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The relation between cost and output is called Costfunction . The cost function of the firm depends upon the production conditions and the prices of the factors used for production. How much costs a firm will incur on production depends on the level of output. Moreover, the quantity of a product that will be offered by the firm for supply in the market depends to a great degree upon the cost of production incurred on the various possible levels of output. Cost of production is the most important force governing the supply of a product. It is thus assumed that whatever the level of output a firm produces, it is produced at the minimum cost possible.

Concepts of Costs Fixed Cost FC : Fixed costs, are those which are independent of output, that is, they do not change with changes in output. Even if the firm closes down for some time in the short run remains in business, these costs have to be borne by it. Fixed costs are also known as ovrhead costs and include charges such as contractual rent, insurance fee, maintenance costs, property taxes, interest on the capital invested, minimum administrative expenses such as manager's salary, watchman's wages etc.

Variable cost [VC]: Variable costs, on the other hand, are those costs which are incurred on the employment variable factors of production whose amount can be altered. These costs include payments such as wages of labour employed, prices of the raw materials, fuel and power used, the expenses incurred on transporting. Variable costs are made only when some amount of output is produced and the total variable costs increase with the increase in the level of production. Variable costs are also called prime costs or direct costs. Total of a business is the sum of its total variable costs and total fixed costs. Thus: TC = TFC + TVC whe re TC stands for total cost, TFC for total fixed cost and TVC for total variable cost.

Since the total fixed cost remains constant whatever the level of output, the total fixed cost curve (TFC) is a horizontal straight line. The total fixed cost curve (TFC) starts from a point on the Y-axis meaning thereby that the total fixed cost will be incurred even if the output is zero.

Average Total Cost (ATC) Average fixed cost is the total fixed cost divided by the number of units of output produced. Average Variable Cost (AVC): Average variable cost is the total variable cost divided by the number of units of output produced. Therefore, Average total cost (ATC) is the sum of the average variable cost [AVC] and average fixed cost [AFC]

Marginal cost {MC] can be found for further units of output where ΔTC represents a change in total cost and ΔQ represents a unit change in output or total product.

Types of Costs. The types of costs that a firm considers relevant for decision making vary from situation to situation. Opportunity Costs: Opportunity cost can be defined as the cost of any decision measured in terms of the next best alternative, which has been sacrificed. Ex: At the firm level, a manager planning to hire a stenographer may have to give up the idea of having an additional clerk in the accounts department. This is applicable even at the national level, where the country allocates higher defense expenditures in the budget at the cost of using the same money for infrastructural projects. In order to maximize the value of the firm, a manger must view costs from this perspective.

Implicit or Imputed cost and Explicit Costs[Economic or Accounting concept of cost]: In most business decisions, the total opportunity costs cannot be accounted for fully because of our inability to include implicit costs. Implicit costs are the value of forgone opportunities that does not involve a physical cash payment. Ex: An entrepreneur who manages his firm has to forgo his salary, which he could have earned if he had worked elsewhere. Though implicit costs are not included in books of accounts, they do play an important role in a decision making process. Explicit costs can be defined as the costs which involves actual payment to other parties. Both costs are equally important while making business decisions, but sometimes implicit costs are ignored as they are not as apparent as explicit costs

Marginal, Incremental, and Sunk Costs : Marginal costs can be defined as the change in the total cost of a firm as a result of change in one unit of output. These costs are important in short-term decision making of the firm to determine the output at which profits can be maximized. On the other hand, incremental cost is the total additional cost that a firm has to incur as a result of implementing a major managerial decision. For example, for Telco, a leading truck manufacturer in India, the marginal cost of making one additional truck in a defined production period would be the labor, components, and energy costs directly associated for making that extra truck .

Sunk costs : Sunk costs are those costs which are incurred in the past or that have to be incurred in the future as a result of a contractual agreement. These costs do not change even though the output is changed. The cost of inventory and future rent charges for a warehouse that have to be incurred as a part of lease agreement are examples of sunk costs. These costs are irrelevant while making decisions because in any case they have to be borne by the firm.

