Answer:
It will maximize at 19 units at price 21 with a profit of 361 dollars
This monopoly will generate a deadweight loss of 190 dollars
While also decreasing the quantiy available from 38 to 19
Explanation:
The company will maximize their profit at the point which marginal cost equals marginal revenue.
Marginal revenue: income from additional unit
Total revenue P x Q
where P = 40 - Q
Revenue = (40 - q ) x q = 40q - q^2
we derivate and get the marginal revenue
-2q+40
We now equalize this with marginal cost of $2 dollars
-2q + 40 = 2
40 - 2 = 2q
38/2 = q = 19
It maximize profit by selling 19 units
Price 40 - Q = 40 - 19 = 21
Profit: (price - cost ) quantity
(21 - 2) * 19 = 361
On a perfectly competitive market price will be equal to the marignal cost thus:
P = 2
giving a quantity of
2 = 40 - Q
q = 38
the deadweight loss would be:
(39 - 19) x (21 - 2) / 2
20 x 19 / 2 = 190
