Suppose a monopolist faces a market demand curve of the form: P = 122 – 0.2Q. This monopolist has a total cost curve given by: TC = 2Q. If the government were to regulate this monopolist and require them to charge a price equal to average cost, this price would be equal to $_____, and the monopolist would make a profit of $______.Group of answer choices2; 36,000.0; 0.2; 0.61; 17,995.62; 18,000.
Question
Suppose a monopolist faces a market demand curve of the form: P = 122 – 0.2Q. This monopolist has a total cost curve given by: TC = 2Q. If the government were to regulate this monopolist and require them to charge a price equal to average cost, this price would be equal to _____, and the monopolist would make a profit of ______.Group of answer choices2; 36,000.0; 0.2; 0.61; 17,995.62; 18,000.
Solution
To solve this problem, we first need to find the average cost (AC). The average cost is the total cost (TC) divided by the quantity (Q). Given that TC = 2Q, the average cost (AC) is 2Q/Q = 2.
Next, we need to find the quantity (Q) at which price (P) equals average cost (AC). We set P = AC and solve for Q:
122 - 0.2Q = 2 0.2Q = 122 - 2 0.2Q = 120 Q = 120 / 0.2 Q = 600
Substitute Q = 600 into the demand curve to find the price:
P = 122 - 0.2 * 600 P = 122 - 120 P = 2
So, the price that the monopolist would be required to charge would be $2.
To find the profit, we subtract the total cost from the total revenue. The total revenue (TR) is price (P) times quantity (Q), and the total cost (TC) is 2Q:
TR = P * Q = 2 * 600 = 1200 TC = 2Q = 2 * 600 = 1200
Profit = TR - TC = 1200 - 1200 = 0
So, the monopolist would make a profit of $0.
Therefore, the answer is 0.
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