Theory of Production | Sahithyan's Notes

A firm is an organization that converts inputs such as labour, materials, and capital into outputs.

Production is the transformation of inputs or resources into goods and services.

The main inputs include:

Capital (K)
Labour (L)
Materials (M)

Production Function

A production function shows the relationship between the quantities of inputs used and the maximum output that can be produced efficiently.

The general production function is:

Q = f(K,L,M)

Where:

Q = Output
K = Capital
L = Labour
M = Materials

Fixed and Variable Inputs

Fixed Input

An input whose quantity cannot be changed practically in the short run.

Variable Input

An input whose quantity can be changed readily by the firm.

Short Run

The short run is a period during which at least one input is fixed.

For example, capital may be fixed while labour is variable.

Therefore:

Q = f(L,K)

When capital is fixed:

Q = f(L)

Q = f(L) is the production function. It shows the relationship between a variable input and the maximum output that can be produced.

Long Run

The long run is a period during which all inputs are variable.

The distinction between short run and long run depends on whether inputs can be adjusted, not simply on the number of days, months, or years.

Total Product

Total Product (TP) is the total amount of output produced using a given amount of the variable input.

Average Product

Average Product (AP) is total output divided by the amount of variable input used.

AP_L = \frac{TP}{L}

Marginal Product

Marginal Product (MP) is the change in total output resulting from using one additional unit of the variable input while other factors remain constant.

MP_L = \frac{\Delta TP}{\Delta L}

Relationship Between TP, AP and MP

When MP > 0, TP increases.
When MP = 0, TP reaches its maximum.
When MP < 0, TP decreases.
When MP > AP, AP increases.
When MP < AP, AP decreases.
When MP = AP, AP is at its maximum.

TP = Total Product, AP = Average Product, and MP = Marginal Product. The diagram shows their relationship as labour increases.