Business Economics · Ch 3 — Production and Cost Analysis
The Production Function — Short Run and Long Run
The Production Function — Short Run and Long Run
For an Odisha CHSE +2 Commerce Business Economics student, production analysis explains the physical side of a firm's activity — how inputs (factors of production) are turned into output — while cost analysis attaches money values to that same activity. The two are studied together because a firm's costs are simply its production relationships priced out. This chapter follows the standard, well-established treatment of the theory of production and cost that the Business Economics paper draws on; it uses ordinary microeconomic principles rather than any single prescribed text.
What a Production Function Is
A production function states the maximum quantity of output that can be produced from every possible combination of inputs, given the state of technology. Writing output as and the factor inputs as land, labour (), capital () and enterprise, the general form is
It is a purely technological (physical) relationship — it is measured in physical units (quintals of rice, metres of cloth, number of chairs), not in rupees, and it assumes the firm uses every input efficiently, so that the output shown is the most that can be got from those inputs.
Fixed Factors and Variable Factors
Inputs are classified by whether their quantity can be changed within the time period under study:
- A fixed factor cannot be changed within the period — its quantity stays the same however much output changes (for example, factory building, plant and heavy machinery in a short period).
- A variable factor can be changed within the period — more or less of it can be applied as output changes (for example, raw material, casual labour, power).
Short Run versus Long Run
This fixed/variable distinction defines the two time periods of production analysis. These are not fixed calendar lengths — they are defined by the adjustability of factors, so the same clock-time can be 'short run' for a shipyard and 'long run' for a roadside tea stall.
| Feature | Short Run | Long Run |
|---|---|---|
| Factors | At least one factor is FIXED | ALL factors are variable |
| How output is raised | Only by using more of the variable factor with the given fixed factor | By changing the scale of ALL factors together |
| Governing law | Law of Variable Proportions (returns to a factor) | Returns to Scale |
| Factor proportions | Change (variable rises against a fixed factor) | Can be held constant (all rise together) |
Section 2 studies the short run through the Law of Variable Proportions; Section 3 studies the long run through Returns to Scale.
A technological relationship showing the maximum output obtainable from each combination of inputs, given the state of technology. It is stated in physical, not money, units.
An input whose quantity cannot be changed within the period under study (e.g. plant and machinery in the short run).
An input whose quantity can be changed within the period under study (e.g. raw material, casual labour).
The short run is a period in which at least one factor is fixed; the long run is a period long enough for all factors to become variable. They are defined by factor adjustability, not by calendar length.