A medical device manufacturer sells its sterilization equipment in a market with an inverse demand curve of P = 6,000 - 400Q, where Q measures the number of sterilizers in thousands and P is the price per unit. The marginal cost of production is constant at $4,000. The profit-maximizing price is $____.

Question

Quizplus · Accepted Answer

To find the profit-maximizing price, first, we need to determine the quantity where marginal revenue (MR) equals marginal cost (MC). The inverse demand curve is P = 6,000 - 400Q. To find MR, we double the slope of the demand curve: MR = 6,000 - 800Q. Setting MR equal to MC (4,000) gives 6,000 - 800Q = 4,000, which simplifies to 2,000 = 800Q, or Q = 2.5. Substituting Q = 2.5 back into the demand curve to find the price: P = 6,000 - 400(2.5) = 6,000 - 1,000 = 5,000.

A Medical Device Manufacturer Sells Its Sterilization Equipment in a Market