Cross elasticity of demand

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In economics, the cross elasticity of demand and cross price elasticity of demand measures the responsiveness of the quantity demand of a good to a change in the price of another good.

It is measured as the percentage change in quantity demanded for the first good that occurs in response to a percentage change in price of the second good. For example, if, in response to a 10% increase in the price of fuel, the quantity of new cars that are fuel inefficient demanded decreased by 20%, the cross elasticity of demand would be -20%/10% = -2.

The formula used to calculate the coefficient cross elasticity of demand is

$E_{A,B} = \left|\frac{\%\ \rm{change}\ \rm{in}\ \rm{quantity}\ \rm{demanded}\ \rm{of}\ \rm{product}\ A}{\%\ \rm{change}\ \rm{in}\ \rm{price}\ \rm{of}\ \rm{product}\ B}\right|$

or:

$E_{A,B}={P_1B + P_2B \over Q_1A + Q_2A}\times{\Delta QA \over \Delta PB}$

Two goods that complement each other show a negative cross elasticity of demand: as the price of good Y, the demand for good X falls

In the example above, the two goods, fuel and cars(consists of fuel consumption), are complements - that is, one is used with the other. In these cases the cross elasticity of demand will be negative. In the case of perfect complements, the cross elasticity of demand is infinitely negative.

Where the two goods are substitutes the cross elasticity of demand will be positive, so that as the price of one goes up the quantity demanded of the other will increase. For example, in response to an increase in the price of carbonated soft drinks, the demand for non-carbonated soft drinks will rise. In the case of perfect substitutes, the cross elasticity of demand is equal to infinity.

Where the two goods are complements the cross elasticity of demand will be negative, so that as the price of one goes up the quantity demanded of the other will decrease. For example, in response to an increase in the price of fuel, the demand for new cars will decrease.

Where the two goods are independent, the cross elasticity demand will be zero: as the price of one good changes, there will be no change in quantity demanded of the other good.

When goods are substitutable, the diversion ratio - which quantifies how much of the displaced demand for product j switches to product i - is measured by the ratio of the cross-elasticity to the own-elasticity multiplied by the ratio of product i's demand to product j's demand. In the discrete case, the diversion ratio is naturally interpreted as the fraction of product j demand which treats product i as a second choice,^[1] measuring how much of the demand diverting from product j because of a price increase is diverted to product i can be written as the product of the ratio of the cross-elasticity to the own-elasticity and the ratio of the demand for product i to the demand for product j. In some cases, it has a natural interpretation as the proportion of people buying product j who would consider product i their `second choice.'