Answer:
Between a price of $4 and $5, the price elasticity of demand is -0.67 (round to one decimal point) and at that point the demand elasticity is inelastic. Between a price of $8 and $9, the price elasticity of demand is -2.67 (round to one decimal point) and at that point the demand elasticity is elastic. Revenue is maximized when the price is at $6 and the demand elasticity equals -1.
Explanation:
The price elasticity of demand can be calculated using the following formula:
Price elasticity of demand = Percentage in quantity demanded / Percentage change in price .................................... (1)
Therefore, we have:
a. Between a price of $4 and $5
Here, we have:
Percentage in quantity demanded = ((60 - 70) / 60) * 100 = -16.67%
Percentage in price = (($5 - $4) / $4) * 100 = 25%
Therefore, we have:
Price elasticity of demand = -16.67% / 25% = -0.67
Since the absolute value |0.67| is less than 1, the demand elasticity is inelastic at this point.
b. Between a price of $8 and $9
Here, we have:
Percentage in quantity demanded = ((20 - 30) / 30) * 100 = -33.33%
Percentage in price = (($9 - $8) / $8) * 100 = 12.50%
Therefore, we have:
Price elasticity of demand = -33.33% / 12.50% = -2.67
Since the absolute value |2.67| is greater than 1, the demand elasticity is elastic at this point.
c. Revenue is maximized when the price is at $_________ and the demand elasticity equals .
Note: See the attached excel file for the Computation of Marginal Revenue
Revenue is maximized when the Marginal Revenue is equal to zero. This occurs when the price is at $6 in the attached excel file (in bold red color).
Since price increased from $5 to $6, we have:
Percentage in quantity demanded = ((50 - 60) / 50) * 100 = -20%
Percentage in price = (($6 - $5) / $5) * 100 = 20%
Therefore, we have:
Price elasticity of demand = 20% / 20% = -1
Since the absolute value |1| is equal to 1, the demand elasticity is unitary at this point.
Conclusion
Between a price of $4 and $5, the price elasticity of demand is -0.67 (round to one decimal point) and at that point the demand elasticity is inelastic. Between a price of $8 and $9, the price elasticity of demand is -2.67 (round to one decimal point) and at that point the demand elasticity is elastic. Revenue is maximized when the price is at $6 and the demand elasticity equals -1.
