Question
You are a painter, and the price of a gallon of paint increases from $3.00 a gallon to $3.50 a gallon. Your usage of paint drops from 35 gallons a month to 20 gallons a month.
Computation of the Price Elasticity of demand
The aim of computing price elasticity of demand is to show how much the demand of a commodity or service respond to a change in the demand of the same commodity or service (Moffat, 2011, P.1). Therefore, the price elasticity of demand in the above case is calculated as follows:
Price elasticity of demand = change in the demanded quantity
Change in the price
PED= (Q2-Q1) ÷ (P2-P1)
(Q2+ Q1)/2 (P2+P1)/2
Q1=35 gallons
Q2=20 gallons
P1=$3.00
P2=$3.50
PED= (20-35) ÷ ($3.50- $3.00)
(20+35)/2 ($3.50 +$3.00)/2
PED= (15) ÷ ($0.5)
(27.5) (3.25)
PED= 0.55 ÷ 0.15
PED= 3.67
The computed price elasticity of demand of the paint gallons is therefore 3.67. This means that a change in price of the paint leads to a change in the quantity used of the paint by 3.67 per cent.
Decision on the type of elasticity and interpretation of the results
Based on the computation above, it can be deduced the midpoint price elasticity of demand of the paint gallons is elastic since the resulting figure of 3.67 is greater than 1. Elastic demand occurs in circumstances where a change in price of the commodity or service causes its demand to largely change as well (Nordhaus, 2001, P.34). In such a situation the computed price elasticity is usually greater than 1. On the other hand, inelastic demand is the exact opposite of elastic demand and occurs in circumstances where an increase in price of a commodity or service leads to a decrease in the quantity demanded of the commodity or service. Lastly, the unitary elasticity occurs when there is no change in the quantity demanded of a commodity or service even after a change in the price of the same commodity or service. In this case the computed price elasticity of demand will be equal to 1.
As mentioned earlier, Price elasticity of demand essentially entails the rate of change on the demand of a product as a result to a change in the price of the same. In a nut shell, elastic demand means that even the slightest change in prices causes a major shift in the quantity demanded of the affected commodities or services (Todd, 2010, p.1). While inelastic demand means that even a big change in the prices of commodities causes very minimal changes in the quantity demanded of the same commodities. In the case of the painter, the price increase by $0.5 causes a big drop in the quantity of paint demanded by 15 gallons hence indicating that the price elasticity of demand of the paint is elastic.
Further interpretation of the results indicates that the price elasticity of demand has some correlation with total revenue such that if the price elasticity of demand is elastic the total revenue obtained is negative. On the other hand if the demand is price inelastic an increase in price will make the total revenue increase as well. In the case of unitary elasticity the total revenue is not affected. In the case of the painter whose price elasticity is elastic the increase in price will cause the total revenue to decrease.
Reference List
Moffat, M. (2011). Price Elasticity of Demand. Web.
Nordhaus, S. (2001). Microeconomics (17th ed.). McGraw-Hill.
Todd, B. (2010). Price Elasticity of Demand. Web.