A perfectly competitive firm has a marginal cost function given by MC=2Q The market has determined a price of P=36. The firm chooses its profit maximizing quantity. At this quantity, the average total cost of production is ATC=28. Given this information , what is the short run profit earned by this perfectly competitive firm? The profit is __ square

To determine the short-run profit earned by the perfectly competitive firm, we need to follow these steps:<br /><br />1. **Find the Profit-Maximizing Quantity:**<br /> In a perfectly competitive market, a firm maximizes its profit by producing the quantity where marginal cost (MC) equals the market price (P). Given:<br /> \[<br /> MC = 2Q<br /> \]<br /> \[<br /> P = 36<br /> \]<br /> Set \( MC = P \):<br /> \[<br /> 2Q = 36<br /> \]<br /> \[<br /> Q = \frac{36}{2} = 18<br /> \]<br /><br />2. **Calculate Total Revenue (TR):**<br /> Total revenue is calculated as the price times the quantity:<br /> \[<br /> TR = P \times Q = 36 \times 18 = 648<br /> \]<br /><br />3. **Calculate Total Cost (TC):**<br /> Average total cost (ATC) is given as 28 at the profit-maximizing quantity. Therefore, total cost is:<br /> \[<br /> TC = ATC \times Q = 28 \times 18 = 504<br /> \]<br /><br />4. **Calculate Profit:**<br /> Profit is the difference between total revenue and total cost:<br /> \[<br /> \text{Profit} = TR - TC = 648 - 504 = 144<br /> \]<br /><br />Thus, the short-run profit earned by the firm is \(\boxed{144}\).