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COST- OUTPUT RELATIONSHIP

Cost- output relationship has two aspects

 Cost -output relationship in short run

 Cost -output relationship in long run

Cost-Output Relation during Short Run or Short Run Cost Curves:

Time element plays an important role in price determination of a firm. During short
period two types of factors are employed. One is fixed factor while others are variable factors of
production. Fixed factor of production remains constant while with the increase in production,
we can change variable inputs only because time is short in which all the factors cannot be
varied.
Raw material, semi-finished material, unskilled labor, energy, etc., are variable inputs
which can be changed during short run. Machines, capital, infrastructure, salaries of managers
and technical experts are included in fixed inputs. During short period an individual firm can
change variable factors of production according to requirements of production while fixed
factors of production cannot be changed.
The cost-output relation during short period can be studied with the help of short run cost
curves based on short run costs as given below:
A. Short Run Total Costs:
Short run total costs of a firm are of following types:
(1) Total Costs:
Those costs which are incurred by a firm in the production of any commodity on the basis
of total fixed cost and total variable cost.
Total costs are calculated on the basis of the following formula:
Total cost (TC) = Total fixed cost (TFC) + Total variable cost (TVC)
Total costs change due to change in the total variable costs only during short period because total
fixed costs (TFC) remain constant.
(2) Total Fixed Cost (TFC):
Those costs which remain constant when the output is zero as well as it is increasing are
called total fixed costs. Such costs are borne by the firm whether there is production or not.
These costs are not concerned with the production of a commodity. Plant, land and building,
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machinery, tools, equipment, implements, contractual rent, insurance fee, maintenance cost,
property tax, interest on the capital, manager’s salary, etc., are the items which are included in
total fixed costs.
(3) Total Variable Costs (TVC):
Those costs which vary with the production of a commodity during short period and they
have direct relation with the change in production. When production is zero these costs will be
zero and when production increases they will move in the same direction. These costs are
incurred on raw material, direct wages and expenses on energy or power. Variable costs are also
called prune costs or direct costs. 

The cost-output relationships can also be shown through the use of graphs. It will be seen
that the average fixed cost curve (AFC curve) falls as output rises from lower levels to higher
levels. The shape of the average fixed cost curve, therefore, is a rectangular hyperbola.
However, the average variable cost curve (AVC curve) starts rising earlier than the ATC
curve. Further, the least cost level of output corresponds to the point LT on the ATC curve and
not to the point LV which lies on the AVC curve

