Question

The table below depicts the cost and demand structure a natural monopoly faces.

a. Calculate total revenues, marginal revenue, and marginal cost at each output level. If this firm is allowed to operate as a monopolist, what will be the quantity produced and the price charged by the firm? What will be the amount of monopoly profit? [Hint: Recall that marginal revenue equals the change in total revenues $(P\times Q)$from each additional unit and that marginal cost equals the change in total costs from each additional unit.]

b. If regulators require the firm to practice marginal cost pricing, what quantity will it produce, and what price will it charge? What is the firm's profit under this regulatory framework? [Hint: Recall that average total cost equals total cost divided by quantity and that profits equal $(P-ATC)\times Q.]$.

c. If regulators require the firm to practice average cost pricing, what quantity will it produce, and what price will it charge? What is the firm's profit under this regulatory framework?

Short answer

Part a: If a firm has monopoly power, then it will give $2$units of output. At this point marginal revenue equals marginal cost. The price charged by a monopolist would be $\$90$at this level.

Part b: Monopoly profits are $\$3$and monopoly losses are $\$31$.localid="1652341498860" $\$31$.

Part c: Profit of the firms by average cost pricing, monopoly profit are $\$0$.localid="1652341503872" $\$0$.

Step-by-step solution

Given Information

Given data: The firm should practice marginal cost pricing, while the firm should practice average cost pricing.

Calculation  of Total Revenue, Marginal Revenue, and Marginal Cost(part a)

(a) Calculate the Total Revenue, Marginal Revenue, and Marginal Cost at each output level as follows:

Thus, If a firm has monopoly power, then it will give$2$units of output. At this point marginal revenue equals marginal cost.

The price charged by a monopolist would be$\$90$at this level.

Calculation of the profits of the firms by total cost and total revenue(part b)

(b) Profit of a firm is calculated by considering total cost and total revenue.

Calculate the profits of the firms as follows:

Profit $=$$($Price $-ATC$$)$$\times$Quantity

$=(\$90-88.5)\times 2$

$=\$3$

Therefore, monopoly profits are $\$3$.

(b) The firm will sell $5$units of quantity because at this level long-run marginal cost equals the price. The price and marginal cost is $\$75$at this level.

Calculate the profits of the firms as follows:

Profit Price Quantity localid="1652341519622" $=$localid="1652341526868" $(\$75-\$81.2)\times 5$

localid="1652341531687" $=-\$31$

Therefore, monopoly loss islocalid="1652341536112" $\$31.$

Calculation of profit of the firms by average cost pricing(part c)

(c) The firm will produce 3 units of quantity because at this level long-run average cost equals the price. The price and average cost is$\$85$per unit at this level.

Calculate the profits of the firms as follows:

Profit $=$$($Price localid="1652341556226" $-$localid="1652341559818" $ATC$$)$localid="1652341549376" $\times$Quantity

localid="1652341563444" $=(\$85-\$85)\times 3$

localid="1652341567082" $=\$0$

Therefore, monopoly profits are localid="1652341570419" $\$0$.