Question

1. There are several ways of Finding out the price elasticity of demand (e) ;depending on the type of data. (a) Percentage change formula (b) Mid-point formula (c) Slope of demand d) Slope of the demand after (natural) logarithmic transformation:

ii. Find out (e) using this method for the following demand curve at P= 10 : lnQ= 20-7ln P

Answer 1

We know from the law of demand how the quantity demanded will respond to a price change: it will change in the opposite direction. But how much will it change? It seems reasonable to expect, for example, that a 10% change in the price charged for a visit to the doctor would yield a different percentage change in quantity demanded than a 10% change in the price of a Ford Mustang. But how much is this difference?

To show how responsive quantity demanded is to a change in price, we apply the concept of elasticity. The price elasticity of demand for a good or service, eD, is the percentage change in quantity demanded of a particular good or service divided by the percentage change in the price of that good or service, all other things unchanged. Thus we can write

Equation 5.2

Because the price elasticity of demand shows the responsiveness of quantity demanded to a price change, assuming that other factors that influence demand are unchanged, it reflects movements along a demand curve. With a downward-sloping demand curve, price and quantity demanded move in opposite directions, so the price elasticity of demand is always negative. A positive percentage change in price implies a negative percentage change in quantity demanded, and vice versa. Sometimes you will see the absolute value of the price elasticity measure reported. In essence, the minus sign is ignored because it is expected that there will be a negative (inverse) relationship between quantity demanded and price. In this text, however, we will retain the minus sign in reporting price elasticity of demand and will say “the absolute value of the price elasticity of demand” when that is what we are describing.