Roaring Lion Studios can produce DVDs at a constant marginal cost of $5 per disk, and the studio has just releasing the DVD for its latest hit film, Ernest Goes to the Hamptons. The retail price of the DVD is $25, and the elasticity of demand for this film is -2. Has the studio selected the profit-maximizing retail price for this DVD?

Question

Quizplus · Accepted Answer

To determine if the studio has selected the profit-maximizing retail price for the DVD, we need to calculate the price elasticity of demand (PED) and compare it to the profit-maximizing output rule, which states that profit is maximized when marginal revenue equals marginal cost. Since the retail price is $25 and the marginal cost is $5, the marginal revenue is $20.

Using the PED formula:

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

We can estimate that a 10% increase in price would result in a 20% decrease in quantity demanded based on the elasticity of demand (-2). Therefore:

-2 = -20%/10%

Solving for the percentage change in quantity demanded at the profit-maximizing price:

-2 = ΔQ / ΔP * P/Q

-2 = ΔQ / (P/Q) * 25

-2 = ΔQ / (Q/25) 
-50 = ΔQ/Q 
-50% = ΔQ/Q

This means that at the profit-maximizing price, a 50% decrease in quantity demanded would result in a 25% increase in price (from $20 to $25). Since the elasticity of demand is greater than one, the optimal price is greater than the price that maximizes revenue (as the same percentage increase in price would lead to a greater percentage decrease in quantity demanded). Therefore, the studio has set the retail price too high, and the correct answer is C.

Roaring Lion Studios Can Produce DVDs at a Constant Marginal