Question

Someone please fully explain how to do this. the answer is 3600

A monopolist faces market demand given by \( P=150-Q \cdot M R=150-2 Q \) and \( M C=\$ 30 . A T C=\$ 30 \). If the monopolist does not price discriminate, what is the value of producer surplus? -Don'

Answer 1

To find the value of producer surplus for a monopolist without price discrimination, we need to calculate the area between the market price (P) and the marginal cost (MC) curve.

Given:

Demand curve: P = 150 - Q

Marginal revenue curve: MR = 150 - 2Q

Marginal cost: MC = $30

Average total cost: ATC = $30

To find the quantity at which the monopolist maximizes profit, we set marginal revenue equal to marginal cost:

MR = MC

150 - 2Q = 30

Solving for Q:

2Q = 150 - 30

2Q = 120

Q = 60

Now we can calculate the market price at this quantity by substituting Q into the demand curve:

P = 150 - Q

P = 150 - 60

P = 90

To find the producer surplus, we need to calculate the area between the market price and the marginal cost curve. In this case, since the marginal cost is constant at $30, the producer surplus is a triangle with a base equal to the quantity (Q) and a height equal to the difference between the market price (P) and the marginal cost (MC).

Area of triangle (producer surplus) = 1/2 * base * height

Area = 1/2 * Q * (P - MC)

Area = 1/2 * 60 * (90 - 30)

Area = 1/2 * 60 * 60

Area = 1/2 * 3600

Area = 1800

Therefore, the value of the producer surplus is $1800.