Market demand is given as Q_D= 75 - 2P.Market supply is given as Q_S= 2P + 15.Each identical firm has MC = 3Q and ATC = 2Q.What is a firm's profit

Question

Quizplus · Accepted Answer

To find the profit-maximizing quantity, we need to equate the market price (since the firm is a price taker) with the firm's marginal cost and solve for Q:

2P + 15 = 3Q

Solving for P:

P = (75 - 3Q) / 2

Setting marginal revenue (MR) equal to MC to find the profit-maximizing quantity:

MR = d(75 - 3Q) / 2 = 37.5 - 1.5Q = MC = 3Q

Solving for Q:

4.5Q = 37.5

Q = 8.33

Since the firm cannot produce a fractional quantity, it will produce 8 units.

To find the profit, we need to use the profit formula:

Profit = (P - ATC)Q

Plugging in the values:

Profit = [(75 - 3(8)) / 2 - 2(8)](8)

Profit = [$24 / 2 - $16]8

Profit = [$8 * 8]

Profit = $64

Therefore, the correct answer is (C) $25.

Market Demand Is Given as QD = 75 - 2P

Market Demand Is Given as Q_D= 75 - 2P