Difficulty: Intermediate | Prerequisites: Consumer Theory notes (indifference curves, MRS)
Production theory describes how firms turn inputs (labour, capital) into output, and how output changes as inputs change. The short run fixes at least one input; the long run lets everything vary. Isoquants and the marginal rate of technical substitution (MRTS) are the production-side equivalents of indifference curves and MRS from consumer theory.
Production function
A function indicating the maximum output per unit of time a firm can produce for every combination of inputs with a given technology. It gives the maximum level of output generated from given levels of input.
Short run
A time period in which at least one input is fixed. All inputs that are variable in the long run (plant size, labour, capital and equipment) may be fixed here.
Long run
The amount of time needed to make all production inputs variable.
Average product (AP)
Output per unit of a particular input. AP of labour = q / L. Graphically, it is the slope of a line from the origin to the corresponding point on the total product curve.
Marginal product (MP)
The additional output produced when an input is increased by one unit, holding all other inputs constant. MP of labour = Change in q / Change in L. It is the slope of the total product curve at that point.
Law of diminishing (marginal) returns
As the use of an input increases with other inputs held fixed, the resulting additions to output will eventually decrease. This is about marginal returns, not total or average.
Labour productivity
The average product of labour for an entire industry or the economy as a whole.
Stock of capital
The total amount of capital available for use in production.
Isoquant
A curve showing all possible combinations of inputs that yield the same total output. Isoquants do not cross. They look like indifference curves and become steeper when you add to one factor and hold the other constant.
Marginal Rate of Technical Substitution (MRTS)
The amount by which one input can be reduced when one extra unit of another input is used, keeping output constant. MRTS = -(Change in K / Change in L) = MPl / MPk.
Think of it as the production-side equivalent of MRS: how easily a firm can swap one input for another without losing output.
Returns to scale
The rate at which output increases as all inputs are increased proportionately.
Increasing returns to scale: output more than doubles when inputs double.
Constant returns to scale: output exactly doubles.
Decreasing returns to scale: output less than doubles.
A firm's production decisions depend on three things: production technology, cost constraints and input choices. Firms exist because of coordination and reduced transaction costs.
The short run is the period in which at least one input is fixed. The long run is the period in which all inputs can be varied. Returns to scale is a long-run concept: it does not make sense to consider returns to scale in the short run because we cannot change all the production inputs.
When MP > AP, the average product is rising.
When MP < AP, the average product is falling.
MP cuts AP from above at AP's maximum point.
Worked example (car detailing): Three employees produce an average of 4 cars per person per hour (total = 12 cars). Five employees produce an average of 3 cars per person per hour (total = 15 cars). Marginal product of adding 2 workers = (15 - 12) / (5 - 3) = 1.5 cars per worker.
Worked example (coffee house): q = 5KL. Average product of labour = q / L = 5KL / L = 5K.
An isoquant shows all combinations of inputs that produce the same output. The slope of the isoquant (with K on the vertical axis and L on the horizontal) is the rate at which the firm can replace capital with labour without changing output.
MRTS = ratio of the marginal products of the inputs = MPl / MPk.
A point on the isoquant with a small MRTS (in absolute value) is associated with high labour use and low capital use.
Worked example: MRTS = K/(4L), L = 100, K = 400. If capital falls by 1 machine hour, the labour needed to maintain output = MRTS at that point = 400/(4 * 100) = 1. One additional hour of labour is needed.
The numerical labels on indifference curves are meaningful only in an ordinal way (Statement I is true). The numerical labels on isoquants are meaningful in a cardinal way, because they represent actual output levels (Statement II is false).
Increasing returns to scale: C = L^0.5 * M^0.75. The exponents sum to 1.25 > 1, so doubling all inputs more than doubles output.
Constant returns to scale: q = K + L. Double both inputs, output doubles.
Decreasing returns to scale: exponents sum to less than 1.
Average product of labour: APl = q / L
Marginal product of labour: MPl = Change in q / Change in L
MRTS (K on vertical, L on horizontal): MRTS = -(Change in K / Change in L) = MPl / MPk
Returns to scale test: Multiply all inputs by t. If output multiplies by more than t, increasing returns. By exactly t, constant returns. By less than t, decreasing returns.
Diminishing returns explain why a restaurant cannot keep adding chefs to a single kitchen and expect proportional output: eventually they get in each other's way. Returns to scale matter for business strategy: industries with increasing returns to scale (software, chip fabrication) tend toward fewer, larger firms.
Students confuse the law of diminishing returns (a short-run concept, one input varies) with decreasing returns to scale (a long-run concept, all inputs vary proportionally). They are different ideas.
A common error is thinking that when AP is falling, MP must also be falling. MP can be positive and rising while AP falls, so long as MP is below AP.
Students often try to evaluate returns to scale in the short run. This does not apply because at least one input is fixed.
Isoquant labels are cardinal (they represent real output), unlike indifference curve labels which are ordinal. Mixing these up is a frequent exam mistake.
⚠️ The MP-AP relationship is tested often: know that MP crosses AP at AP's maximum, from above.
⚠️ Expect a question asking whether it makes sense to consider returns to scale in the short run (answer: no).
⚠️ Identifying returns to scale from a production function requires summing the exponents (for Cobb-Douglas) or applying the doubling test.
⚠️ MRTS calculation questions give you K, L and the MRTS formula, then ask how much additional labour is needed if capital falls by one unit.
True or false: The law of diminishing returns applies when all inputs are increased proportionally. (False, it applies when only one input increases and others are held fixed.)
Fill in the blank: AP is at its maximum when MP = ______. (AP)
True or false: q = K + L exhibits constant returns to scale. (True.)
Fill in the blank: MRTS equals the ratio of the ______ of the inputs. (marginal products)
True or false: Returns to scale is a meaningful concept in the short run. (False.)
Q: Three employees produce AP = 4 cars/person/hour, five employees produce AP = 3 cars/person/hour. What is the MP of labour from 3 to 5 employees?
A: Total at 3 = 12, total at 5 = 15. MP = (15 - 12) / (5 - 3) = 1.5 cars.
Q: Joe's coffee house has q = 5KL. What is the average product of labour?
A: AP = q / L = 5KL / L = 5K.
Q: MRTS = K/(4L), L = 100, K = 400. How much additional labour is needed if capital falls by one machine hour?
A: MRTS at that point = 400 / (4 * 100) = 1. One hour of additional labour is needed.
Q: C = L^0.5 * M^0.75. What returns to scale does this exhibit?
A: Exponents sum to 1.25 > 1, so increasing returns to scale for all output levels.
Q: Does it make sense to consider returns to scale in the short run?
A: No, because we cannot change all the production inputs in the short run.
Q: Statement I says indifference curve labels are ordinal. Statement II says isoquant labels are ordinal. Which is true?
A: I is true, II is false. Isoquant labels represent actual output quantities (cardinal).
Production theory mirrors consumer theory: isoquants correspond to indifference curves, and MRTS corresponds to MRS. The cost theory notes (next document) build directly on this by adding input prices through isocost lines and finding the cost-minimising input combination. Returns to scale determine the shape of the long-run average cost curve.
production function, short run, long run, marginal product, average product, law of diminishing returns, diminishing marginal returns, isoquant, MRTS, marginal rate of technical substitution, returns to scale, increasing returns, constant returns, decreasing returns, labour productivity, Cobb-Douglas, intermediate microeconomics, FIU