Production: types of utility, production function and law of variable proportions

1. Meaning of production

Man cannot create matter; he can only change its form, place or time of availability so that it satisfies wants better. In economics production means the creation of utility, or the creation of goods and services that have exchange value. A farmer, a carpenter, a transporter, a shopkeeper, a teacher and a lawyer are all producers.

2. Types of production (by the utility created)

• Form utility: changing the shape or form of raw material. Cotton into cloth, timber into furniture, iron ore into steel. Most manufacturing creates form utility.
• Place utility: moving goods from where they are less useful to where they are more useful. Transporting Kolar mangoes to Delhi, or coal from the pit-head to a power plant. Transport and trade create place utility.
• Time utility: storing goods from a time of plenty to a time of scarcity. Holding rice from harvest to the lean season in a warehouse or cold storage. Warehousing and banking (which makes present savings available later) create time utility.
• Possession (ownership) utility: transferring a good to the person who values it more. A dealer selling a car to a buyer.
• Service utility: direct services of doctors, advocates, teachers.
• Knowledge utility: advertising and salesmanship telling consumers about a product.

3. The production function

A production function is the technical relation between physical inputs and the physical output of a firm, for a given state of technology. Stigler: the relationship between inputs of productive services per unit of time and outputs of product per unit of time.

Q = f(L, K, N, E, T), where Q is output, L labour, K capital, N land, E enterprise and T technology.

• Short-run production function: at least one input (plant, capital) is fixed; output is changed by varying the other. This gives the law of variable proportions. Q = f(L, K̄).
• Long-run production function: all inputs can be varied, and in the same proportion. This gives the laws of returns to scale (topic 4 of this unit).
• Cobb-Douglas production function: Q = A L^a K^1−a, tested by C.W. Cobb and P.H. Douglas (1928) on American manufacturing data. Because the exponents add up to one, it shows constant returns to scale.

Principles of Economics covers this topic in its note on the production function and law of variable proportions, and the factors themselves in factors of production.

4. Total, average and marginal product

• Total product (TP): total output from a given quantity of the variable factor.
• Average product (AP) = TP / L.
• Marginal product (MP): addition to TP from one more unit of the variable factor. MP_n = TP_n − TP_n−1.

5. Law of variable proportions

Statement: as more and more units of a variable factor are applied to a given quantity of fixed factors, total product first increases at an increasing rate, then at a diminishing rate, and finally falls. Put in terms of marginal product: MP first rises, then falls, and eventually becomes negative. The law describes what happens when the proportion in which factors are combined changes, hence its name.

Assumptions: technology is constant; one factor is fixed and the other variable; units of the variable factor are homogeneous; factors can be combined in varying proportions; the analysis is short-run.

One acre of land (fixed) with workers added (variable), output in quintals:

6. The three stages

1. Stage I: increasing returns. From the origin to the point where AP is at its maximum and equals MP (3 workers). MP rises at first (to 14) and stays above AP, pulling AP up. Reasons: the fixed factor is under-used at first; adding labour allows better use of it, and division of labour and specialisation become possible. The fixed factor is indivisible, so it is used more fully as labour is added.
2. Stage II: diminishing returns. From the maximum of AP to the point where MP is zero and TP is at its maximum (7 workers). Both AP and MP fall, MP below AP, but TP still rises. Reason: the fixed factor is now scarce relative to the variable factor; each worker has less land to work with. Factors are imperfect substitutes for each other.
3. Stage III: negative returns. Beyond 7 workers MP is negative and TP falls. Too many workers crowd the land and get in each other’s way.

Describe the diagram: workers on the horizontal axis, output on the vertical. TP rises steeply, then gently, peaks at 7 and turns down. AP and MP are inverted U-shapes; MP rises and falls faster than AP, cuts AP at AP’s highest point (end of Stage I) and crosses the horizontal axis where TP peaks (end of Stage II).

7. Importance

The law explains why costs rise in the short run (rising MP means falling marginal cost, and diminishing MP means rising marginal cost), and so gives the U-shape of the short-run cost curves in the next note. Applied to agriculture it explains why intensive cultivation of a fixed area eventually yields diminishing returns, which is the basis of Ricardo’s theory of rent and of Malthus’ theory of population. The old “law of diminishing returns” of the classical economists is Stage II of this law.

How this is examined

February 2025 (100-mark) set “Briefly explain the law of variable proportions” for 16 marks; January 2026 (80-mark) set “Production function” as a 6-mark note. For the long answer: meaning of production function, statement, assumptions, the schedule, the three stages with reasons, the diagram described, and the rational-stage point. For the short note: definition, the general form, short-run and long-run forms, and the Cobb-Douglas function in a line. A note on form, place and time utility is the natural question on syllabus item (i).