Is it correct that if the marginal cost in the following question is zero, then the total revenue and profit would be same?
If I am correct I picked B $60 for the answer to the question.
The table depicts the total demand for premium channel digital cable TV subscriptions in a small urban market. Assume that each digital cable TV operation pays a fixed cost of $100,000 per year to provide premium digital channels in the market area and that the marginal cost of providing the premium channel service to a household is zero.
Quantity--- Price
0--- ---------$120
3,000---------$100
6,000---------$80
9,000---------$60
12,000--------$40
15,000--------$20
18,000--------$0
If there were only one digital cable TV company in this market, what price would it charge for a premium digital subscription to maximize its profits?
A. $40
B. $60
C. $80
D. $100
Profit is total revenue minus 100,000 fixed cost of premium channels.
The monthly charge that maximizes revcenue maximizes profits. Just multiply the numbers in the quantity and price columns for revenue. The maximum occurs at a $60 price. You are correct about that.
To determine the price that would maximize profit for a digital cable TV company, we need to calculate the total revenue and total cost at each price level.
The total revenue (TR) is the product of the quantity sold and the price per subscription.
The total cost (TC) consists of the fixed cost and the variable cost, where the marginal cost is zero in this case. Therefore, the total cost is equal to the fixed cost ($100,000 in this case).
The profit is calculated by subtracting the total cost from the total revenue.
Let's calculate the total revenue, total cost, and profit at each price level:
At a price of $120, the quantity demanded is 0, and the total revenue is 0 * $120 = $0. The total cost is $100,000, so the profit is -$100,000.
At a price of $100, the quantity demanded is 3,000, and the total revenue is 3,000 * $100 = $300,000. The total cost is $100,000, so the profit is $200,000.
At a price of $80, the quantity demanded is 6,000, and the total revenue is 6,000 * $80 = $480,000. The total cost is $100,000, so the profit is $380,000.
At a price of $60, the quantity demanded is 9,000, and the total revenue is 9,000 * $60 = $540,000. The total cost is $100,000, so the profit is $440,000.
At a price of $40, the quantity demanded is 12,000, and the total revenue is 12,000 * $40 = $480,000. The total cost is $100,000, so the profit is $380,000.
At a price of $20, the quantity demanded is 15,000, and the total revenue is 15,000 * $20 = $300,000. The total cost is $100,000, so the profit is $200,000.
At a price of $0, the quantity demanded is 18,000, and the total revenue is 18,000 * $0 = $0. The total cost is $100,000, so the profit is -$100,000.
From this analysis, we can see that the price that maximizes profit is $440,000 at a price of $60.
Therefore, the correct answer is B. $60.