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# Long run cost functions for Managerial Economics Mcom Delhi University

## Long run cost functions for Managerial Economics Mcom Delhi University

Long run cost functions for Managerial Economics Mcom Delhi University

#### Concept of Cost Function:

The relationship between output and costs is expressed in terms of cost function. By incorporating prices of inputs into the production function, one obtains the cost function since cost function is derived from production function. However, the nature of cost function depends on the time horizon. In microeconomic theory, we deal with short run and long run time.

A cost function may be written as:

Cq = f(QPf)

Where Cq is the total production cost, Qf is the quantities of inputs employed by the firm, and Pf is the prices of relevant inputs. This cost equation says that cost of production depends on prices of inputs and quantities of inputs used by the firm.

#### Importance of Cost Function:

The study of business behaviour concentrates on the production process—the conversion of inputs into outputs—and the relationship between output and costs of production.

We have already studied a firm’s production technology and how inputs are combined to produce output. The production function is just a starting point for the supply decisions of a firm. For any business decision, cost considerations play a great role.

Cost function is a derived function. It is derived from the production function which captures the technology of a firm. The theory of cost is a concern of managerial economics. Cost analysis helps allocation of resources among various alternatives. In fact, knowledge of cost theory is essential for making decisions relating to price and output.

Whether production of a new product is a wiser one on the part of a firm greatly depends on the evaluation of costs associated with it and the possibility of earning revenue from it. Decisions on capital investment (e.g., new machines) are made by comparing the rate of return from such investment with the opportunity cost of the funds used.

The relevance of cost analysis in decision-making is usually couched in terms of short and long periods of time by economists. In all market structures, short run costs are crucial in the determination of price and output. This is due to the fact that the basis for cost function is production and the prices of inputs that a firm pays.

On the other hand, long run cost analysis is used for planning the optimal scale of plant size. In other words, long run cost functions provide useful information for planning the growth as well as the investment policies of a firm. Growth of a firm largely depends on cost considerations.

The position of the U-shaped long run AC of a firm is suggestive of the direction of the growth of a firm. That is to say, a firm can take a decision whether to build up a new plant or to look for diversification in other markets by studying its existence on the long run AC curve. Further, it is the cost that decides the merger and takeover of a sick firm.

Non-profit sector or the government sector must also have a knowledge of cost function for decision-making. Whether the Narmada Dam is to be built or not, it should evaluate the costs and benefits ‘flowing’ from the dam.

### Long run cost functions for Managerial Economics Mcom Delhi University

Fixed and Variable Costs

Fixed costs do not vary with output. These costs include interest expenses, rent on leased plant and equipment, depreciation charges associated with the passage of time, property taxes, and salaries for employees not laid off during periods of reduced activity. Because all costs are variable in the long run, long-run fixed costs always equal zero.

Variable costs fluctuate with output. Expenses for raw materials, depreciation associated with the use of equipment, the variable portion of utility charges, some labor costs, and sales commissions are all examples of variable expenses. In the short run, both variable and fixed costs are often incurred. In the long run, all costs are variable.

Long run cost functions for Managerial Economics Mcom Delhi University:

Long Run Cost

Long-run cost is variable and a firm adjusts all its inputs to make sure that its cost of production is as low as possible.

Long run cost = Long run variable cost

In the long run, firms don’t have the liberty to reach equilibrium between supply and demand by altering the levels of production. They can only expand or reduce the production capacity as per the profits. In the long run, a firm can choose any amount of fixed costs it wants to make short run decisions.

### Long run cost functions for Managerial Economics Mcom Delhi University

Long run and short run cost functions

In the long run, the firm can vary all its inputs. In the short run, some of these inputs are fixed. Since the firm is constrained in the short run, and not constrained in the long run, the long run cost TC(y) of producing any given output y is no greater than the short run cost STC(y) of producing that output:

TC(y STC(y) for all y.

Now consider the case in which in the short run exactly one of the firm’s inputs is fixed. For concreteness, suppose that the firm uses two inputs, and the amount of input 2 is fixed at k. For many (but not all) production functions, there is some level of output, say y0, such that the firm would choose to use k units of input 2 to produce y0, even if it were free to choose any amount it wanted. In such a case, for this level of output the short run total cost when the firm is constrained to use k units of input 2 is equal to the long run total cost: STCk(y0) = TC(y0). We generally assume that for any level at which input 2 is fixed, there is some level of output for which that amount of input 2 is appropriate, so that for any value of k,

TC(y) = STCk(y) for some y.

(There are production functions for which this relation is not true, however:

For a total cost function with the typical shape, the following figure shows the relations between STC and TC. ### Long run and short run average cost functions

Given the relation between the short and long run total costs, the short and long run average and marginal cost functions have the forms shown in the following figure. Note:

• The SMC goes through the minimum of the SAC and the LMC goes through the minimum of the LAC.
• When SAC = LAC we must have SMC = LMC (since slopes of total cost functions are the same there).

In the case that the production function has CRTS, the LAC is horizontal, as in the following figure. ### Long run cost functions for Managerial Economics Mcom Delhi University

Recommended Mcom Notes

M. Com. (Part-I,Part-II)

### Short run cost functions for Managerial Economics Mcom Delhi University

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