Cost Output Relationship in the Short Run

 

Cost Output Relationship in the Short Run

The  relation between the cost and output is technically described as the “Cost Function”.

Cost function can be stated as follows:

C= f[Q,W,F,T]

Where C= Cost

             Q= Amount of production

             W= prices of factors of production

             F= Productivities of factors of production

            T= Improvements in techniques of production

These are also called the determinants of the cost of production.

Short-run cost production function: Short-run is a period of time within which the firm can vary its output by varying only the quantity of variable inputs such as labor, and raw materials while fixed inputs like plant, machinery, etc, remain constant. As the quantity of variable inputs is changed, the proportions between the fixed and the variable factors get changed and the production function is governed by the law of variable proportions. Hence, the costs of the firm in the short-run are divided into fixed cost and variable costs.

Fixed costs- Fixed costs are also known as supplementary or overhead costs. Fixed costs do not vary with the change in output and must be paid even though production has been stopped temporarily. It includes the rent of the land, interest on capital invested in machinery, insurance premiums, and the salaries of the permanent employees. Thus these costs are independent of output and are referred to as unavoidable contractual costs.

Variable costs- Variable costs are also known as prime costs or direct costs because the volume of the output produced by the firm depends directly upon them. These costs include the cost of raw materials, transport, fuel, water, power, and the cost of daily labor employed. They are incurred only when the production is going on.

The distinction between variable and fixed costs applies in the short run. In the long-run, all the costs become variable because of the change in the scale of production.

Short-run Total, Average and Marginal costs: Total cost is defined as the actual cost that must be incurred to produce a given quantity of output. Total cost includes total fixed cost and total variable cost.

    TC=TFC+TVC

Average cost per unit is the total cost divided by the number of units produced. It is the sum average fixed cost and average variable cost.

AC=AFC+AVC

AC=TC/Q

Marginal cost may be defined as the change in the total cost as one more unit of output is produced or we can say it implies additional cost incurred to produce an additional unit.

MCn  =TCn-TCn-1

MC= ΔTC/ΔQ

Output in Units	TFC [in Rs]	TVC [in Rs]	TC [in Rs]	AFC [in Rs]	AVC [in Rs]	AC [in Rs]	MC [in Rs]
0	100	---	100	---	---	---	---
1	100	40	140	100	40	140	40
2	100	60	160	50	30	80	20
3	100	72	172	33.3	24	57.3	12
4	100	80	180	25	20	45	8
5	100	120	220	20	24	44	40
6	100	204	304	16.6	34	50.6	84

Above cost-schedule shows the response of total cost, average cost, and marginal cost resulting from the change in output.

Above the diagram shows the response of Total cost after the change in output. The total fixed cost [TFC] curve is horizontal and parallel to OX- axis. It remains constant and the same in the short run. It also indicates that the total fixed cost will be incurred even if the output is zero.

The shape of the TVC  is an inverted-S shape. It increases with the increase in the units of output. It is zero when output is zero and it increases with an increase in output, though the rate of increase is not constant. Initially, it increases but at a diminishing rate, and later, it increases at an increasing rate.

Total cost [TC] is the sum of total fixed cost and total variable cost. It includes both explicit and implicit costs. The shape of the TC  is also an inverted-S shape because of TVC. It begins from the point of TFC rather than the origin.

 Average and Marginal cost and the relation between Marginal and Average Cost:

AFC curve has a negative slope. AFC and output have an inverse relationship. It is higher at the smaller level of output and lowers at a higher level of output.

AVC decrease in the beginning and later increases when the output increases beyond the optimum level.

AC is the sum of AVC and AFC.  AC is the cost per unit of output produced. In the short-run, AVC and AC curve tends to be U-shaped.

Initially, AC tends to fall because of increasing returns and proper utilization of inputs. At the point of the optimum level of output, AC drops to its minimum. It is also called the least cost output level.

Beyond the optimum level, if the firm still continues increasing output, AC starts rising because of the diminishing returns.

MC is independent of TFC and directly related to TVC as it implies additional cost incurred to produce an additional unit. MC curve is also U-shaped. It decreases initially, goes to a minimum, and starts increasing at a later stage.

It is clear from the diagram that MC and AC both fall initially, MC falls faster than AC and reaches its minimum before AC. That’s why initially MC curve lies below AC curve.

At the later stage, MC increases faster than AC, and MC curve lies above the AC curve.

MC intersects AC curve at the minimum of the AC and the point of intersection shows the optimum level of output.

After this point, if the firms still continue to increase the production, the average cost will also increase and it will give diminishing returns.

The marginal cost helps in determining the level of output while the Average cost helps in determining the amount of profit and loss. 

Dr. Swati Gupta

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