Unit 2: Cost and Production Analysis - Subjective Questions

Theory of production studies how a firm transforms inputs into outputs using a given technology. It explains the relationship between the quantities of factors of production used and the maximum quantity of output that can be produced.

The main inputs are:

• Land: Natural resources used in production.
• Labour: Human effort, both physical and mental.
• Capital: Machines, tools, buildings, and equipment.
• Entrepreneurship: The ability to organize resources and bear risks.

A production function expresses this relationship as:

where is output, is labour, is capital, is land or natural resources, and is entrepreneurship. In a short period, some inputs are fixed, while in a long period all inputs can be varied. The production function assumes that technology remains constant.

A production function shows the maximum output that can be produced from different combinations of inputs with a given state of technology. It can be represented as:

where is output, is labour, and is capital.

Assumptions of a production function:

• Technology remains unchanged during the analysis.
• Inputs are divisible and can be combined in different proportions.
• The firm uses inputs efficiently.
• The relationship between inputs and output is technically determined.
• The quantity and quality of inputs are known.

Importance:

• It helps determine the most efficient input combination.
• It explains the effects of changing one or more inputs.
• It provides the basis for studying productivity and costs.
• It helps firms make production and resource-allocation decisions.
• It forms the foundation for analyzing the laws of returns and economies of scale.

The short-period production function and the long-period production function differ mainly in the flexibility of inputs.

Thus, short-period analysis studies changes in output caused by varying one input, whereas long-period analysis studies changes resulting from changing all inputs in the same or different proportions.

The law of variable proportions states that when additional units of a variable factor are combined with fixed quantities of other factors, total product initially increases at an increasing rate, then at a diminishing rate, and eventually decreases, assuming technology remains constant.

The law has three stages:

• Stage I: Increasing returns: Total product increases at an increasing rate initially and then at a decreasing rate. Marginal product rises first and later begins to fall, while average product continues to rise until its maximum point.
• Stage II: Diminishing returns: Total product continues to increase but at a diminishing rate. Marginal product is positive but declining, and average product also declines. This is the rational stage of production.
• Stage III: Negative returns: Total product decreases because excessive use of the variable factor causes overcrowding and inefficiency. Marginal product becomes negative.

The law is relevant in the short run because at least one factor remains fixed.

The three stages can be explained through the behavior of total product (), average product (), and marginal product ():

Stage I: Increasing returns

• increases at an increasing rate initially and later at a decreasing rate.
• rises initially, reaches its maximum, and then begins to fall.
• rises throughout this stage.
• The stage ends when reaches its maximum and .

Stage II: Diminishing returns

• continues to rise but at a diminishing rate.
• declines but remains positive.
• declines because .
• The stage ends when reaches its maximum and .

Stage III: Negative returns

• begins to decline.
• becomes negative.
• The excessive variable input reduces efficiency because fixed resources become overcrowded.

A rational producer operates in Stage II, since Stage I leaves some fixed resources underutilized and Stage III results in negative marginal productivity.

Total product () is the total quantity of output produced by all units of a variable input combined with fixed inputs.

Average product () is output per unit of the variable input:

where represents the quantity of labour.

Marginal product () is the addition to total product resulting from the use of one more unit of the variable input:

Their relationships are:

• When , rises.
• When , falls.
• When , is at its maximum.
• When , is at its maximum.
• When , declines.

The curve intersects the curve at the maximum point of the curve. These relationships help explain the different stages of production.

The three phases of the law of variable proportions arise because the variable factor interacts differently with fixed factors at different levels of employment.

Causes of increasing returns

• Better utilization of fixed factors.
• Greater specialization and division of labour.
• Increased efficiency in the use of machinery.
• Economies resulting from cooperation among workers.

Causes of diminishing returns

• The fixed factor becomes relatively scarce.
• Additional workers have less capital and space to work with.
• Opportunities for specialization are gradually exhausted.
• Coordination and supervision become more difficult.

