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?

A) Yes
B) No, the retail price is too low
C) No, the retail price is too high
D) We do not have enough information to answer this question.

Question

Richard Daniel · Accepted Answer

Final Answer : C, Explanation :  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 priceWe 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/QThis 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.

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