Question

Given the demand curve for a monopolist: Qd= 60 -2 P and the marginal revenue curve: MR = 30 -Q. Marginal cost equals average cost at $14. What is the price and quantity that the profit-maximizing monopolist will produce? Graph these curves andlabel theequilibrium points.

b) Ifthis were a competitive industry, what price and quantity would be produced? Show this on the above graphand show your work (answers) below.

c) What is the monopolist's profit? What is the consumer surplus at the monopolist's price? The dead weight loss to society? Write your formulas as well as the answers.Show these areas on the graph above or draw a new one below(remember -neatness counts).

Answer 1

Given:

Demand function: Qd = 60-2P

Mariginal revenue curve: MR = 30-Q

Marginal cost: MC = $14

Average cost: AC = $14

a.) Profit maximizing price and quantity that the monopolist will produce at:

To maximize profit Monopolist produces where the marginal cost is equal to the marginal revenue and charges the highest price consumers are willing to pay for this quantity.

That is,

firstly it will produce where MR = MC

then equivalent to this quantity charges the price from the demand function.

Therefore monopolists will produce 16 units.

Now putting this quantity into the demand function, we get the price monopolist will charge.

Therefore monopolist will charge $22 for the quantity of 16 units.

Answer:

Monopolist profit-maximizing:

Price = $22

Quantity = 16 units

Description to diagram:

Here D is the demand curve, MR is the marginal revenue curve. And MC and average cost curve coincide as they are the same at $14. The monopolist produces where the marginal cost curve is equal to the marginal revenue and charges price equivalent to the demand curve. So the monopolist profit-maximizing point is Em where the price is Pm and quantity is Qm.

b.) If this firm is a perfectly competitive firm, the profit-maximizing price, and quantity produced:

The perfectly competitive firm produces where the marginal cost is equal to the price. And charges the price equal to the marginal cost.

As marginal cost = $14, therefore perfect competitive firm charges $14.

therefore the competitive price is:

From the demand function, the inverse demand function is:

Now in the perfectly competitive, market the firm maximizes his profit and produces where the marginal cost is equal to the price.

Therefore,

Therefore if the firm acted as a perfectly competitive firm, it will produce 32 units and charge a price of $14.

Answer: If this were a competitive firm, the profit-maximizing:

Price: P_c = $14

Quantity Q_c = 32 units

Description to diagram:

The competitive firm produces where the marginal cost is equal to the price and charges price equivalent to the quantity. The competitive firm profit-maximizing output and price are shown at Ec point. where the quantity is Qc and price is Pc

c.) Monopolist profit:

Since profit is the difference between total revenue and total cost. And total revenue is the price times quantity and the total cost is the average cost times quantity.

As the monopolist charges a price of $22 and its average cost is $14, and it produces a quantity of 16 units. Therefore putting these values into the formula of profit, we get:

Therefore the monopolist profit is $128.

Description to diagram:

Profit is because of the difference between price and the average cost of the monopolist. As we can see that the average cost is lower than the price, therefore the monopolist earns profit equivalent to this area shown.

Consumer surplus at the monopolist price:

Consumer surplus is the gain experiences by consumers because of the difference between their maximum willingness to pay and the price they actually pay.

where the Pmax is the consumer maximum willingness to pay, it is the price, where the quantity demanded, is zero.

Therefore putting Qd = 0 into the demand function, we get the consumer's maximum willingness to pay.

Therefore the maximum willingness to pay is $30, and as we know that:

Monopolist price: Pm = $22

Monopolist quantity: Qm = 16 units

Pmax = $30

Therefore consumer surplus at the monopolist price is:

Therefore consumer surplus at the monopolist pricing is $64.

Description to diagram:

Consumer surplus is the area below the demand curve and above the price. (here monopolist price). Therefore the area shown is the consumer surplus at the monopolist pricing.

The deadweight loss to society at the monopolist pricing:

Deadweight loss is the loss to society because of the inefficient quantity production. A monopolist produces less than the competitive quantity and charges a higher price than the competitive price. Therefore it creates a deadweight loss to society.

Where:

Pm is the monopolist price = $22

Pc is the competitive price = $14

Qm is the monopolist quantity = 16 units

Qc is the competitive quantity = 32 units

Therefore deadweight loss to society at monopolist price is:

Therefore at the monopolist price, the deadweight loss to society is $64.

Description to diagram:

Deadweight loss is the triangle shown in the diagram. It is because of the difference between competitive equilibrium and monopolist equilibrium quantity and pricing.