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

Answer:

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

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

= $Price\times Quantity$

= $1,200Q - 40Q^{2}$

The marginal revenue of the last unit is

= $\frac{d}{dx} TR$

= 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 = $1,200 - 40\times 12.5$

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 = $1,200 - 40\times 10$

P = $800