Say your friend Nick sells skateboards. He sells 30 a week at $150. He then raises his price to $175 and sells 25. Use the midpoint formula to determine a fractional numerical value for the price elasticity of demand.A.24/26B.4/24C.4/143D.22/26E.13/11
Question
Say your friend Nick sells skateboards. He sells 30 a week at 175 and sells 25. Use the midpoint formula to determine a fractional numerical value for the price elasticity of demand.A.24/26B.4/24C.4/143D.22/26E.13/11
Solution
The price elasticity of demand can be calculated using the midpoint formula:
Elasticity = (Q2 - Q1) / ((Q2 + Q1) / 2) / (P2 - P1) / ((P2 + P1) / 2)
Where: Q1 = initial quantity sold = 30 Q2 = final quantity sold = 25 P1 = initial price = 175
Substituting these values into the formula, we get:
Elasticity = (25 - 30) / ((25 + 30) / 2) / (175 - 150) / ((175 + 150) / 2) Elasticity = -5 / 27.5 / 25 / 162.5 Elasticity = -0.1818 / 0.1538 Elasticity = -1.1818
The negative sign indicates that the quantity demanded and price move in opposite directions, as expected. The magnitude of the elasticity is 1.1818, which is greater than 1, indicating that the demand is elastic.
So, none of the options A-E match this result.
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