Question

Given below are price and cost figures for a monopolist: $$ \begin{array}{|l|l|l|} \hline \text { Quantity } & \text { Price } & \text { Total Cost } \\ \hline 0 & 200 & 145 \\ \hline 1 & 180 & 175 \\ \hline 2 & 160 & 200 \\ \hline 3 & 140 & 220 \\ \hline 4 & 120 & 250 \\ \hline 5 & 100 & 300 \\ \hline 6 & 80 & 370 \\ \hline 7 & 60 & 460 \\ \hline 8 & 40 & 570 \\ \hline \end{array} $$ a) Find the Total Revenue, Marginal Revenue, and Marginal cost columns. Where is profit maximized? b) How will a tax of \(\$ 100\) per day affect profit maximization?

Short answer

a) The profit-maximizing output level is 3 units, where MR (100) is equal to MC (20). b) After imposing a tax of \(\$100\), the profit-maximizing output level remains at 3 units, but the overall profit will decrease due to the increased Total Cost (\$320).

Step-by-step solution

1. Calculate Total Revenue

To compute Total Revenue (TR), multiply the Quantity (Q) by the price (P) for each row in the table: Quantity(Q) Price(P) Total Revenue(TR) 0 200 0 1 180 180 2 160 320 3 140 420 4 120 480 5 100 500 6 80 480 7 60 420 8 40 320

2. Calculate Marginal Revenue

To compute Marginal Revenue (MR), find the difference between the corresponding Total Revenues for each consecutive quantity: Quantity(Q) Marginal Revenue(MR) 0 - 1 180 2 140 3 100 4 60 5 20 6 -20 7 -60 8 -100

3. Calculate Marginal Cost

To compute Marginal Cost (MC), find the difference between the corresponding Total Costs for each consecutive quantity: Quantity(Q) Marginal Cost(MC) 0 - 1 30 2 25 3 20 4 30 5 50 6 70 7 90 8 110

4. Determine the profit-maximizing output level

To find the profit-maximizing output level, compare the Marginal Revenue (MR) and Marginal Cost (MC) for each quantity. The profit maximizes when Marginal Revenue equals Marginal Cost. Comparing MR and MC, we can see that MR > MC when the quantity is between 3 and 4. Thus, the profit-maximizing output level is at 3 units.

5. Analyze the effect of a tax on profit maximization

After the tax of \(\$100\) per day is imposed, the Total Cost for each output level will increase by \(\$100\). Profit maximization is determined by comparing MR and MC. To find the new profit-maximizing output level, simply look for the point at which this new MR (which remains unchanged) equals the new MC, which increases by the amount of the tax. Since the tax is the same for all output levels, the change in MC will not affect the comparison of MR and MC, meaning the profit-maximizing output level remains at 3 units. However, the overall profit will decrease due to the tax. The new Total Cost at the profit-maximizing output level (i.e. at Q = 3) will be \(220 + \$100 = \$320\).

Key concepts

Total Revenue Calculation

Understanding how to calculate total revenue is essential for any business, including monopolies. Total revenue (TR) represents the total income a firm receives from selling its goods and services. For a monopolist, the calculation is simple: Total Revenue is equal to the quantity of goods sold (Q) multiplied by the price (P) of those goods. This relationship is typically linear in textbook examples but can vary in real-world situations due to price changes as output varies.
As shown in the textbook example, when the quantity sold increases, the total revenue may not always increase. It depends on how much the price has to drop to sell the additional unit. It's crucial to realize that in a monopoly, price typically decreases as quantity increases, which can lead to varying total revenue at different output levels.
Estimating correct total revenue is vital for managing a firm's resources and for making strategic decisions that maximize profits, which is the main goal of a monopolistic firm.

Marginal Revenue

Marginal revenue (MR) is another crucial concept for monopolies and plays a key role in decision-making processes. It's defined as the additional revenue a firm earns by selling one more unit of a good or service. Mathematically, it's the change in total revenue due to a one-unit change in quantity sold.
For students and practitioners, calculating marginal revenue helps in understanding the diminishing returns on selling additional units, often experienced by monopolists. As the exercise reveals, after a certain quantity, the marginal revenue can become negative, indicating that selling more units could lead to lower profits. Understanding MR helps in identifying the optimum level of output where profit is maximized, which is the intersection where MR equals marginal cost (MC).

Marginal Cost

Marginal cost (MC) is the cost of producing one additional unit of a good. It's fundamental in identifying the optimal output level for a monopoly. The marginal cost helps monopolists determine the cost of increasing production and whether it's beneficial to produce more goods. As seen in the provided exercise, the MC increases with each additional unit, reflecting the common reality that producing more can eventually become more expensive due to factors such as limited resources or the need for more intensive labor.
Comparing marginal revenue and marginal cost is essential because it guides monopolists on when to stop production to maximize profits. The point where MR and MC meet is typically where profits are highest since producing past that point would result in a higher cost than revenue for additional units.

Profit Maximization

Profit maximization is a pot of gold at the end of the rainbow for businesses. It's the process of finding the output level where a firm makes the most money. In the context of a monopoly, profit maximization occurs where the difference between total revenue and total cost is greatest. There's a sweet spot in the production process where marginal revenue equals marginal cost, beyond which it's not profitable to produce more.
The textbook exercise shows us how determining the profit-maximizing quantity requires comparing MR and MC for each unit of output. It vividly illustrates how monopolists must understand their revenue and costs at each step to ensure they don't produce too little or too much, risking their overall profits.

Tax Effects on Monopolies

Taxes are a reality for all businesses, and monopolies are no exception. A tax imposed on a monopolist can significantly affect its profitability by increasing the costs of production. However, it's interesting to note that, as shown in the textbook exercise, a lump-sum tax, such as a flat fee per day, may not affect the quantity at which profit is maximized, but it will reduce the overall profit.
Why is the profit-maximizing output unaffected? Because a lump-sum tax does not change the marginal cost or marginal revenue; it merely shifts the total cost curve upward. However, if the tax were per unit of good produced, it could change the marginal cost curve and possibly the quantity that maximizes profit.
This concept is a critical reminder that taxes have varied implications depending on their structure, and understanding these nuances is crucial for sound economic and business strategies.