The most basic characteristic of a differential equation is its order. The second derivative is less than zero, which means our function is concave

and has a relative maximum when Q equals 24. The second derivative of MC is positive for all values of Q, therefore the

MC function is convex, and is at a relative minimum when q is equal to 8. Take the first derivative of a function and find the function for

the slope. Since this is a continuous function, there must be a point where the slope crosses

from positive to negative. With the help of activity-based costing, costs can be assigned to activities within each category.

- Instead, it is simply an analysis concept used to optimize decisions.
- Among several alternatives, management opts for the most profitable one.
- It includes relevant and significant costs that exert a material impact on production cost and product pricing in the long run.
- The calculation of incremental cost shows a change in costs as production expands.
- Sunk costs refer to costs that a business has already incurred, but that cannot be eliminated by any management decision.

The sales revenues for each alternative and the costs that differ between alternatives are the relevant amounts in these decisions. Total fixed costs often remain the same between pricing alternatives https://adprun.net/ and, if so, may be ignored. In selecting a price for a product, the goal is to select the price at which total future revenues exceed total future costs by the greatest amount, thus maximizing income.

## How much oil does a front differential take?

These are expenses incurred by outside parties but are not directly the responsibility of the business. Potential gains or profits are lost when one option is selected over another. Despite not being a typical “cost” in the sense of out-of-pocket expenses, they nonetheless represent the value of the second-best choice.

## Differential Cost Analysis: Meaning and Its Practical Applications

(a) You are required to determine the differential cost of producing 1500 units by increasing capacity to 100%. Consider a company engaged in plastic bag manufacturing that acquires an advanced machine to double its current production of plastic bags. As soon as the company puts the new machine into use, the government bans the manufacturing of plastic bags in the country and makes it a crime for any person to manufacture or sell plastic bags. The new regulation renders the machine and the produced plastic bags obsolete, and the company cannot change the government’s decision.

## Applications of Differential Cost

For instance, avoidable costs are costs that can be eliminated by choosing one option over another, such as closing a department. For instance, the price of extra flour, yeast, and labor would be included in the incremental expenses if a bakery decided to create one more loaf of bread. Businesses can choose wisely by weighing the varying costs involved with each option against the anticipated advantages (like higher revenue or cost savings). They depict the alteration in costs that results from a particular choice. Businesses looking to maximize efficiency and profitability must thoroughly understand these costs and how they operate. They receive a special order for producing Mugs of 1000 units at a rate of ₹ 5/- per unit.

An opportunity cost is the benefit foregone when one alternative is selected over another. For example, if a product line is eliminated, these costs are simply allocated to the remaining product lines. It is advisable to accept the second proposal provided differential cost formula facilities exist for the production of additional numbers of ‘utility’ and to convert them into ‘Ace’. The first proposal results into a loss and hence is not acceptable. These can be determined from the analysis of routine accounting records.

The variable costs are related directly to each product line, and thus are eliminated if the product line is eliminated. A manufacturing concern sells one of its products under the brand name ‘utility’ at Rs. 3.50 each, the cost of which is Rs. 3.00 each. The variable cost of manufacture between these levels is 15 paise per unit and fixed cost Rs. 40,000. Differential cost analysis aids businesses in determining the long-term financial effects of strategic decisions like market development, the introduction of new products, or capital expenditures. It assists in determining how profitable these choices will be in the long run.

When two levels of activities are being considered, the differential cost is obtained by deducting the cost at one level from another level. The alternative actions may arise due to change in sales volume, price, product mix, or such actions as make or buy or continue or stop production, etc. The move places the opportunity cost of choosing to stick to the old advertising method at $4,000 ($14,000 – $10,000). The $4,000 is the income that ABC would forego for remaining with the old marketing techniques and failing to adopt the more sophisticated marketing models. In the case of ABC Company, moving to television ads and social media marketing exposes the company to a broader customer base. If the company earned $10,000 using the current marketing platforms, moving to the more advanced advertising platforms might result in a 40% revenue increase to $14,000.

## Customer Decisions

In the above case, the output level should be fixed at Rs.3 lakhs where the selling price is at Rs.160 per machine. Under differential cost method, the decision criterion is that it would be profitable to increase the output as long as the incremental revenue equals or exceeds the differential cost. Up to Rs.3 Lakhs level the incremental revenue is more than differential cost thereby adding to the profit figure. After that level the differential cost is more than the incremental revenue thus resulting in a loss on additional output. For the company to know if the new selling price is viable, it calculates the differential cost by deducting the cost of the current capacity from the cost of the proposed new capacity. The differential cost is then divided by the increased units of production to determine the minimum selling price.

The difference in total costs between two or more alternative courses of action is known as differential costs, often called incremental costs. They are the extra expenses encountered by choosing one course of action over another. The differential revenue is obtained by deducting the sales at one activity level from the sales of the previous level. The differential cost is compared to the differential revenue to determine the most profitable level of production and the best selling price. Management will decide to increase the level of production when the differential revenue is higher than the differential cost. In the last financial year, it sold 100,000 units at $100 per unit.

Avoidable costs—costs that can be avoided by selecting a particular course of action— are always differential costs and must be considered when deciding between alternative courses of action. Differential analysis requires that we consider all differential revenues and costs—costs that differ from one alternative to another—when deciding between alternative courses of action. The total cost figures are considered for differential costing and not the cost per unit. A particular subset of incremental costs, called marginal cost, may concentrate just on the price of the last unit produced. Incremental costs are the extra expenses spent when a business produces one more unit of a product, offers an additional service, or takes a certain action. These expenses are directly related to the increasing output or activity by one unit.

It also aids in choosing whether to add new products or expand existing product lines. It enables businesses to streamline operations, eliminate waste, and concentrate on areas where cost savings can make a big difference. Controlling needless expenses is crucial for maintaining financial stability. The analysis makes it easier to identify which expenses are avoidable and which are directly tied to particular choices.

We just need to consider only such revenues and costs which change. Based on this analysis, Pacific Paper should process product A further to increase income by $5 per unit sold. The company should not process product B further because that would decrease income by $1 per unit sold. If Rios Company continues to operate at 50% capacity (producing 5,000 units without the special order) it would generate income of only $12,000. By accepting the special order, net income increases by $6,000 ($18,000 net income with special order – $12,000 net income without special order). Although these five decisions are not the only applications of differential analysis, they represent typical short-term business decisions using differential analysis.