Lesson preview · Long Run Production
Isoquants
~7 min · Free to read
In the long run, the firm can adjust both labor and capital. To analyze these choices, we use isoquants — curves that show all combinations of L and K that produce the same output. If you’ve studied indifference curves, isoquants work exactly the same way, but for production instead of utility.
Key Term
Isoquant
An isoquant (“equal quantity”) is a curve showing all input combinations that yield the same level of output .
Properties:
- Downward-sloping: to maintain output, using less K requires more L
- Convex to the origin: diminishing MRTS
- Higher isoquants = more output
- Isoquants never cross (same logic as indifference curves)
The marginal rate of technical substitution (MRTS) is the rate at which a firm can substitute capital for labor while keeping output constant. It’s the (negative of the) slope of the isoquant — analogous to the MRS for consumer theory.
The MRTS equals the ratio of marginal products — how productive each input is at the margin
Why is the MRTS = MPL/MPK? Add one unit of labor and output rises by MPL. To keep output unchanged, you must remove enough capital to reduce output by the same amount — that means removing MPL/MPK units of capital. The isoquant is convex because as you use more labor and less capital, labor becomes relatively less productive (diminishing MPL) and capital becomes relatively more productive (rising MPK), so the MRTS falls.
Worked Example
A firm produces 100 units using (L=2, K=8) or (L=4, K=5). Calculate the MRTS between these two points. Interpret its meaning.
Check yourself · no marks
If two isoquants crossed, what logical contradiction would arise?
Commit to one first. Guessing and being wrong beats reading the answer cold.
Practice · 1 / 4
An isoquant shows all input combinations that produce:
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