Question

Hercules Films is also deciding on the price of the video release of its film Bride of the Son of Frankenstein. Again, marketing estimates that at a price of p dollars it can sell q = 260,000 − 13,000p copies, but each copy costs $4 to make. What price will give the greatest profit?

Answer 1

Answer:

The profit maximizing price will be $12.

Explanation:

At the price p, the estimated quantity is,

q = 260,000 − 13,000p

The cost of each copy is $4.

Total revenue

= $P\ \times\ Q$

= $(260,000\ -\ 13,000p)\ \times\ p$

= $260,000p\ -\ 13,000p^2$

Total cost

= $Cost\ \times\ Q$

= $4\ \times\ (260,000\ \times\ 13,000p)$

= 1,040,000 - 52,000p

Marginal revenue

= $\frac{d}{dp} (260,000p\ -\ 13,000p^2)$

= 260,000 - 26,000p

Marginal cost

= $\frac{d}{dp}$ 1,040,000 - 52,000p

= -52,000

The profit will be maximized when the marginal revenue is equal to marginal cost.

Marginal revenue = Marginal cost

260,000 - 26,000p = -52,000

26,000p = 260,000 + 52,000

26,000p = 312,000

p = 12

Answer 2

The price which gives the greatest profit is $12

How to find profit maximization price

• The profit maximization price is when marginal revenue is equal to marginal cost

q = 260,000 − 13,000p

C = $4

Total revenue = Price × quantity

= p × 260,000 − 13,000p

= 260,000p - 13,000p²

Marginal revenue (d/dp) = 260,000 - 26,000p

Total cost = cost × quantity

= 4 × 260,000 − 13,000p

= 1,040,000 - 52,000p

Marginal cost (d/dp) = 52,000

MR = MC

260,000 - 26,000p = 52,000

26,000p = 260,000 + 52,000

26,000p = 312,000

p = 312,000 ÷ 26,000

p = $12

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