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© 1999-2003 Douglas A. Ruby Revised:01/17/2003 Demand-Side Shocks Microeconomics |
On the demand-side of the market, elasticities can be calculated for any of the relevant exogenous variables. In all cases, elasticity measures the percentage change in quantity demanded relative to a percentage change in one of the exogenous variables. Income Elasticity of Demand
Income elasticities measure the response in quantity demanded to a change in consumer income. In this case, the corresponding elasticity may be positive for normal goods, negative for
inferior goods, or equal to zero for income neutral
goods. This elasticity is computed as follows:
h If both numerator and denominator are of the same sign (both increase or both decrease) then the corresponding good or service is a normal good. If numerator and
denominator are opposite in sign (one increases as the other decreases), then the
good is an inferior good. Finally if the value of the numerator is zero (quantity
demanded does not change with income), then the good is income neutral. The table
below summarizes these results:
Cross-Price Elasticity of Demand
Cross-Price elasticity of demand measures the response of quantity demanded of one good to changes in the price of a second (related) good. This elasticity is computed as follows: h If the two goods are P In this case the price of good-y and the quantity demanded of good-x move in the same direction and thus the cross-price elasticity would be positive. If the two goods are P Where in this case the price of good-y and quantity demanded of good-x move in opposite directions. The corresponding cross-price elasticity would be negative. Finally if changes in the price of one good has no effect on the quantity demanded
of the other, then the cross-price elasticity would be zero and the two goods are
unrelated. The following table summarizes these results:
Elasticities and Non-Linear Demand
The following demand equation represents a non-linear relationship between quantity demanded and market price. Q This expression is a valid demand relationship Noting that the price-elasticity of demand may be written as: hIn this last expression the (DQ/ DP) term represents the slope of the demand equation. Thus, if we differentiate the non-linear demand equation given above and substitute, we have the following
The parameter (exponent) 'a' is the price elasticity of demand. A more specific non-linear demand equation (one where many of the exogenous variables are explicitly defined) may be defined as follows: Q It can be shown (through partial differentiation) that the parameters a,b,f,g all represents various types of elasticity measures. That is: a = hThus if we have the following (estimated) equation: Q we can state that demand for this particular |