Direct and Indirect Costs: Direct costs are the costs, which can be directly associated to the production of a given product. The use of raw material, labor input, and machine time involved in the production of each unit of that product can be determined. On the other hand, there are certain costs like stationery, office and administrative expenses including electricity charges, depreciation of plant and buildings, and other such expenses that cannot be separated and directly attributed to individual units of production. These costs are therefore classified as Indirect or overhead costs in the accounting process.

Fixed and Variable Costs: Fixed costs are those costs, which do not vary with the changes in the output of a product. They are associated with the existence of a firm's plant and, therefore, must be paid even if the firm's level of output is zero. Costs incurred as a result of payment of interest on borrowed capital, contractual rent for equipment or building, depreciation charges on equipment and buildings, and the salaries of top level management and key personnel are generally fixed costs. Variable costs are those costs that vary with the level of output. They include payment for raw materials, charges for fuel and electricity, payment of wages and salaries of temporary staff, and payment of sales commission, etc. For example, in the case of hotel industry there is a high variation in occupancy rates according to different seasons.

Cost Functions A cost function determines the behavior of costs with the change in output. The cost-output relationship gains importance when the firm has to allocate resources and determine a price for the output. The cost function can be a schedule, graph or a mathematical relationship showing the minimum achievable cost for producing various quantities of output. It indicates the functional relationship between total cost and total output. If C represents total cost and Q represents the level of output, then the cost function is represented as C = C (Q).

Cost functions are derived functions. They are derived from the production functions, which identify the efficient methods of production available at any particular point of time. The cost function can be derived from the input cost combinations of the firm, The input costs of the two inputs of production i.e. labor (L) and capital (K) are given to be constant as the wage rate (w) and rent (r), respectively. If Land K represent the amounts of the two inputs that are used for the production of Q level of output, the firm will always select those combinations of the two inputs, which lie on the expansion path. Along any expansion path, the level of output increases as we gradually depart from the origin.

Therefore, we can say that along any expansion path the demand for any factor of production will depend on the level of output, to be produced. So, if Land K are the amounts of the factors of production and Q is the level of output then it can be said that Land K are functions of Q. That is, L =gl (Q) and K = g2 (Q)

Short run Cost Functions Short run cost functions help in determining the relationship between output and costs in the short run. With a particular change in production output, the change in total, average and marginal costs can be determined for a given set of cost functions for a firm. The short run average total costs (SRA TC) and average variable costs (AVC) are slightly U-shaped. The marginal cost (MC) curve intersects both the average variable cost curve and short run average total cost curve at their lowest points. The cost functions the representative of the short-run costs incurred by majority of firms

The level of output where the average total cost is minimum is known as the short run capacity of a firm. This is also the optimum level output since the average total cost is minimized at tills point (M). The short-run average. total cost function (SRATC) is minimum at the point Q1 which is the short-run capacity of the firm. Any variation of output from Q1 leads to higher short run average total cost. However, if the output is more than its short run capacity, it is due to over-utilization of the firm's plant and machinery. If the quantity produced goes beyond Q1 the short run average total cost of the firm rises as a result of high marginal cost.

The Long-run Cost Function Long run can be defined as a sufficiently long period that allows the firm to adjust factors of production to meet market demand. In the long run, the firm chooses the combination of inputs that minimizes the cost of production at a desired level of output. The firm identifies the plant size, types and sizes of equipment, labor skills and raw materials that on combination give the maximum output at the lowest cost, considering the technology available and the production methods used. As the inputs are chosen for producing a desired level of output, all the inputs in the long run are variable.

