Source: Seminar Practice Questions, Chapters 5 & 6 | Microeconomic Theory, Texas A&M University
Tags: short run, long run, fixed inputs, variable inputs, marginal product, average product, isoquant, returns to scale, technical change, production function, MRTS
Chapter 6 introduces the theory of production. The short run has at least one fixed input; the long run allows all inputs to vary. Key relationships include the connection between marginal product and average product (MP crosses AP at AP's maximum), the shape of isoquants (convex because of diminishing marginal returns along substitution paths), and returns to scale (how output responds when all inputs increase proportionally). Technical change shifts the production function and can be neutral, labour-saving, or capital-saving.
Short run
A time period in which at least one input is fixed and cannot be adjusted. The defining feature is the presence of a fixed factor of production, not a specific calendar length.
Long run
A time period long enough for all inputs to be variable. No fixed factors remain.
Marginal product of labour (MPL)
The additional output produced by one more unit of labour, holding all other inputs constant.
Average product of labour (APL)
Total output divided by the number of units of labour employed. Represents output per worker.
Isoquant
A curve showing all combinations of inputs that produce the same level of output. Analogous to an indifference curve in consumer theory.
Marginal rate of technical substitution (MRTS)
The rate at which one input can be substituted for another while holding output constant. Equals the ratio of marginal products (MPL / MPK). The slope of the isoquant.
Returns to scale
How output responds when all inputs are increased by the same proportion:
Constant returns to scale: output increases by the same proportion as inputs
Increasing returns to scale: output increases by a larger proportion than inputs
Decreasing returns to scale: output increases by a smaller proportion than inputs
Neutral technical change
A technological improvement that increases output without altering the ratio of inputs used. The same input proportions produce more output than before.
Labour-saving technical change
A technological improvement that reduces the amount of labour needed relative to capital for a given output level. Shifts the MRTS so that less labour is used per unit of capital.
The short run is defined by the presence of at least one fixed input, not by a calendar duration
For Joey's lawn-cutting service, the lawn mower is the fixed input; hiring a new worker is the variable adjustment
The short run for Joey is the time it takes to both hire a worker and buy another mower (because in the short run he cannot change his capital stock)
Hiring an additional employee alone is a short-run adjustment (labour is the variable input)
The long run is when all inputs, including capital equipment, can be changed
When MPL > APL, average product is rising (the marginal worker adds more than the current average)
When MPL < APL, average product is falling (the marginal worker adds less than the current average)
When MPL = APL, average product is at its maximum
This is the key exam point: the marginal product curve intersects the average product curve at the peak of the average product curve
At this intersection, APL is at a maximum, but MPL is not necessarily at a maximum (MPL peaks earlier, then declines and passes through APL's peak on the way down)
If Jennifer alone produces 100 units, and with Applicant A total output is 175 units:
Applicant A's marginal product = 175 - 100 = 75 units
Average product with Applicant A = 175 / 2 = 87.5 units per worker
If Jennifer with Applicant B produces 155 units:
Applicant B's marginal product = 155 - 100 = 55 units
Average product with Applicant B = 155 / 2 = 77.5 units per worker
Isoquants are convex to the origin because of the changing marginal products along the curve
As you move down an isoquant (more labour, less capital):
MPL falls (diminishing marginal returns to labour as labour increases)
MPK rises (capital becomes scarcer, so each remaining unit of capital is more productive)
This means you need increasing amounts of labour to replace each unit of capital, which produces the convex shape
The MRTS (= MPL / MPK) diminishes as you move along the isoquant, confirming the convexity
Returns to scale describe what happens when all inputs are scaled up proportionally
If a farmer doubles land (10 to 20 acres) but keeps the tractor at 1, and output doubles (1,000 to 2,000 bushels), this looks like it could be constant returns to scale, but note: not all inputs doubled
In the practice question, only land doubled while capital stayed fixed. Output doubled. Since the input that increased (land) doubled and output doubled, but capital did not increase, the farmer is getting increasing returns to scale (output grew proportionally more than the overall input increase, because one input stayed the same)
More precisely: if we consider the bundle of inputs, not all inputs doubled, yet output still doubled. The farmer got 2x output with less than 2x total inputs, which implies increasing returns to scale
Technical change shifts the production function, allowing more output from the same inputs (or the same output from fewer inputs)
Three types:
Neutral technical change: output rises but the input ratio stays the same. Same number of workers per machine, but each combination produces more. Joey's switch to petrol mowers, keeping one worker per mower, is neutral technical change: the ratio of labour to capital is unchanged, but productivity increased.
Labour-saving technical change: the new technology reduces the need for labour relative to capital
Capital-saving technical change: the new technology reduces the need for capital relative to labour
Marginal product: MPL = ΔQ / ΔL (change in output per additional unit of labour)
Average product: APL = Q / L (total output divided by total labour)
MRTS: MRTS = MPL / MPK = -(slope of the isoquant)
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.
⚠️ The short run is defined by fixed inputs, not by a time period like "one month" or "one year." Questions often test this by describing a specific business scenario and asking what constitutes the short run for that firm.
⚠️ MPL = APL at the maximum of APL, not at the maximum of MPL. The marginal product curve peaks first, then declines and crosses the average product curve at its peak. This is a very frequently tested relationship.
⚠️ When calculating marginal product, it is the additional output from the additional worker, not the total output or the average. Applicant A's MP = 175 - 100 = 75, not 175 or 87.5.
⚠️ Isoquant convexity comes from MPL falling and MPK rising as you substitute labour for capital. Students sometimes say both marginal products fall or both rise, which is incorrect.
⚠️ For returns to scale, you must scale all inputs proportionally. If only some inputs change, you are observing marginal returns to a single factor, not returns to scale. However, exam questions sometimes present scenarios where not all inputs scale equally and ask you to infer returns to scale from the result.
⚠️ Neutral technical change preserves input ratios. If the worker-to-machine ratio stays the same but output per unit goes up, it is neutral. Joey's petrol mowers are the classic example.
Q: Joey owns one lawn mower and cuts grass in summer. What defines the short run for his business?
A: The short run is the time it takes to hire an additional employee and buy another lawn mower. In the short run, his capital (the mower) is fixed, so he can only adjust labour. The long run begins when he can also change his capital stock.
Q: If the average product of labour equals the marginal product of labour, what can you conclude?
A: The average product of labour is at its maximum. When MPL = APL, the marginal worker is producing exactly the average amount, so the average is neither rising nor falling.
Q: Jennifer produces 100 units alone. With Applicant A, total output is 175. What is Applicant A's marginal product?
A: 75 units. Marginal product is the additional output from the additional worker: 175 - 100 = 75.
Q: Why are isoquants convex to the origin?
A: As labour increases and capital decreases along an isoquant, the marginal product of labour falls while the marginal product of capital rises. This means progressively more labour is needed to replace each unit of capital, producing a convex shape.
Q: A farmer doubles land from 10 to 20 acres, keeps one tractor, and output doubles from 1,000 to 2,000 bushels. What are the returns to scale?
A: Increasing returns to scale. Output doubled even though only one input (land) doubled while capital stayed constant. The farmer got proportionally more output than the proportional increase in total inputs.
Q: Joey switches from push mowers to petrol mowers, still using one worker per mower, but cuts more grass per hour. What type of technical change is this?
A: Neutral technical change. The ratio of labour to capital is unchanged (still one worker per mower), but each combination now produces more output.
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