**Elasticity**

The magnitude of change we can expect from a supply or demand shock is determined by shape of the two curves.

The elasticity of the curves can determine how much the quantity or price changes upon a shock.

A perfectly inelastic demand curve is shown below.

When there are no substitutes for a particular product, for example body parts for a transplant, then the demand curve for that product will be inelastic. When there is a supply shock, the quantity doesn't change - only the price changes.

On the other hand, we have a perfectly elastic demand curve below.

A very substitutable product will be elastic. A possible example of an elastic good is toilet paper, where we'll simply switch to another brand if a particular brand becomes expensive. Once the price increases, the quantity sold will drop drastically.

Elasticity can be expressed as:

If the quantity falls by 2% for every 1% increase in price, then we have E = -2. Therefore, an inelastic good will have E = 0, and a perfectly elastic good will have E = -infinity. E will typically be between 0 and -infinity.

Suppose now that a producer sells Q goods at price P, they will make revenue R = PQ. The change in revenue with respect to price, would be:

From this formula, if we are a producer, we should only raise prices when E is between 0 and -1.

**Estimating Elasticities**

Theoretical economics can show us the direction of change, but empirical economics is what we use to show us the absolute values of change. However, the most difficult part of empirical economics is causation vs correlation.

Take the example in the previous article, we saw that the price of pork rose when the price of beef rose.

If we wanted to calculate E here, we might try to plug in the numbers in the formulae. Since both the price and quantity increased in this case, we may say that we have a positive elasticity - higher price led to higher quantity. However, this is one of the most dangerous mistakes we can make. In this case, the increase in demand is actually what's causing the price to increase, and not the other round. We can only use this formula to find the amount of change in quantity per percentage change in price. Since quantity is driving the price in this case, and not the other round, we cannot apply the elasticity formula.

What we are measuring here is actually the elasticity of the supply.

However, when we change the supply as in the following diagram, we can actually get the correct answer.

What we want is to be able to measure the slope of the demand curve. By shifting the supply curve, keeping the demand curve unchanged, we can measure the elasticity.

**Taxation Example**

Suppose that we have vendors selling 100 million units of a particular type of product for $10 each. The government comes along and imposes a tax on the vendors, asking for $1 per unit. This increase in price effectively shifts the supply curve up. In order to make the same amount, the producers would have to charge $11 for each unit. However, this causes the equilibrium to drop to 97 million units, at $10.5 per unit.

In this case, we can clearly see that the equilibrium points have traveled on the demand curve, so we can calculate the elasticity using the formula.

Since we see that the elasticity is -0.6, this means that we can continue raising prices further to increase profits.

Of course, we are assuming elasticity is constant. However, since elasticity is a curve for straight demand lines, we are actually just measuring the LOCAL elasticity around that price change.

It can be seen that the amount of money the government earns is the final equilibrium quantity multiplied by the amount of tax. This can be represented by the shaded region. We can clearly see that the amount of money the government makes depends on the elasticity of demand.

If demand is perfectly inelastic, then the amount the government makes is simply Q * tax per unit. If the product demand is elastic, then the government will make a lot less money as the price needs to be fixed.

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