To calculate the price elasticity of demand between $2.00 and $1.50 given an increase in quantity demanded from 50 to 100, we first compute the percentage changes in quantity and price and then apply the formula. The calculation yields a price elasticity of demand of -3, indicating an elastic demand where the quantity demanded changes proportionally more than the price change.
The price elasticity of demand measures how the quantity demanded of a good responds to changes in its price. To calculate the price elasticity of demand, we use the formula:
Price Elasticity of Demand (PED) = (% change in quantity demanded) / (% change in price)
In graph (3), the price changes from $2.00 to $1.50. Assuming the quantity demanded increases from 50 to 100 units as the price decreases, we can apply the formula.
First, we calculate the percentage change in quantity:
- (Quantity after change - Quantity before change) / ((Quantity after change + Quantity before change) / 2) x 100
- (100 - 50) / ((100 + 50) / 2) x 100 = 100%
Second, we calculate the percentage change in price:
- (Price after change - Price before change) / ((Price after change + Price before change) / 2) x 100
- ($1.50 - $2.00) / (($1.50 + $2.00) / 2) x 100 = -33.33%
Finally, the PED between $2.00 and $1.50:
- PED = 100% / -33.33%
- PED = -3 (rounded to the nearest whole number)
The negative sign indicates that the relationship between price and quantity demanded is inverse. A PED of -3 means the demand is elastic because the absolute value of PED is greater than 1, indicating that a change in price leads to a proportionally larger change in quantity demanded.