8. Calculate the price elasticity demand, given Q1=500 , Q2=1000 , P1=55,P2=50
To calculate the price elasticity of demand, we need to use the formula:
Elasticity = (Percentage change in quantity demanded) / (Percentage change in price)
First, we need to calculate the percentage change in quantity demanded.
Percentage change in quantity demanded = ((Q2 - Q1) / ((Q1 + Q2) / 2)) * 100
Let's plug in the values:
Q1 = 500
Q2 = 1000
Percentage change in quantity demanded = ((1000 - 500) / ((500 + 1000) / 2)) * 100
= (500 / 750) * 100
= 66.67%
Next, we need to calculate the percentage change in price.
Percentage change in price = ((P2 - P1) / ((P1 + P2) / 2)) * 100
Let's plug in the values:
P1 = 55
P2 = 50
Percentage change in price = ((50 - 55) / ((55 + 50) / 2)) * 100
= (-5 / 52.5) * 100
= -9.52%
Now, we can calculate the price elasticity of demand using the formula mentioned earlier:
Elasticity = (Percentage change in quantity demanded) / (Percentage change in price)
= (66.67%) / (-9.52%)
Finally, we can calculate the price elasticity of demand:
Elasticity ≈ -6.999
Note that the negative sign indicates that the demand is elastic, meaning that a change in price will result in a proportionally larger change in quantity demanded.