Katherine advertises to sell cookies for $4 a dozen. She sells 50 dozen, and decides that she can charge more. She raises the price to $6 a dozen and sells 40 dozen. What is the elasticity of demand? Are the cookies elastic or inelastic? Show your calculations for full marks.
I got 0.55
0.78
To calculate the elasticity of demand, we need to use the formula:
Elasticity of Demand = ((Q2 - Q1) / ((Q2 + Q1) / 2)) / ((P2 - P1) / ((P2 + P1) / 2))
Where:
Q1 = Initial quantity demanded
Q2 = Final quantity demanded
P1 = Initial price
P2 = Final price
Given:
Q1 = 50 dozen
Q2 = 40 dozen
P1 = $4 per dozen
P2 = $6 per dozen
Now, let's substitute the given values into the formula:
Elasticity of Demand = ((40 - 50) / ((40 + 50) / 2)) / (($6 - $4) / (($6 + $4) / 2))
Simplifying further:
Elasticity of Demand = (-10 / (90 / 2)) / ($2 / ($10 / 2))
Elasticity of Demand = (-10 / 45) / (2 / 5)
Elasticity of Demand = -0.222 / 0.4
Elasticity of Demand = -0.55
Therefore, the elasticity of demand is -0.55.
To determine whether the cookies are elastic or inelastic, we look at the absolute value of the elasticity of demand:
Absolute Value of Elasticity = | -0.55 | = 0.55
If the absolute value is less than 1, the demand is inelastic. If it is greater than 1, the demand is elastic. In this case, since the absolute value of the elasticity is 0.55, the cookies are considered inelastic in demand.