Question

Suppose that a monopolist has a constant average total cost of production and marginal cost of production equal to $6, and has a demand for its product represented as

price	quantity bought and sold (units)
$10	1
$9	2
$8	3
$7	4
$6	5

1. Calculate the total and marginal revenue for each quantity produced and sold
2. Find the profit-maximizing (optimal) quantity produced and sold and the price/unit.
3. Calculate the profit or loss at the optimal quantity of production and sales.

Answer 1

(a)

Total revenue is calculated as follows -

Total revenue = Price * Quantity

Marginal revenue is calculated as follows -

Marginal revenue = Change in total revenue/Change in quantity

Based on the above formula, following is the complete table -

Price	Quantity	Total Revenue	Marginal Revenue
$10	1	$10	$10
$9	2	$18	$8
$8	3	$24	$6
$7	4	$28	$4
$6	5	$30	$2

(b)

In order to maximize profit, a monopolist produce that level of output corresponding to which MR equals MC.

The marginal cost is $6.

The MC equals MR corresponding to 3 units of output.

The price corresponding to 3 units of output is $8 per unit.

So,

The profit-maximizing quantity produced and sold is 3 units.

The price is $8 per unit.

(c)

Calculate the profit -

Profit = Total Revenue - Total Cost

Profit = [Price * quantity] - [ATC * quantity]

Profit = [$8 * 3] - [$6 * 3] = $24 - $18 = $6

Thus,

The profit at the optimal quantity is $6