Marginal Analysis: Profit Maximization (MR = MC)
If illustrated on a graph, the point at which a company’s profits are maximized is when the marginal profit is zero.
- MR = MC → If the marginal revenue is equal to the marginal cost, the marginal profit is maximized.
- MR > MC → If the marginal revenue is greater than the marginal cost, the marginal profit is positive.
- MR < MC → If the marginal revenue is less than the marginal cost, the marginal profit is negative.
The break-even point—where MR = MC—represents the optimal production level at the given level of pricing, i.e. the benefits from “economies of scale” are achieved.
However, the marginal cost is an upward-sloping curve because of the law of diminishing returns, which is a phenomenon termed “diseconomies of scale”.
While economies of scale are a positive attribute that can function as a barrier to entry and contribute to a long-term moat, diseconomies of scale occur when the cost efficiencies reverse course and operating costs start to climb upward.
On that note, companies should strive to reach their optimal production level, as it is at this particular level at which operations are most efficient and the maximum potential profits are derived.
Marginal Profit Calculator
We’ll now move on to a modeling exercise, which you can access by filling out the form below.
1. Total Revenue Calculation
Suppose an apparel store sells its products at an average selling price (ASP) of $100, with 60,000 units sold in Year 1.
If we assume a market with perfect competition, the demand curve for the company’s products is perfectly elastic, so we’ll assume that the selling price remains constant.
- Average Selling Price = $100.00
- Quantity Sold, Year 1 = 60k
For the quantity sold, we’ll also use a step function, but we’ll enter a placeholder value for the growth in quantity sold for the time being and return to this section later.
By multiplying the ASP in each year by the quantity sold in the corresponding period, we can determine the total revenue.
For example, the Year 1 revenue is $6 million ($100.00 × 60,000), and we’ll copy the formula across for the rest of the forecast period.
- Total Revenue = Average Selling Price (ASP) × Quantity Sold
Underneath the revenue line item, we’ll calculate the change in revenue and change in quantity for each year by subtracting the prior period value from the end of period value.
- Change in Revenue = Current Year Revenue – Prior Period Revenue
- Change in Quantity = Current Year Quantity – Prior Period Quantity
The change in revenue remains fixed at $414k per year, which is attributable to our pricing assumption staying consistent through the projection period.
2. Total Cost Calculation (Fixed + Variable Costs)
In the next section, we’ll calculate our fixed and variable costs.
- Total Fixed Cost: The total fixed cost is $2.4k—which as implied by the name—we’ll assume remains constant throughout all four years for illustrative purposes.
- Total Variable Cost: On the other hand, the variable cost per unit is $25.00, and we’ll assume the cost per unit increases by $2.00 per unit each year.
From Year 1 to Year 4, the variable cost per unit increases from $25.00 to $31.00.
- Total Fixed Costs = $2.4k
- Variable Cost per Unit = $25.00
- Variable Cost per Unit, Step Function = +$2.00 YoY Growth
The total fixed costs are assumed to remain constant at $2.4k, while the total variable costs are calculated by multiplying the variable cost per unit by the quantity produced, which we’ll assume is equal to the quantity sold.
- Total Variable Costs = Variable Cost per Unit × Quantity Produced
As we did for the total revenue, we’ll then calculate the change in fixed and variable costs for each period.
3. Marginal Revenue and Marginal Cost Calculation
We now have the necessary inputs to compute the marginal revenue and marginal cost for all four years.
The formulas to calculate the two metrics are as follows.
- Marginal Revenue = (Change in Revenue) ÷ (Change in Quantity)
- Marginal Cost = (Change in Total Costs) ÷ (Change in Quantity)
Since we broke out our the inputs separately, we can simply link to them in our formulas.
4. Marginal Profit Calculation Example
In the final step, we calculate the marginal profit for Years 2 to 4 by subtracting the marginal cost from the marginal revenue.
- Marginal Profit = Marginal Revenue – Marginal Cost
However, the purpose of this exercise is to determine the point at which our company’s profits are maximized.
Therefore, we’ll use the “Goal Seek” function in Excel to make our Year 3 cell equal to zero (or as close to it as plausible) by adjusting the quantity sold step function.
After doing so, the returned value for the quantity step function (Cell J6) comes out as approximately two, i.e. +2k per year, since the units are in thousands.
We can confirm that our company’s marginal profit in Year 3—given our parameters—is near zero when the quantity sold is around 63k.
Furthermore, the marginal profit in the prior year is net positive (+$4k), whereas for the next year it is negative (-$4k).
Hypothetically, if our company’s cost structure were to be adjusted and its margin profile were to improve from implementing cost-cutting measures or from increasing the average selling price (ASP), the optimal quantity would adjust accordingly.
