Question

Consider a monopoly where the inverse demand for its product is given by P = 50 - 2Q. Total costs for this monopolist are estimated to be C(Q) = 100 + 2Q + Q2. At the profit-maximizing combination of output and price, monopoly profit is:

A $32.
B $64.
C $92.
D $128.

Answer 1

The monopoly profit is determined by finding where marginal revenue equals marginal cost and using that quantity to calculate total revenue and total cost. The correct profit is $68, not among the provided options A, B, C, or D.

Step-by-step explanation:

To find the monopoly profit, we first calculate marginal revenue (MR) by differentiating the total revenue (TR) function, which is P*Q. Since P = 50 - 2Q, TR becomes 50Q - 2Q^2. Consequently, MR, the derivative of TR with respect to Q, is 50 - 4Q. Next, we differentiate the total cost (C) function to get marginal cost (MC) which is 2 + 2Q. The profit-maximizing quantity (Q) is found where MR=MC. Thus, setting 50 - 4Q = 2 + 2Q gives us Q=12.

To find the profit-maximizing price (P), we substitute Q into the inverse demand function: P = 50 - 2*12, resulting in P=26. Now, calculate total revenue (TR) by multiplying Q by P: 12*26, yielding a TR of 312. Finally, calculate total cost (TC) by substituting Q into the C(Q) function: 100 + 2*12 + 12^2, which equals 244. Profit (π) is TR minus TC; thus, π = 312 - 244, totaling 68.