Determining Profit Maximizing Level of Production -- Marginal Cost and Marginal Revenue
Maximum profit is the level of output where MC equals MR.
As long as the revenue of producing another unit of output (MR) is greater than the cost of producing that unit of output (MC), the firm will increase its profit by using more variable input to produce more output.
The law of (the reality of) diminishing marginal productivity demonstrates that adding input will eventually reduce production and increase cost. When the production level reaches a point that cost of producing an additional unit of output (MC) exceeds the revenue from the unit of output (MR), producing the additional unit of output reduces profit. Thus, the firm will not produce that unit.
Profit is maxmized at the level of output where the cost of producing an additional unit of output (MC) equals the revenue that would be received from that additional unit of output (MR).
- Maximum profit is not maximum productivity unless cost of variable input is zero (variable input is free), or price of output is infinite; since neither of these is likely to occur, we can confidently state that maximum profit is not earned by maximizing production. Restated, MC is infinite where production is maximized. MR would need to be infinite to maximize profit where production is maximized. Since no one will pay us an infinite price for our product, MC will equal MR at a level of production that is less than maximum production.
Graph 24 (AFC, AVC, ATC, MC & MR -- again)
An example to illustrate the impact of technology
An advance in technology shifts the TPP curve; it also shifts the TVC curve (usually lowering the TVC). However, acquiring new technology probably means incurring a fixed cost which shifts the TFC curve (usually raising the TFC). The manager needs to decide whether the increase in TFC due to adopting technology is adequately offset by the reduction in the TVC to justify investing in the new technology.
Graph 30 (Impact of Technology on Total Production)
Graph 31 (Impact of Technology on Marginal Production)
In summary
- Profit is NOT maximized at maximum production.
- Advances in production technology increases output from the same level of variable input.
- The MC cost is the firm's supply curve for the output.
The next section describes how marginal cost illustrates the firm's supply of the output.
The Profit Maximization Rule states that if a firm chooses to maximize its profits, it must choose that level of output where Marginal Cost (MC) is equal to Marginal Revenue (MR) and the Marginal Cost curve is rising. In other words, it must produce at a level where MC = MR.
Profit Maximization Formula
The profit maximization rule formula is
MC = MR
Marginal Cost is the increase in cost by producing one more unit of the good.
Marginal Revenue is the change in total revenue as a result of changing the rate of sales by one unit. Marginal Revenue is also the slope of Total Revenue.
Profit = Total Revenue – Total Costs
Therefore, profit maximization occurs at the most significant gap or the biggest difference between the total revenue and the total cost.
Why is the output chosen at MC = MR?
At A, Marginal Cost < Marginal Revenue, then for each additional unit produced, revenue will be higher than the cost so that you will generate more.
At B, Marginal Cost > Marginal Revenue, then for each extra unit produced, the cost will be higher than revenue so that you will create less.
Thus, optimal quantity produced should be at MC = MR
Application of Marginal Cost = Marginal Revenue
The MC = MR rule is quite versatile so that firms can apply the rule to many other decisions.
For example, you can apply it to hours of operation. You decide to stay open as long as the added revenue from the additional hour exceeds the cost of remaining open another hour.
Or it can be applied to advertising. You should increase the number of times you run your TV commercial as long as the added revenue from running it one more time outweighs the added cost of running it one more time.
Profit Maximization Example
In the early 1960s and before, airlines typically decided to fly additional routes by asking whether the extra revenue from a flight (the Marginal Revenue) was higher than the per-flight cost of the flight.
In other words, they used the rule Marginal Revenue = Total Cost/quantity
Then Continental Airlines broke from the norm and started running flights even when the added revenues were below average cost. The other airlines thought Continental was crazy – but Continental made huge profits.
Eventually, the other carriers followed suit. The per-flight cost consists of variable costs, including jet fuel and pilot salaries, and those are very relevant to the decision about whether to run another flight.
However, the per-flight cost also includes expenditures like rental of terminal space, general and administrative costs, and so on. These costs do not change with an increase in the number of flights, and therefore are irrelevant to that decision.
