Theory of Production and Cost Notes

Theory of Production

• Production: Transformation of resources (inputs) into commodities (outputs).

• Inputs: Economic resources used in the production of goods and services.

  • Fixed Input: Quantity cannot be varied during the period.

  • Variable Input: Quantity can be changed during the period.

• Outputs: Outcomes of the production process.

Period of Production

• Short-run: Period where some inputs (fixed inputs) cannot be changed.

• Long-run: Period where all factors of production can be varied.

• Distinction between short-run and long-run is based on input adjustments, not a specific calendar period.

Production Function with One Variable Input

• Table 4.1: Hypothetical Schedule of TP, MP, and AP
  L: Variable Input, TP: Total Product, MP: Marginal Product, AP: Average Product

• Figure 4.1: TP, MP, and AP Curves Showing Three Stages of Production

Relationship Between Total Product, Marginal Product, and Average Product

• Relationship between MP and AP:

  • When MP > AP, AP is rising.

  • When $MP = AP$, AP is maximum.

  • When MP < AP, AP is falling.

• Relationship between TP and MP:

  • When TP increases at an increasing rate, MP increases.

  • When TP increases at a diminishing rate, MP declines.

  • When TP reaches its maximum, MP becomes zero.

  • When TP begins to decline, MP becomes negative.

Stages of Production

• Table 4.2: Stages of Production

The Law of Diminishing Marginal Returns

• As more of one factor input is employed (other inputs held constant), a point will be reached where additional quantities of the varying input will yield diminishing marginal contributions to total product.

• Table 4.3:

• Operates only if technology does not change.

• Starts to operate after the MP curve reaches its maximum.

• Universal because the tendency of diminishing returns is all pervading and so it applies sooner or later in every field of production.

Production Function with Two Variable Inputs

• A firm produces 20 units of output using two variable inputs, X and Y (labor and capital).

• Isoquant Schedule: Tabular representation of various combinations of two variable inputs which give the same level of output.

• Table 4.4: Factor Combinations to Produce a Given Level of Output (Isoquant Schedule)

Isoquant

• Also known as iso-product curve, equal-product curve, or production indifference curve.

• A curve showing different combinations of two inputs that produce a given level of output.

• Figure 4.3: Isoquant

Isoquant (or Equal-Product) Map

• When the whole array of isoquants is represented on a graph, it is called an Isoquant Map

• A higher isoquant represents a higher level of output.

Properties of Isoquants

• Isoquant is downward-sloping to the right.

• No two isoquants intersect or touch each other.

• Isoquants are convex to the origin.

• Convexity of an isoquant is the result of the principle of diminishing marginal rate of technical substitution (MRTS) of one factor in place of the other.

• A ridge line is the locus of points of isoquants where marginal product of input is zero.

• Outside the ridge lines, the marginal products of inputs are negative, i.e., more of both inputs are required to produce a given level of output.

• The economic region of production is the region bounded by the ridge lines.

Marginal Rate of Technical Substitution (MRTS)

• MRTS is the rate at which factors can be substituted at the margin without altering the level of output.

• $MRTS_{of labour for capital} = \frac{\Delta K}{\Delta L}$

• $\Delta K$ represents change in units of capital and $\Delta L$ represents change in units of labour.

Returns to Scale (Production with all Variable Inputs)

• When all factor inputs can be varied, keeping their proportion constant, it is called a change in the scale of operations.

• The behavior of output subsequent to such changes in the quantities of all factor inputs in the same proportion (i.e., keeping the factor proportions unaltered) is known as ‘returns to scale.’

• IRS (Increasing Returns to Scale): Output increases by a greater proportion than the proportion of increase in all the inputs.

• CRS (Constant Returns to Scale): Output increases by the same proportion as of inputs increase.

• DRS (Decreasing Returns to Scale): Output increases by a smaller proportion than the proportion of increase in input increases.

• Figure 4.8: Returns to Scale

Reasons for Increasing and Decreasing Returns

• Reasons for Increasing Returns:

  • Greater division of labor and specialization which increases productivity.

  • Use of more productive specialized machinery

• Reasons for Decreasing Returns:

  • Difficulty in management and coordination when scale of operation becomes bigger and bigger

Effect of Technological Change on Production Function

• Figure 4.9: Technological Progress Shifts Production Function Upward

Theory of Cost

• Explicit Costs: Actual money expenses directly incurred for purchasing the resources.

  • Examples: Payments for raw materials and power; wages to the hired workers; rent for the factory building; interest on borrowed money etc.

• Implicit Costs: Imputed costs of the factors of production owned by the producer himself/herself

  • For instance, rent of his/her own land, interest on his/her own capital, and salary for his/her own services as manager, etc.

• $Economic Cost = Explicit Cost + Implicit Cost$

Time Element and Cost

• Short run: A period of time during which production can be varied only by changing the quantities of variable factors and not of fixed factors.

  • In short-run production, we have two types of costs - fixed costs and variable costs.

• Long run: A period which is long enough for the inputs of all factors of production to be varied.

  • In the long run, all costs are variable costs.

• Table 4.7: Total Fixed Cost, Total Variable Cost, and Total Cost

• Figure 4.10: Behavior of Short-Run Total Costs

Behaviour of average cost

• Table 4.8: Behaviour of average cost

• Figure 4.11: Behaviour of Average Costs

Why is the AVC Curve U-shaped?

• The U-shape of the AVC curve follows directly from the law of variable proportions.

• The average variable cost falls up to the optimum capacity level of output due to increasing returns, and it increases thereafter due to diminishing returns to the variable factor.

Marginal Cost in the Short Run

• Marginal cost has nothing to do with fixed cost

• The U-shape of the MC curve is because of the law of variable proportions

Relation Between Average and Marginal Cost

• When MC is less than the AC, the average cost falls with increases in output.

• When the MC is greater than the AC, the average cost is rising.

• When MC is equal to AC, the average cost is minimum.

Relationship Between Production and Cost

• Table 4.9: Production and Cost in the Short Run

• Figure 4.14: Cost and Production Short Run

• Figure 4.15: Relationship Between Production and Cost

• TVC and TP of labour are inversely related.

• AVC and AP of labour are inversely related.

• MC and MP of labour are inversely related.

• Assuming that labour is the variable input and that the wage rate (W) is given, we give below an algebraic proof for the relationship between MC and MP.

  • $\Delta TVC = \Delta L \times W$

  • $Since \quad MC={\Delta TVC \over \Delta Q}$

  • $MC = {\Delta L \times W \over \Delta Q} = {W \over {\Delta Q / \Delta L}} = {W \over MP_L}$

  • $Where, \quad MP_L = {\Delta Q / \Delta L}$