The accompanying table shows the price and yearly quantity sold of ice cream con
ID: 1231820 • Letter: T
Question
The accompanying table shows the price and yearly quantity sold of ice cream cones on Sidfield Island.Price of Ice Cream Cones Quantity of Ice Cream Cones Demanded
$1 3000
$2 2400
$3 1600
$4 800
a. Using the midpoint method (show your work), calculate the price elasticity of demand when the price of an ice cream cone rises from $1 to $2. What does this estimate imply about the price elasticity of demand for ice cream cones?
That the price is contingent on demand .
b. Using the midpoint method (show your work), calculate the price elasticity of demand when the price of an ice cream cone rises from $3 to $4. What does this estimate imply about the price elasticity of demand for ice cream cones?
c. Notice that the estimates from (a) and (b) above are different. Why do price elasticity of demand estimates change along the demand curve?
Explanation / Answer
a) The midpoint elasticity formula is [(Q2 - Q1)/((Q2 + Q1)/2)]/[(P2 - P1)/((P2 + P1)/2)] where Q is quantity demanded and P is price (1 is the old price or quantity, 2 is the original) [(2400-3000)/((2400+3000)/2)]/[(2-1)/(2+1)/2)] [(-600)/(5400/2)]/[(1/(3/2)] [(-600)/(2700)]/(1/1.5) = -0.222/0.666 = -0.333 The price elasticity of demand here is -0.333 indicating that demand is relatively inelastic b) [(800-1600)/((800+1600)/2)]/[(4-3)/(4+3)/2)] [(-800)/(2400/2)]/[1/(7/2)] [(-800/1200)]/[1/3.5] (-0.666/0.286) = -2.333 The price elasticity of demand here is -2.333 indicating that demand is very elastic c) The two values for the price elasticity of demand are different because elasticity measures percent changes in price and quantity, as such they depend on both the amount of the change, and the starting point. In the case of a linear demand curve, the amount of change from one value to the next is constant along the demand curve, but the starting point (the initial price or quantity) changes. As such moving along a demand curve from a low price to a higher price will mean that elasticity will increase.
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