Limitations of the Profit Maximization Rule (MC = MR)
1. Real World Data
In the real world, it is not so easy to know exactly your Marginal Revenue and Marginal Cost of the last products sold. For example, it is difficult for firms to know the price elasticity of demand for their goods – which determines the MR.
2. Competition
The use of the profit maximization rule also depends on how other firms react. If you increase your price, and other firms may follow, demand may be inelastic. But, if you are the only firm to increase the price, demand will be elastic.
3. Demand Factors
It is difficult to isolate the effect of changing the price on demand. Demand may change due to many other factors apart from price.
4. Barriers to Entry
Increasing prices to maximize profits in the short run could encourage more firms to enter the market. Therefore firms may decide to make less than maximum profits and pursue a higher market share.
Similar Posts:
- Perfect Competition
- Price Elasticity of Demand (PED)
- Oligopoly Market Structure
- Theory of Production: Cost Theory
- Economies of Scale
Monopoly Profit-Maximization by Analyzing a Table
Consider the following table with cost and revenue data for a hypothetical monopolist:
| Quantity | TFC | TVC | TC | AVC | ATC | MC | Price | Total Revenue | Marginal Revenue |
| 0 | 5,000 | 0 | 5,000 | – | – | – | 38 | 0 | – |
| 100 | 5,000 | 3,000 | 8,000 | 30 | 80 | 30 | 37 | 3,700 | 37 |
| 200 | 5,000 | 5,000 | 10,000 | 25 | 50 | 20 | 36 | 7,200 | 35 |
| 300 | 5,000 | 6,000 | 11,000 | 20 | 36.67 | 10 | 35 | 10,500 | 33 |
| 400 | 5,000 | 6,800 | 11,800 | 17 | 29.50 | 8 | 34 | 13,600 | 31 |
| 500 | 5,000 | 8,000 | 13,000 | 16 | 26 | 12 | 33 | 16,500 | 29 |
| 600 | 5,000 | 10,000 | 15,000 | 16.67 | 25 | 20 | 32 | 19,200 | 27 |
| 700 | 5,000 | 13,000 | 18,000 | 18.57 | 25.71 | 30 | 31 | 21,700 | 25 |
| 800 | 5,000 | 16,500 | 21,500 | 20.63 | 26.88 | 35 | 30 | 24,000 | 23 |
| 900 | 5,000 | 22,000 | 27,000 | 24.44 | 30 | 55 | 29 | 26,100 | 21 |
Problem: What are the profit-maximizing output and price for the above monopolist? What is the profit at this output? What is the average profit at this output?
Solution: Like the purely competitive firm, a monopolist maximizes profits at the quantity where marginal cost and marginal revenue are equal, or where marginal cost comes closest to marginal revenue, as long as marginal cost does not exceed marginal revenue, marginal cost is not falling, and price exceeds average variable cost.
Applying the profit-maximizing rule, we conclude that the firm maximizes profits at
| Quantity | = 600 units |
| Price | = $32 |
| Profit (TR-TC) | = $19,200-$15,000 = $4,200 |
| Average Profit (TP / Q) | = $7 ($4,200 / 600) |
Video Explanation
For a video explanation of a monopoly firm’s profit maximization using a table, please watch:
Monopoly Profit-Maximization by Analyzing a Graph
In a table, we find the profit-maximizing output by identifying the point at which marginal cost and marginal revenue are equal, as long as marginal cost does not exceed marginal revenue, marginal cost is not falling, and price exceeds average variable cost.
The graph below indicates that at output Qpm, marginal cost equals marginal revenue in the upward sloping portion of the marginal cost curve. At this output, the price is Ppm. For a monopolist, the marginal revenue curve and the demand (price) curve are different. Therefore, marginal revenue and price at the profit-maximizing output are different. From the MC=MR point, go straight up to the demand curve in order to identify the profit-maximizing price. This price is greater than the firm’s average variable cost, so the company will not need to shut down. The price is also greater than the firm’s average total cost, so the company is making an economic (above-normal) profit. Because there are barriers to entry into this industry, it is possible that the firm can continue to make economic profits in the long run, as well.
For a video explanation of a monopolist’s profit-maximizing quantity and price using a graph, please watch: