The price elasticity of demand for Rosie's Roses fresh flowers the week of Valentine's Day is 1.10 and is 1.60 other days of the year. If Rosie's Roses faces a constant marginal cost of $0.75 per rose, what is the profit- maximizing off- peak load price to charge on days not on the week of Valentine's Day?
A)$1.25
B)$8.50
C)$2.00
D)$5.00

Question

Quizplus · Accepted Answer

First, we need to determine the optimal price to charge on Valentine's Day. Based on the price elasticity of demand, we know that it is lower (i.e. more inelastic) on Valentine's Day (PED = 1.10) compared to other days of the year (PED = 1.60).

To find the optimal price on Valentine's Day, we can use the following formula:

optimal price = (1 + 1/ PED) x marginal cost

Substituting in the values, we get:

optimal price = (1 + 1/1.10) x $0.75 = $1.41

Therefore, the optimal price to charge on Valentine's Day is $1.41 per rose.

Next, we need to determine the optimal price to charge on all other days of the year. Since demand is more elastic on these days, we should aim for a lower price to increase demand and maximize profits.

Using the same formula as above, we get:

optimal price = (1 + 1/1.60) x $0.75 = $1.47

However, this price is not feasible as it is lower than the marginal cost of producing the roses. Therefore, we need to adjust the price to cover the cost while still attracting customers.

Assuming a rounded price, we can try $2.00 per rose. Using the midpoint formula for price elasticity of demand, we can check the elasticity of demand at this price:

% change in quantity demanded = ((new quantity - old quantity) / ((new quantity + old quantity) / 2)) x 100%

% change in price = ((new price - old price) / ((new price + old price) / 2)) x 100%

PED = % change in quantity demanded / % change in price

Let's assume that at the original price of $2.50, the quantity demanded was 1,000 roses. At the new price of $2.00, the quantity demanded increases to 1,400 roses.

% change in quantity demanded = ((1,400 - 1,000) / ((1,400 + 1,000) / 2)) x 100% = 40%

% change in price = ((2.00 - 2.50) / ((2.00 + 2.50) / 2)) x 100% = -20%

PED = 40% / -20% = -2

Since the absolute value of PED is greater than 1, demand is elastic at this price. This means that a decrease in price will result in a more than proportionate increase in quantity demanded. Therefore, a price of $2.00 per rose is a feasible and optimal price to charge on days not on the week of Valentine's Day.

The answer is C) $2.00.

The Price Elasticity of Demand for Rosie's Roses Fresh Flowers