The accompanying table below shows the demand schedule facing a monopolist who produces at a constant marginal cost of $5
Price . Q
9 0
8 1
7 2
6 3
5 4
4 5
3 6
2 7
1 8
0 9
To analyze the demand schedule facing the monopolist and determine the profit-maximizing quantity and price, we can use marginal revenue (MR) and marginal cost (MC) analysis.
1. Calculate total revenue (TR) by multiplying the quantity (Q) by the corresponding price for each row in the demand schedule.
Price Q TR
------------------------
9 0 0
8 1 8
7 2 14
6 3 18
5 4 20
4 5 20
3 6 18
2 7 14
1 8 8
0 9 0
2. Calculate marginal revenue (MR) by finding the difference in total revenue (ΔTR) between each subsequent quantity (Q) change.
Price Q TR ΔTR MR
--------------------------------
9 0 0 - -
8 1 8 8 8
7 2 14 6 6
6 3 18 4 4
5 4 20 2 2
4 5 20 0 0
3 6 18 -2 -2
2 7 14 -4 -4
1 8 8 -6 -6
0 9 0 -8 -8
3. Calculate marginal cost (MC) using the given constant marginal cost of $5. The MC will always be $5 regardless of the quantity.
4. Determine the profit-maximizing quantity and price:
- The monopolist will maximize profits where MR = MC.
- From the MR column, we can see that the MR becomes negative when the quantity exceeds 4 units. This means that producing more than 4 units will result in a decrease in total revenue.
- At Q = 4, MR equals MC ($2 = $5), which is the profit-maximizing quantity.
- The corresponding price for Q = 4 is $5.
Therefore, the monopolist's profit-maximizing quantity is 4 units, and the price is $5.