PRODUCTION AND COSTS
Production Function
Production function is the relationship between physical input such as labour, capital and physical
output of a good. It is expressed in the following form:
q = f (x1, x2)
It means by using x1 amount of factor 1 and x2 amount of factor 2, you will be able to produce q amount of good.
Fixed and variable factors
Factors of production are classified as fixed factors and variable factors. Fixed factors are those factors of the
application which does not change with a change in output. Variable factors are those factors of the application
which varies with a change in output.
Concept of period in production
The time period in which a firm makes changes in its production by changing only its variable factors but not
its fixed factors is termed as short run. The time period in which a firm can change all the factors of production
is termed as long run.
Concepts Related to Production
• Total Product (TP) is the sum total of each unit of the variable factor used in the process production. Average
Product (AP) is the physical output per unit of the variable factor used in the process production.
• Marginal Product (MP) is the additional output attributed to an additional unit of the variable factor,
while other factors remaining constant.
Relationship between MP and TP
Here the table and the diagram given below shows the relationship between MP and TP:
• Till the third unit of variable factor, MP increases from 4 to 28 units and the TP increases for every
additional unit. So long as MP is increasing, TP is increasing at an increasing rate.
• But when MP starts diminishing at the 4th unit of variable factor input, the TP increases only at a decreasing rate
• When 7th unit was applied, MP is zero, there is no addition to TP and TP is at maximum level.
• When MP is negative, TP starts declining at the 8th unit. TP diminishes from 84 to 80 and the MP is negative 4 (-4).
Relationship between AP and MP
Here the table and the diagram given below shows the following relationship between AP and MP:
• AP increases as long as MP is greater than AP. Till the point p, AP is at maximum.
• AP decreases when MP < AP. Beyond the point p, AP is at its top.
• AP is at its maximum when AP = MP.
• MP curve cuts AP from above at its maximum. MP may be zero or negative, but AP remains positive.
Returns to a Factor: Law of Variable Proportion
Law of variable proportion states that as more and more of the variable factor input is combined with the fixed
factor input, eventually a point will be reached where the marginal product of the variable factor input starts declining.
Returns to Scale
If all factors are increased in the same proportion, the scale of production increases. It is a situation, where all factors
are variable factors and are possible only in the long run. Returns to scale relates to the behaviour of total output as
all factors are changed in same proportion. Three aspects of returns to scale are.
• Increasing returns to scale happens when increase in output is proportionately greater than the increase in output
in factor input, while the factor ratio remains constant.
• Constant returns to scale happens when increase in output is proportionately equal to increase in factor input,
while the factor ratio remains constant.
• Diminishing returns to scale happens when increase in output is proportionately lesser than the increase in
factor input, while the factor ratio remaining constant.
Cost Function
A cost function shows the functional relationship between cost and output. It gives the least cost combinations
of inputs corresponding to various levels of output.
Short run cost
• Short run costs: are the cost during which some factors are fixed in supplies such as plant and
machinery. These are divided into
• Fixed costs: Fixed costs are the sum total of expenditure incurred by the producer on the purchase or
hiring of fixed factors of production. It does not change with change in quantity of output. It remains
the same whether the output is zero or maximum.
• Variable costs: Variable costs are the expenditure incurred by the producer on the use of variable factors
of production. It changes with change in quantity of output.Its cost is zero when output is zero.
• Average costs: Cost per unit of output produced is called an average cost i.e. AC=TC/Q. It is the sum total of
average fixed cost (AFC) and average variable cost (AVC).
• Average fixed cost is the fixed cost per unit of output. AFC curve slopes downward to the right. It shows that AFC
decreases as output increases. It is a rectangular hyperbola curve. It means that the product of AFC and output is
equal to TFC which remains constant at all levels of output.
• TFC = AFC * Q
• Average variable cost: is the variable cost per unit of output. AVC curve is U-shaped. This is in accordance with the
law of variable proportions. It falls so long as returns to a factor are increasing. It rises when returns to a factor are
decreasing.
• Marginal cost: Marginal cost (MC) is the change in total cost when an additional unit of output is produced. It is also
U-shaped curve in accordance with the law of variable proportions. Falling MC is in accordance with rising marginal
product (MP), when there are increasing returns to a factor. Rising MC is in accordance with falling MP when there are
diminishing returns to a factor.
Shapes of the short run cost curves
• MC curve should be shown cutting both AC and AVC at their lowest points.
• When AC falls, MC falls faster than AC. Then the MC remains below AC curve.
• When AC rises, MC rises faster than AC. Then the MC curve is above AC curve.
• As MC falls faster than AC, it reaches its lowest point earlier than AC. Then the MC starts increasing even when AC is declining.
• MC must cut AC from its lowest point.
Long run costs
In the long run, all the inputs are variable. Hence, there is no distinction between variable costs and fixed costs. All
costs are variable cost in the long run. Shape of long run total cost (LTC) remains the same as short run total costs.
Initially, LTC curve increases at a diminishing rate then it tends to increase at a constant rate and finally it rises at
an increasing rate. This curve starts from the origin because all the costs are variable cost which varies with output.
Therefore, when output is zero, the variable costs are also zero.
Long run average cost is defined as cost per unit of output. Long run marginal cost is the change in total cost per
unit of change in output. The sum of all marginal costs up to certain output level gives the total cost at that particular
level. Like short run average and marginal cost curves, long run average and marginal cost curves are also U-shaped.