The table below shows the marginal revenue and costs for a monopolist.
Demand, Costs, and Revenues
| Price (dollars) | Quantity Demanded | Marginal Revenue (dollars) | Marginal Cost (dollars) | Average Total Cost (dollars) |
|---|---|---|---|---|
| $130 | 200 | $110 | $25 | $139.00 |
| 120 | 300 | 90 | 32 | 103.30 |
| 110 | 400 | 70 | 40 | 87.50 |
| 100 | 500 | 50 | 50 | 80.00 |
| 90 | 600 | 30 | 62 | 77.00 |
| 80 | 700 | 10 | 77 | 77.00 |
What is the monopolist's profit at the profit-maximizing level of output?
A. $10,000
B. $80,000
C. $50,000
D. $0
Answer (2)
Find the quantity where marginal revenue equals marginal cost: MR = MC at quantity 500.
Calculate total revenue: $TR = Price \t Quantity = $100 \t 500 = 50 , 000 .
Calculate total cost: $TC = ATC \t Quantity = $80 \t 500 = 40 , 000 .
Calculate profit: $Profit = TR - TC = $50,000 - 40 , 000 = \t $10 , 000 .
Explanation
Understanding the Problem We are given a table with the price, quantity demanded, marginal revenue, marginal cost, and average total cost for a monopolist. Our goal is to find the monopolist's profit at the profit-maximizing level of output. Profit is maximized when marginal revenue (MR) equals marginal cost (MC).
Finding the Profit-Maximizing Quantity Looking at the table, we need to find the quantity where MR = MC. We can see that when the quantity is 500, the marginal revenue is $50, and the marginal cost is also $50. Therefore, the profit-maximizing level of output is 500 units.
Calculating Total Revenue At a quantity of 500, the price is $100. Total Revenue (TR) is calculated as Price \t Quantity. So, TR = $100 \t 500 = $50,000.
Calculating Total Cost At a quantity of 500, the average total cost (ATC) is $80. Total Cost (TC) is calculated as ATC \t Quantity. So, TC = $80 \t 500 = $40,000.
Calculating Profit Profit is calculated as Total Revenue (TR) - Total Cost (TC). So, Profit = $50,000 - $40,000 = $10,000.
Final Answer Therefore, the monopolist's profit at the profit-maximizing level of output is $10 , 000 .
Examples
Understanding profit maximization is crucial for businesses. Imagine a small bakery trying to determine how many cakes to bake each day. By analyzing their marginal revenue (the income from selling one more cake) and marginal cost (the cost to bake one more cake), they can find the optimal number of cakes to bake that maximizes their profit. This concept applies to various businesses, from small shops to large corporations, helping them make informed decisions about production levels and pricing strategies.
The monopolist's profit at the profit-maximizing level of output is calculated to be $10,000. This is derived from total revenue of $50,000 and total cost of $40,000 when producing 500 units. Therefore, the correct choice is A. $10,000.
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