve. This means that given the slightest change in price, the consumers will dramatically change their spending habits (that is to say, that consumers set the price). This manifests as a horizontal demand curve (at the price they set).
The only power suppliers have here is to set the quantity sold (they are price takers). If there are more suppliers, the supply curve shifts right and there is more quantity sold. Visa versa, if there are less suppliers the supply curve shifts left and there is less quantity sold.

This is important when determining how price changes will affect measures like total revenue, quantity consumed etc. This also applies regardless of whether you are talking about goods sold, wages paid, taxes paid etc.

[Example] The government is thinking of applying a tax on a good which exhibits perfectly elastic demand. Who bears the cost?

1. The supplier
2. The customer
3. The supplier and the customer share the tax burden

[Solution] One way to look at this is that if the good exhibits perfectly elastic demand, then the customers have all the bargaining power. This means that if any supplier were to simply "pass along the tax" and make the consumer pay, the consumer would just go to a different supplier. This means the supplier is forced to take on all the tax. The solution is 1. Notice this also means it eats into the producer surplus.

If the good were perfectly demand inelastic, the suppliers have all the bargaining power then the customer would bear all the tax and the solution would be 2. This would eat into the consumer surplus.

If the good were neither perfectly demand elastic or inelastic, the supplier and customer would split the difference in fractions based on who had more relative bargaining power. Both producer and consumer surplus would diminish. The solution would be 3.