Question

Suppose a monopolist has the following demand and marginal revenue schedules with marginal cost \(=\) average \(\cos t=\$ 5\) . $$ \begin{array}{|c|c|c|} \hline \underline{P} & \begin{array}{c} \text { Quantity } \\ \text { Demanded } \end{array} & \begin{array}{c} \text { Marginal } \\ \text { Revenue } \end{array} \\ \hline 40 & 0 & 30 \\ \hline 30 & 1 & 10 \\ \hline 20 & 2 & -10 \\ \hline 10 & 3 & \\ \hline \end{array} $$ Because a monopolist can manipulate output and price, it is often alleged that a monopolist will charge the highest price he can get. Why is this assertion wrong?

Short answer

The assertion that a monopolist will charge the highest price possible is incorrect because a monopolist seeks to maximize profit, which occurs when marginal revenue (MR) equals marginal cost (MC). In this case, the profit-maximizing price is $30, not the highest listed price of $40. Higher prices result in reduced profit since demand decreases. Monopolists will charge the price that maximizes profit, based on the intersection of marginal revenue and marginal cost.

Step-by-step solution

Understand Profit Maximization

For a monopolist to maximize their profit, they will produce the quantity at which their marginal revenue (MR) equals their marginal cost (MC). This equilibrium point will allow the monopolist to make the greatest possible profit.

Find the Marginal Revenue and Marginal Cost equilibrium point

We are given the following table of price, quantity demanded, and marginal revenue for a monopolist: $$ \begin{array}{|c|c|c|} \hline \underline{P} & \begin{array}{c} \text { Quantity } \\\ \text { Demanded } \end{array} & \begin{array}{c} \text { Marginal } \\\ \text { Revenue } \end{array} \\\ \hline 40 & 0 & 30 \\\ \hline 30 & 1 & 10 \\\ \hline 20 & 2 & -10 \\\ \hline 10 & 3 & \\\ \hline \end{array} $$ We know that the monopolist's constant marginal cost is \(5. Now let's find the equilibrium point. The quantity demanded where MR (\)10) is closest to MC, which occurs in row 2, with a price of \(30 and a quantity demanded of \)1.

Compare equilibrium price with the highest possible price

The given table suggests that the monopolist could charge a price of \(40, which is the highest price listed. However, at this price, the quantity demanded is \)0, and the monopolist will not generate any revenue. On the other hand, at the equilibrium price of $30, the monopolist will earn revenue.

Explain why the assertion is wrong

We have found that the monopolist's profit-maximizing price is \(30, not the highest possible price of \)40. Charging a higher price than $30 would lead to reduced profit since the quantity demanded would decrease. Therefore, it is not true to say that a monopolist will always charge the highest price possible. Instead, they will charge the price that maximizes their profit, based on the intersection of marginal revenue and marginal cost.

Key concepts

Profit Maximization

Profit maximization is a fundamental concept in economics, especially for monopolists. A monopolist aims to determine the level of output that will optimize profits. This does not mean setting the highest possible price, but rather identifying the price where total costs and total revenues result in the greatest profit.

In simple terms, profit is calculated as total revenue minus total costs. A monopolist adjusts the price and output until the difference between these two is maximized. This process involves analyzing the relationship between additional units sold, referred to as marginal units. These marginal units generate additional revenue known as marginal revenue (MR), weighed against an additional cost termed marginal cost (MC).

The key strategy is to continue producing until marginal revenue equals marginal cost (MR = MC). Any production beyond this point would cost more than what it would earn, thereby reducing profit.

Marginal Revenue

Marginal revenue is the extra income a firm receives from selling one more unit of a product. For a monopolist, marginal revenue doesn't equal the price they charge, unlike in competitive markets. This means that as they increase production, the additional revenue from selling each new unit decreases.

We can appreciate this through the demand schedule provided in our exercise. As the monopolist increases the production from 0 to 1 unit, the marginal revenue drops to $10, a decline from what was initially a lot higher when no units were sold.

Therefore, tracking marginal revenue is crucial for a monopolist because it helps determine the balance point where additional production would no longer boost profits. This understanding aids in pinpointing profit-maximizing output levels, reflecting how much demand changes with each unit's price adjustment.

Marginal Cost

Marginal cost is the cost of producing an additional unit of a good. In our exercise, the monopolist's marginal cost is constant at $5. This cost consistency simplifies determining the profit-maximizing quantity.

In profit maximization, the marginal cost serves as a benchmark. It is at the point where marginal cost and marginal revenue are equal that the monopolist maximizes profits. Producing beyond this point means the cost to produce another item exceeds the revenue it generates, a non-profit-maximizing scenario.

Understanding the relationship between marginal cost and marginal revenue is essential for the monopolist to avoid unnecessary expenses that would not be compensated by equivalent revenue, thereby avoiding diminished profits.

Demand Schedule

A demand schedule outlines how much of a product consumers are willing to purchase at varying prices. It reflects the relationship between price and quantity demanded, serving as a vital tool for monopolists to understand market dynamics.

In our exercise, it is evident the demand schedule reveals different price-quantity scenarios. Initially, at the highest price of $40, the quantity demanded is zero, indicating no sales at this price point. As price decreases, demand increases, more so at a price of $30, where one unit is demanded.

For monopolists, studying the demand schedule helps in setting the right price, deriving maximum profits while meeting market demands. It helps uncover the potential drop in demand with higher prices, or conversely, increased sales with reduced prices, ultimately influencing how a monopolist tailors the pricing strategy to maximize revenue.