Marginal Rate of Technical Substitution (MRTS)

What MRTS means

The marginal rate of technical substitution (MRTS) measures the rate at which a firm can replace one input (typically labor, L) with another (typically capital, K) while keeping output constant. It describes trade-offs between inputs along an isoquant — the curve showing all input combinations that yield the same level of output.

Key points:
* MRTS quantifies how many units of capital can be given up for an additional unit of labor (or vice versa) without changing output.
* It is a producer-side concept, distinct from the consumer-focused marginal rate of substitution (MRS).
* In practice, MRTS helps firms choose cost-minimizing input combinations and understand how substitutability changes as input use changes.

Formula

MRTS (L for K) can be expressed as:
MRTS = −ΔK / ΔL = MP_L / MP_K

Where:
* K = capital
* L = labor
* MP_L = marginal product of labor (additional output from one more unit of labor)
* MP_K = marginal product of capital
* −ΔK / ΔL = the reduction in capital when labor is increased by one unit, holding output constant

Equivalently, the slope of the isoquant is dK/dL = −MRTS, so the absolute value of the isoquant’s slope at a point equals the MRTS at that point.

Interpreting MRTS and isoquants

• On an isoquant graph with labor on the x-axis and capital on the y-axis, the MRTS at a point tells you how much K can be reduced if L increases by one unit while staying on the same isoquant.
• A falling MRTS along an isoquant (diminishing MRTS) means successive units of labor replace fewer units of capital — substitutability decreases as you add more of one input.
  Example: If adding one unit of labor lets you reduce 4 units of capital, MRTS = 4. If the next unit of labor allows reducing only 3 units of capital, MRTS = 3, illustrating diminishing MRTS.

Role in production decisions

• Cost minimization: For a firm choosing input quantities given input prices (wage w and rental price of capital r), the cost-minimizing condition is:
  MP_L / MP_K = w / r
  i.e., MRTS = w/r. At that point, the marginal rate of technical substitution equals the input price ratio.
• Input allocation: MRTS helps managers decide whether to substitute labor for capital (or vice versa) when relative input prices or technologies change.
• Productivity trade-offs: Understanding MRTS clarifies how changes in one input affect the effective need for the other while maintaining output.

MRTS vs. MRS

• MRTS applies to producers and input combinations in production; it measures technical substitutability between inputs.
• MRS applies to consumers and consumption bundles; it measures the rate at which a consumer is willing to trade one good for another while keeping utility constant.

Takeaways

• MRTS is the rate at which inputs can be substituted without changing output and equals the ratio of marginal products (MP_L / MP_K).
• Isoquants visually represent MRTS; the absolute slope of an isoquant at a point equals the MRTS there.
• Diminishing MRTS is common: as you add more of one input, it typically replaces fewer units of the other.
• Firms use MRTS together with input prices to identify cost-minimizing input mixes (MRTS = price ratio).