Question

A monopoly market is characterized by the inverse demand curve P = 1,200 – 40 Q and a constant marginal cost of $200. If the marginal cost of production rises to $400, the profit-maximizing output level _____ units and the price rises by _____.

Answer 1

The profit maximizing output level declines by 2.5 units and the price rises by $100.

Step-by-step explanation:

In a monopoly market the inverse demand curve is given as,

P = 1,200 - 40Q

The marginal cost of production of the last unit is $200.

The total revenue is

=
`Price* Quantity`

=
`1,200Q - 40Q^(2)`

The marginal revenue of the last unit is

=
`(d)/(dx) TR`

= 1,200 - 80Q

At equilibrium the marginal revenue is equal to marginal price,

MR = MC

1,200 - 80Q = 200

80Q = 1,000

Q = 12.5

Putting the value of Q in the inverse demand function,

P =
`1,200 - 40* 12.5`

P = $700

Now, if the marginal cost rises to $400,

At equilibrium the marginal revenue is equal to marginal price,

MR = MC

1,200 - 80Q = 400

80Q = 800

Q = 10

Putting the value of Q in the inverse demand function,

P =
`1,200 - 40* 10`

P = $800