Another important point to be noted is that in Fig. the marginal cost curve (MC curve)
intersects both the AVC curve and ATC curve at their minimum points. This is very simple to
explain. If marginal cost (MC) is less than the average cost (AC), it will pull AC down. If the
MC is greater than AC, it will pull AC up. If the MC is equal to AC, it will neither pull AC up
nor down. Hence, MC curve tends to intersect the AC curve at its lowest point.
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Similar is the position about the average variable cost curve. It will not make any
difference whether MC is going up or down. LT is the lowest point of total cost and LV is the
lowest point of variable cost.
B. Average Costs or Per Unit Costs:
During short period average costs or per unit costs can be divided into following
categories:
(1) Average fixed costs (AFC)
(2) Average variable costs (AVC)
(3) Average Costs (AC)
4) Marginal Cost (MC).
(1) Average Fixed Cost (AFC):
The average fixed cost is the total fixed cost divided by the volume of output. There is an
inverse relation between output and average fixed cost. With the increase in output average fixed
cost decreases and with the decrease in output the average fixed cost will increase. The shape of
average fixed cost curve becomes rectangular hyperbola with the increase in output.
It is calculated from the following formula:
AFC = TFC/O
O is volume of output AFC and TFC are average fixed cost and total fixed cost.
(2) Average Variable Cost (AVC):
The average variable cost is total variable cost divided by the volume of output. Average
variable cost falls with the increase in output, reaches at its minimum and then starts rising. By
the operation of law of increasing returns the AVC decreases, and by the operation of constant
returns leads to constancy in AVC and the law of diminishing returns leads to increase in AVC.
The shape of AVC is U-shaped because of the operation of the laws of returns during short
period.
The AVC is calculated by the formula given below:
AVC = TVC/O
AVC and TVC are average variable cost and total variable cost while O is the volume of output.
(3) Average Cost (AC):
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Average cost is also called average total cost (ATC) during short period because it is the
aggregate of AFC and AVC. AC can be calculated from total cost (TC) divided by the volume of
output or by aggregating AVC and AFC.
The following is the formula of calculating AC:
AC = TC/O
AC and TC are average cost and total cost while O is the volume of output.
Another formula for the calculation of AC is as given under:
AC = AFC + AVC
The AC curve decreases with the increase in output and remains constant up to a point
and thereafter it increases with the increase in output. Its shape is U-shaped because of the
operation of the laws of return during short period.
(4) Marginal Cost (MC):
It is an addition to total cost by producing an additional unit of output. It can be
calculated as the change in total cost divided by an additional unit change in the output.
The formula for its calculation is as given below:
MC = ΔTC/ΔO
MC is marginal cost, ΔTC is change in TC and ΔO is change in the volume of output.
For example, if the total cost (TC) of 5 units of a commodity is Rs. 550 and 6 units of a
commodity is Rs. 600, then the marginal cost of 6th units is Rs. 50.
It can be calculated on the basis of the above formula as given under:
MC = ΔTC/ΔO = 50/1 = 50 or Rs. 50
The MC cost changes with the change in AVC and it is independent of fixed cost. In the
beginning the MC falls, reaches at its minimum and thereafter continuously rises. MC is also U-
shaped. The MC curve cuts the AC and AVC curves at their minimum points.
The cost-output relation during short period can be seen from Table 2.
The table reveals the trends in total costs (TFC and TVC), average cost (AFC and TVC)
and MC. TFC remains constant and TVC goes on increasing and consequently TC is also
increasing. AFC is decreasing, but it is positive. AVC decreases, remains constant and thereafter
increases. AC also decreases, remains constant and shows an increasing trend. MC increases,
remains constant and thereafter shows an increasing trend.
There is a close relationship between AC and MC as given below:
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 AC and MC fall in the beginning but MC falls more rapidly than AC and MC is below
AC or AC is greater than MC (AC>MC).
 When AC rises, MC also rises but it rises more rapidly than the AC and MC is greater
than AC (MC>AC).
 When AC is minimum it is equal to AC. The MC curve cuts the AC curve at its minimum
point.
Cost-Output Relation during Long Run or Long Run Cost Curves:
Long period gives sufficient time to business managers to change even the scale of
production. All the factors of production are variable. All the costs are variable costs and there is
no fixed cost. The supply of goods can be adjusted to their demands because scale of production
and factors of production can be changed. In the long run we can study the long run average cost
curve and long run marginal cost curve.
I. Long Run Average Cost (LAC):
In the long run, all the factors of production are variable and the firm has a variety of
choices to select the size of the plants and the factors of production to be employed. Various
short run average cost curves represent the various sizes of the plants available to a firm. We can
get the long run average cost curve with the help of all the short run average cost curves. The
long run average cost curve envelopes all the short run average cost curves in it. It is also called
an ‘Envelope Curve’ or ‘Planning Curve’.
The long run average cost curve is also a flat U-shaped curve as shown in the following
diagram:
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The diagram shows long run cost on OY-axis and output on OX-axis. SAC, SAC1, SAC2,
SAC3 and SAC4 are short run average cost curves which represent the different size of plants.
LAC has been drawn by combining all those points of least cost of producing the corresponding
output. The least per unit cost of production is OQ, OQ1, OQ2, OQ3, OQ4, and OQ5 respectively.
II. Long Run Marginal Cost (LMC):
The long run marginal cost is an addition to the long run total cost when an additional
unit of a commodity is produced. It is calculated as the short run marginal cost is calculated.
Long run marginal cost curve is also U-shaped but the fall and rise in the marginal cost curve is
not sharp but it is gradual.
Conclusion:
In the short run SAC curve is U-shaped because the laws of return operate but in the long
run LAC is also U-shaped because the laws of return of scale operate, namely, law of increasing
returns to scale, law of constant returns to scale and the law of diminishing returns to scale.
As the level of output is expanded or scale of operation is increased by the large firm they
will enjoy economies of scale but if these firms produce beyond their installed capacity then they
might get diseconomies of scale. Economies of scale bring down the fall in unit cost and
diseconomies results into rise in it.