The table shows the demand schedule of a monopolist. Calculate marginal revenue and fill in the revenue column in the table. Assume that output can only be sold in integer amounts (ie., 1 unit, 2 units, etc.). Once you have filled in marginal revenue, identify the quantity produced by the monopolist in this market. Not all numbers in the answer bank will be used. Marginal revenue Quantity Price $13 Marginal cost $6 1 Answer Bank 2 $12 $7 $9 $0 $10 $6 $3 3 $11 $8 $4 $1 $12 $5 $11 4 $10 $9 5 $9 $10 $8 $2 $13 $7 6 S8 $11 How many units does the monopolist produce? Units
The correct answer and explanation is:
Let’s calculate the total revenue (TR) and marginal revenue (MR) first.
Total Revenue (TR) = Price × Quantity
Marginal Revenue (MR) = Change in Total Revenue / Change in Quantity
| Quantity | Price | Total Revenue (TR) | Marginal Revenue (MR) |
|---|---|---|---|
| 1 | $13 | 13 | – |
| 2 | $12 | 24 | $11 |
| 3 | $11 | 33 | $9 |
| 4 | $10 | 40 | $7 |
| 5 | $9 | 45 | $5 |
| 6 | $8 | 48 | $3 |
How Many Units Does the Monopolist Produce?
A profit-maximizing monopolist produces where marginal revenue (MR) equals marginal cost (MC). Given that MC = $6:
- When Q = 1, MR is undefined.
- When Q = 2, MR = $11, which is greater than MC ($6).
- When Q = 3, MR = $9, which is still greater than MC.
- When Q = 4, MR = $7, which is just above MC.
- When Q = 5, MR = $5, which is below MC.
Thus, the monopolist produces 4 units, as this is where MR is still higher than MC but approaching it.
Explanation:
A monopolist maximizes profit by setting output where MR = MC. Since MR is higher than MC at 4 units but drops below MC at 5 units, the monopolist stops at 4. Beyond that, producing more would reduce profit because the additional revenue from selling an extra unit would be less than the cost of producing it.
Now, let’s generate an image illustrating the demand, marginal revenue, and cost relationship.
Here’s a graph illustrating the monopolist’s demand, marginal revenue, and marginal cost. You can see that the monopolist produces 4 units where MR equals MC. Let me know if you need any modifications!
