Question

3. A monopolist producing with a constant marginal cost of $8 has the following demand for its product. Price $20 $18 $16 $14 $12 $10 $8 Quantity 1 2 3 4 5 6 7 Find the optimal output, price and calculate the resulting monopoly profit.

Answer 1

The price and output schedule of the monopolist is as follows:

Output Price Total Marginal Marginal

Revenue Revenue Cost

1    20 20 --- 8   

2    18 36 16 8

3 16 48 12     8

4 14     56    8     8

5 12   60 4     8

6 10    60     0 8

7 8 56 -4 8

In the above schedule , we have calculated the total revenue by multiplying the Price with output.

Then we have calculated the marginal revenue for each output by subtracting the total revenue at an output level from the next output level.For example marginal revenue at output level- 2 equals :

(total revenue_{output level 2 -} total revenue_{output level 1} )

Marginal revenue_{output level 2} = 36 - 20 = $16

As the firm produces at a constant marginal cost , so the marginal cost = $8 at each level of output.Also the firm incurs no other costs , so the marginal cost  = average cost = $8 at each level of output.

Total cost at each level of output = Output × Average cost

Monopolist point of Production:

A monopolist produces at a point where the marginal cost equals the marginal revenue.

We notice that at output level - 4 the marginal revenue is equal to the marginal cost.The price at this level output is $14.

So Optimal level of output = 4; Optimal Price = $14

The formula for profit is as follows:

Total revenue - Total Cost

Total revenue at output level- 4 = $56

Total cost_{output level 4} = Average Cost × Ouput

Total Cost_{output level 4} = 8 × 4 = $32

Profit = 56 - 32 = $24

Profit = $24