Coca-Cola in dispensers located on a golf course sells for $1.25 a can, and golfers buy 1,000 cans. Assume the course raises the price to $1.26 (assume a penny raise is possible) and sales fall to 992 cans.
a. Using the midpoint formula, what is the price elasticity of demand for Coke
at these prices?
b. Assume the demand for Coke is a linear line. Would the elasticity of demand
be elastic or inelastic at 75 cents a can?
c. At $2.00 a can?
a. To calculate the price elasticity of demand (PED) using the midpoint formula, we need the following information:
- Original price (P1) = $1.25
- New price (P2) = $1.26
- Original quantity (Q1) = 1,000 cans
- New quantity (Q2) = 992 cans
The midpoint formula for price elasticity of demand is:
PED = (Q2 - Q1) / [(Q2 + Q1)/2] / (P2 - P1) / [(P2 + P1)/2]
Substituting the given values:
PED = (992 - 1000) / [(992 + 1000)/2] / ($1.26 - $1.25) / [($1.26 + $1.25)/2]
Calculating it:
PED = -8 / (996) / ($0.01) / ($1.255)
Simplifying:
PED ≈ -8 * 2 / 996 ≈ -0.016064257
Therefore, the price elasticity of demand for Coke at these prices is approximately -0.016.
b. To determine whether the elasticity of demand would be elastic or inelastic at $0.75 per can, we need more information about the linear demand function. Without it, we cannot accurately determine the elasticity.
c. Similarly, without information about the specific linear demand function at $2.00 per can, we cannot determine the elasticity of demand at that price.