Sandy's Sandwich Sitdown priced its lunch treats at $2.00
, they sold 250 per day When the price was $3.00 they sold 200 per day Based on this information and using the average-values formula, the absolute value of the price elasticity of demand for lunch treats is
A. 2.50
B. 0.56 correct answer
C.1.79
D.0.40
The formula for price elasticity of demand is given by:
E = (Q2 - Q1) / ((Q2 + Q1) / 2) / (P2 - P1) / ((P2 + P1) / 2)
where Q1 and Q2 are the quantities demanded at price P1 and P2 respectively.
Given that Q1 = 250, Q2 = 200, P1 = $2.00, and P2 = $3.00, we can calculate the price elasticity of demand:
E = (200 - 250) / ((200 + 250) / 2) / ($3.00 - $2.00) / (($3.00 + $2.00) / 2)
= (-50) / (425 / 2) / $1.00 / ($5.00 / 2)
= -50 / 212.5 / 1 / 2.5
= -50 / 106.25
= -0.47
Since price elasticity of demand is a positive value, we take the absolute value:
|E| = 0.47
Therefore, the absolute value of the price elasticity of demand for lunch treats is 0.47.
Based on the above calculation, demand for lunch treats
is considered to be
a. inelastic
b. unit-elastic
c. elastic
Since the absolute value of the price elasticity of demand is less than 1 (0.47), the demand for lunch treats is considered to be inelastic.
To calculate the price elasticity of demand, we need to use the following formula:
Price Elasticity of Demand = ((Q2 - Q1) / ((Q2 + Q1) / 2)) / ((P2 - P1) / ((P2 + P1) / 2))
Let's substitute the given values into the formula:
Q1 = 250 (quantity sold when the price was $2.00)
Q2 = 200 (quantity sold when the price was $3.00)
P1 = $2.00
P2 = $3.00
Price Elasticity of Demand = ((200 - 250) / ((200 + 250) / 2)) / (($3.00 - $2.00) / (($3.00 + $2.00) / 2))
Simplify inside the parentheses:
Price Elasticity of Demand = ((-50) / (450 / 2)) / ($1.00 / ($5.00 / 2))
Price Elasticity of Demand = ((-50) / 225) / ($1.00 / 2.5)
Simplify the division:
Price Elasticity of Demand = (-0.2222) / (0.4)
Evaluate the division:
Price Elasticity of Demand = -0.5556
Taking the absolute value, the answer is approximately 0.56.
Therefore, the correct answer is B. 0.56.
To find the absolute value of the price elasticity of demand, we need to use the average-values formula. The formula for calculating price elasticity of demand is:
E = (Q2 - Q1) / [(Q1 + Q2) / 2] / (P2 - P1) / [(P1 + P2) / 2]
Here, Q1 is the initial quantity demanded (200), Q2 is the new quantity demanded (250), P1 is the initial price ($3.00), and P2 is the new price ($2.00).
Let's plug in the values:
E = (250 - 200) / [(200 + 250) / 2] / ($2.00 - $3.00) / [($3.00 + $2.00) / 2]
Simplifying further:
E = 50 / [450 / 2] / (-$1.00) / [$5.00 / 2]
E = 50 / 225 / (-$1.00) / $2.50
E = 50 / (-$1.00) / $2.50
E = -20 / -0.40
E = 50
The absolute value of the price elasticity of demand is 0.40.
Therefore, the correct answer is D. 0.40.