Danny “Dimes” Donahue is a neighborhood’s 9-year-old entrepreneur. His most recent venture is selling homemade brownies that he bakes himself. At a price of R1.50 each, he sells 100. At a price of R1.00 each, he sells 300. Instructions: Use the midpoint method and round your answer to two decimal places. Do not include a negative sign (-). a. What is the elasticity of demand? b. Is demand elastic or inelastic over this price range? multiple choice 1ElasticInelastic c. If demand had the same elasticity for a price decline from R1.00 to R0.50 as it does for the decline from R1.50 to R1.00, would cutting the price from R1.00 to R0.50 increase or decrease Danny’s total revenue? multiple choice 2IncreaseDecrease
Question
Danny “Dimes” Donahue is a neighborhood’s 9-year-old entrepreneur. His most recent venture is selling homemade brownies that he bakes himself. At a price of R1.50 each, he sells 100. At a price of R1.00 each, he sells 300. Instructions: Use the midpoint method and round your answer to two decimal places. Do not include a negative sign (-). a. What is the elasticity of demand? b. Is demand elastic or inelastic over this price range? multiple choice 1ElasticInelastic c. If demand had the same elasticity for a price decline from R1.00 to R0.50 as it does for the decline from R1.50 to R1.00, would cutting the price from R1.00 to R0.50 increase or decrease Danny’s total revenue? multiple choice 2IncreaseDecrease
Solution
a. The elasticity of demand is calculated using the midpoint method as follows:
Elasticity = ((Q2 - Q1) / ((Q2 + Q1) / 2)) / ((P2 - P1) / ((P2 + P1) / 2))
Where: Q1 is the initial quantity demanded (100 brownies) Q2 is the final quantity demanded (300 brownies) P1 is the initial price (R1.50) P2 is the final price (R1.00)
So, the elasticity of demand is:
Elasticity = ((300 - 100) / ((300 + 100) / 2)) / ((1.00 - 1.50) / ((1.00 + 1.50) / 2)) Elasticity = (200 / 200) / (-0.50 / 1.25) Elasticity = 1 / -0.4 Elasticity = -2.5
Since we are asked not to include a negative sign, the elasticity of demand is 2.5.
b. Demand is considered elastic if the elasticity is greater than 1, and inelastic if it is less than 1. Since the elasticity of demand in this case is 2.5, the demand is elastic.
c. If demand has the same elasticity for a price decline from R1.00 to R0.50 as it does for the decline from R1.50 to R1.00, then cutting the price from R1.00 to R0.50 would increase Danny’s total revenue. This is because when demand is elastic, a decrease in price leads to an increase in total revenue.
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