Question

A medical device manufacturer sells its sterilization equipment to consumers 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. A) Solve for the profit-maximizing price and quantity. B) The Patient Protection and Affordable Care Act signed into law by President Barack Obama levies a tax on medical devices. Suppose the tax raises the marginal cost of production from $4,000 to $4,400. What are the new profit-maximizing price and quantity? C) Suppose instead the law calls for a 20% tax on a firm's total revenue and leaves their marginal cost unchanged, what are the profit- maximizing price and quantity under this scenario?

Answer 1

(A) : profit-maximizing quantity (Q) = 2.5

profit-maximizing price (P) = $5,000

(B) : profit-maximizing quantity (Q) = 2

profit-maximizing price (P) = $5,200

(C) : profit-maximizing quantity (Q) = 1.25

profit-maximizing price (P) = $5,500

Here, Q refers to quantity(number) of sterlizers in thousands.

Marginal Revenue (MR) is the addition to firm's revenue (additional income) from the sale of one more unit of output.

MR = Change in Total Revenue / Change in Quantity.

Marginal Cost (MC) is the addition to firm's total cost (i.e., it is the additional cost) when one or more unit of output is produced.

and the firm maximize profits when MR = MC

Explanation :