Causes of negative returns

• Excessive use of the variable factor creates overcrowding.
• Workers interfere with one another.
• Fixed equipment is overused.
• Supervision and coordination become highly inefficient.

Therefore, increasing returns result from better utilization, diminishing returns from the scarcity of fixed factors, and negative returns from excessive overcrowding.

The theory of cost examines the relationship between the quantity of output produced and the expenditure incurred by a firm. It helps a producer determine the least-cost method of production and make pricing and output decisions.

Important cost concepts include:

• Fixed cost: Cost that does not change with output in the short run, such as rent and insurance.
• Variable cost: Cost that changes with output, such as raw materials and wages of casual labour.
• Total cost: The sum of fixed and variable costs:
  
• Average cost: Cost per unit of output:
  
• Average fixed cost: Fixed cost per unit:
  
• Average variable cost: Variable cost per unit:
  
• Marginal cost: Addition to total cost caused by producing one more unit:
  

Cost analysis is essential for determining profit, output, and the efficient scale of production.

The different cost concepts are distinguished as follows:

• Explicit cost: Actual monetary payments made by a firm to purchase or hire resources. Examples include wages, rent, electricity bills, and payments for raw materials.
• Implicit cost: The opportunity cost of using resources owned by the entrepreneur. Examples include the entrepreneur's own labour, capital, and building.
• Accounting cost: The total of explicit or recorded monetary expenses shown in the firm's accounts.
• Economic cost: The sum of explicit and implicit costs:
  

Accounting cost is useful for financial reporting, while economic cost is more useful for decision-making because it includes opportunity costs. Economic profit is calculated as:

A firm may earn accounting profit while earning zero or negative economic profit if the value of the owner's resources is high.

The relationship among total cost (), average cost (), and marginal cost () is important in understanding firm behavior.

• Total cost:
  
  It generally increases as output increases.
• Average cost:
  
  It usually has a U-shaped curve because it first falls and later rises.
• Marginal cost:
  
  It represents the additional cost of producing one more unit.

Their main relationships are:

• When , falls.
• When , rises.
• When , is at its minimum.
• The curve cuts the curve at its minimum point.
• Since fixed cost does not change with output, the change in total cost is caused by variable cost; therefore, is also the change in total variable cost divided by the change in output.

In the short run, some factors are fixed and others are variable. The main short-run cost curves are:

Total fixed cost curve

Total fixed cost () remains constant at all output levels. It is represented by a horizontal line parallel to the output axis.

Total variable cost curve

Total variable cost () changes with output. It generally increases slowly at first and then more rapidly because of the law of variable proportions.

Total cost curve

Total cost is the sum of fixed and variable costs:

The curve has the same shape as the curve but starts above the origin by the amount of fixed cost.

Average fixed cost curve

It continuously declines as output rises and is rectangular hyperbola-shaped.

Average variable cost and average cost curves

Both and are generally U-shaped. They initially fall due to increasing productivity and later rise due to diminishing returns.

Marginal cost curve

The curve is generally U-shaped and cuts both the and curves at their minimum points.

The short-run average cost () curve is generally U-shaped because of the behavior of average fixed cost and average variable cost.

• At low levels of output, average fixed cost falls rapidly because the fixed cost is distributed over more units.
• Average variable cost also falls initially because of specialization, better utilization of fixed resources, and increasing productivity.
• As output expands, the decline in and causes to fall.
• After a certain output level, the fixed factors become increasingly scarce relative to the variable factors.
• The law of variable proportions causes productivity to decline, so rises.
• Eventually, the rise in becomes greater than the fall in , causing to rise.

Thus:

The falling portion reflects economies in resource use, the minimum point represents the most efficient short-run output, and the rising portion reflects diminishing returns.

The long-run production function shows the maximum output that can be produced when all factors of production are variable. It examines changes in output when all inputs are increased in the same proportion.

If inputs are multiplied by a factor , output may change as follows:

Increasing returns to scale

Output increases by more than the proportionate increase in inputs. If all inputs are doubled and output more than doubles, increasing returns exist:

Constant returns to scale

Output increases in exactly the same proportion as inputs:

Decreasing returns to scale

Output increases by less than the proportionate increase in inputs:

Returns to scale are a long-run concept because the firm has sufficient time to change the size of its plant and all other inputs.