If there is an unexpected rise in the demand and the firm wants to increase the output from Q, to Q2, the firm can increase variable inputs 'like labor and raw material. In such circumstances, the short run average cost will be high. If the demand lasts for a longer period, then a larger investment in the plant and equipment is required. This would reduce the per unit cost to C2, A short run average cost function like SAC2 can be determined for the new set of inputs.

Break Even Analysis An important application of cost analysis in the decision making of the firm regarding the level of output at which i will break even, that is, at which its total revenue will equal total cost and therefore it will attain no profit, no loss position. Break-even analysis is also sometimes called profit contribution analysis. Break-even analysis is also applied to determine the quantity of output sold at which the firm will realise its target level of profits. Break even analysis can be made by assuming first, linear cost-output and revenue-output relationships and, secondly, by assuming non-linear cost and revenue functions. Break-even analyses is based on revenue functions and cost function. When price of the product remains constant as the firm expands its production and sales, the total revenue will be linearly related to output.

Linear Break-Even Analysis- Graphical Method. Thus, the total revenue function TR in Fig, represents the total revenue that the firm will earn at each level of output, assuming that the price (P) product for the firm remains constant. Similarly, total cost function TC is a straight line starting from point F on the Y-axis and thus represents the linear relationship between been total cost and output. It may be noted that in our analysis of cost function we have-explained that average Marginal cost falls over a range of output in the beginning and then begins to rise.

Managers of business firms who use the break-even analysis are interested in a relevant middle ranges of output without considering the extremes of low and very high ranges of output which average variable cost falls or rises. Hence linear cost function represented by the straight-line curve is generally used in break-even analysis. TFC is the total fixed cost line, w ith the given fixed cost equal to OF. The vertical distance between the total cost line TC and tot al fixed cost line TFC represents the total variable cost.

It will be further seen that the slope of the revenue curve (which indicates the price at which additional units of the good are sold) is greater than the slope of the total cost curve (which indicates the additional variable cost Incurred per unit of output by the firm). This means the price which the firm receives for every unit of the good sold exceeds the additional cost incurred per unit of output on labour, raw materials and other variable factors

It will be seen, that up to quantity QB of the commodity produced and sold total cost exceeds total revenue indicating that the firm will suffer losses if it produces and sells less than QB quantity of the commodity. At output QB produced and sold, the total revenue received equals total cost (TR = TC) and therefore at this output level the firm neither makes profits, nor incur s losses. In other words, at QB quantity of output produced and sold, the firm just breaks even. Therefore, output level QB or intersection point E at which the firm neither make profits, nor suffers losses is called a break-even point.

Break-even level of output shows the minimum level of output required to be sold if the firm will just be in no profit, no loss position. The firm will undertake the production of a commodity if it estimates that it will be able to sell the quantity of output equal to or greater than the break-even point.

Merits & Demerits of Break-even Analysis The advantages of break even analysis are as follows: It is an inexpensive method. It helps the managers to decide whether it's worthwhile to go in for a more intensive (a costly) analysis. It helps in designing product specifications as each design has its own implications for cost. It serves as a substitute for estimating the unknown factors that may arise in the future. By deciding that operating profit must at least be zero i.e. the break-even point a fair demand can be estimated.

The demerits of break even analysis are described below: In break even analysis, it is assumed that the selling price and the variable costs per unit are known for each level of production. However, in practice these are not mown. Thus, the relevance of break even analysis depends upon the degree of accuracy in determining the costs of production. It does not permit a proper evaluation of cash flows. It is generally accepted in basic financial theory that the value of a proposed project's anticipated cash flows must be considered to arrive at sound decisions. If the discounted value of the cash flows exceeds the required investment outlay in cash, then the project is acceptable. Break-even analysis assumes that the firm's project exists in isolation. There are alternative uses for the firm's funds in every case. For example, a manufacturer's vacant plant could be leased to another company to earn some returns; it could also be used for manufacturing another product. We must, therefore, always consider not only the value of an individual project, but also how it compares to other uses of the funds and facilities.

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