The law of variable proportions and returns to scale both explain changes in output, but they differ in several ways.

The law of variable proportions is concerned with factor proportions, whereas returns to scale are concerned with the overall size or scale of operation.

The long-run average cost curve () shows the minimum average cost of producing each level of output when all factors are variable. It is obtained by selecting the least-cost plant size for every possible output level.

The curve is often called the planning curve or envelope curve because it envelopes a series of short-run average cost curves representing different plant sizes.

The long-run marginal cost curve () shows the addition to long-run total cost resulting from producing one more unit of output:

Their relationship is:

• When , falls.
• When , rises.
• When , is at its minimum.

The shape of the curve reflects economies and diseconomies of scale. The curve intersects the curve at the minimum point of the latter.

Economies of scale are reductions in long-run average cost resulting from an increase in the scale of production.

Internal economies of scale

These arise within the firm as a result of expanding its own operations. Major types include:

• Technical economies: Use of specialized machinery and large-scale production methods.
• Managerial economies: Employment of specialized managers and departmental supervision.
• Purchasing economies: Bulk buying of raw materials at lower prices.
• Financial economies: Easier access to credit at favorable rates.
• Marketing economies: Lower advertising and distribution costs per unit.
• Risk-bearing economies: Diversification of products and markets.

External economies of scale

These arise outside the individual firm but within the industry or region. Examples include:

• Development of specialized suppliers.
• Better transport and communication facilities.
• Availability of skilled labour.
• Research and training institutions.
• Knowledge spillovers among firms.

Internal economies reduce the firm's own cost, while external economies reduce costs because of the growth of the industry or business environment.

Diseconomies of scale occur when a proportionate increase in all inputs leads to a less than proportionate increase in output, causing long-run average cost to rise.

Internal diseconomies

These arise within a firm when it becomes excessively large. Causes include:

• Difficulties in communication between departments.
• Delays in decision-making.
• Problems of coordination and supervision.
• Bureaucratic administration.
• Lower employee morale and reduced motivation.
• Inefficient control over a very large organization.

External diseconomies

These arise when the expansion of an industry increases costs for all firms in the area. Causes include:

• Rising prices of scarce raw materials.
• Shortage of skilled labour and higher wage rates.
• Traffic congestion and increased transport costs.
• Higher land rents.
• Pollution and pressure on infrastructure.

Diseconomies of scale explain the rising portion of the long-run average cost curve. They indicate that a firm or industry has expanded beyond its most efficient scale.

Short-run and long-run cost curves differ because of the number of inputs that can be changed.

The long-run cost curves are therefore more flexible because all inputs can be altered.

Average variable cost is defined as:

Marginal cost is:

Suppose output increases by one unit. The effect on depends on whether the cost of the additional unit, represented by , is lower than, equal to, or higher than the existing .

• If , the additional unit costs less than the average cost of existing units, so falls.
• If , the additional unit costs more than the existing average, so rises.
• If , the additional unit has exactly the average cost, so is at its minimum.

This can also be shown through differentiation. If:

then the minimum value of occurs when:

which implies that:

Therefore, the marginal cost curve intersects the average variable cost curve at the minimum point of the curve.

The optimum scale of production is the level of output at which a firm produces at the minimum possible long-run average cost. It is also called the minimum efficient scale.

The optimum scale occurs at the minimum point of the curve:

At this point:

• The firm fully exploits economies of scale.
• Long-run average cost is at its lowest.
• The firm has selected the most efficient plant size for the output level.
• Resources are used in the most economical combination.

Before the optimum scale, falls because of economies of scale. At the optimum scale, the firm enjoys the lowest unit cost. Beyond the optimum scale, may rise because of diseconomies of scale.

The minimum efficient scale is important for determining the size of firms, the degree of competition, and whether an industry is likely to contain many small firms or a few large firms.