Title: Marginal Revenue Product (MRP) — What It Is, How to Calculate It, and Practical Steps for Business Decisions
Key takeaways
– Marginal Revenue Product (MRP) measures the additional revenue generated by employing one more unit of a resource (worker, machine, land).
– MRP = Marginal Physical Product (MPP) × Marginal Revenue (MR). MPP is the additional output from one more unit of the resource; MR is the additional revenue from selling one more unit of output.
– A firm should hire or buy a resource up to the point where the resource’s price equals its (discounted) MRP.
– In practice you must account for diminishing marginal returns, pricing power (MR differs if the firm is price taker vs. price maker), timing of revenues (discounting), and measurement uncertainty.
– Conceptually related to the work of John Bates Clark and Knut Wicksell (see sources).
What is Marginal Revenue Product (MRP)?
MRP — also called marginal value product — is the incremental revenue a firm receives from adding one additional unit of a production factor, holding other inputs constant. It links physical productivity (how many extra units produced) to revenue (how much each extra unit sells for).
Basic formula
MRP = MPP × MR
Where:
– MPP (marginal physical product) = change in quantity produced from adding one unit of the resource.
– MR (marginal revenue) = change in total revenue from selling one more unit of output.
If a firm is a price taker in the product market (perfect competition), MR equals the market price, so MRP = MPP × price.
Why MRP matters
– Optimal hiring/purchasing rule: Employ a unit of input only if its cost ≤ MRP (or ≤ discounted MRP when timing differs).
– Helps set bid prices for capital and labor and supports cost–benefit choices for incremental investments.
– Underlies much of labor demand theory: wages tend toward discounted MRP in competitive markets.
Short numeric examples
1) Tractor example (from Investopedia):
– Extra tractor increases output by 3,000 bushels (MPP = 3,000).
– Market price of wheat = $5 per bushel (MR = $5).
– MRP = 3,000 × $5 = $15,000.
Decision rule: Buy the tractor only if its cost ≤ $15,000 (ignoring financing, depreciation, etc.).
2) Worker-hour example:
– An additional worker-hour produces 4 extra units (MPP = 4).
– Each unit sells for $10 (MR = $10).
– MRP = 4 × $10 = $40 per hour.
Decision rule: Hire the worker-hour if wage per hour ≤ $40 (adjust for payroll taxes, benefits, training, and timing).
Practical step-by-step guide for applying MRP in business decisions
1. Define the incremental decision clearly
– Are you hiring one more worker, adding an extra machine, or increasing a shift by one hour? The decision must be marginal.
2. Estimate the Marginal Physical Product (MPP)
– Use field trials, pilot projects, historical data, or production-function estimates.
– Prefer experimental or controlled comparisons (A/B testing, before-after with controls).
– Watch for diminishing marginal returns—MPP typically falls as you add more of a fixed input.
3. Estimate Marginal Revenue (MR)
– If you are a price taker (commodity markets), MR ≈ market price.
– If you have market power, estimate MR from the demand curve: MR = change in total revenue / change in quantity. For a linear demand curve, MR can be derived analytically.
– Consider possible price effects from increasing supply (especially if the incremental output is large relative to market demand).
4. Compute MRP
– Multiply MPP × MR for the marginal unit.
5. Adjust for timing (discounting) and recurring flows
– If the additional resource generates revenue only after a delay (e.g., seasonal crop, long production cycle), compute the present value of the expected incremental revenue stream.
– Concept: Discounted MRP (DMRP) = present value of future MRPs. For a single future payment, DMRP = MRP / (1 + r)^t, where r is discount rate and t is time to revenue. For repeated flows, sum the discounted stream.
6. Compare to marginal cost (price of the resource)
– Include direct price (wage, rental, purchase price), plus taxes, training, maintenance, financing costs, and opportunity cost.
– If cost ≤ DMRP, the marginal investment/hire is justified.
7. Perform sensitivity analysis
– Test results against different estimates of MPP, MR, prices, and discount rates.
– Identify break-even values for key assumptions.
8. Monitor and update
– After implementing, measure actual MPP and realized revenue, and refine future estimates.
Special considerations and limitations
– Diminishing marginal returns: As you hire or add more of one factor while holding others constant, MPP typically decreases.
– Measurement error: Estimating MPP and MR can be noisy. Use experiments or conservative assumptions.
– Price effects and market power: For firms that can influence market prices, MR < price. Using price instead of MR will overstate MRP.
– Timing and liquidity: Employers pay wages now but may collect revenue later—this justifies discounting (DMRP).
– Bargaining and labor market frictions: Wages don’t necessarily equal MRP; bargaining, minimum wages, unions, and monopsony power can create differences.
– General-equilibrium feedbacks: Widespread adoption of a resource may change product prices and factor markets.
– Externalities and non-monetary benefits: MRP ignores external benefits (learning-by-doing, network effects) unless explicitly included in revenue estimates.
MRP and wages: discounted MRP (DMRP)
– The textbook rule in competitive labor markets is to hire labor up to the point wage = MRP. In practice, because employers receive some revenue later, they implicitly compare wages to the present value of the worker’s future marginal revenue (DMRP).
– Conceptual formula for a single future payment: DMRP = MRP / (1 + r)^t. For ongoing contributions, DMRP = sum of discounted expected MRPs over the relevant time horizon.
– When offered wages are below a worker’s outside opportunities (or below DMRP), the worker gains bargaining power to seek higher pay. Conversely, if wage is above DMRP the employer has incentive to reduce employment or cut wages.
Practical checklist before you purchase a capital good or hire:
– Define the marginal unit and time horizon.
– Collect baseline output and revenue data.
– Run a pilot test or use a control group if possible.
– Estimate MPP and MR; document assumptions.
– Calculate MRP and DMRP (if timing matters).
– Include all marginal costs (training, insurance, financing).
– Run sensitivity and break-even analyses.
– Decide and implement, then monitor actual outcomes.
Quick example: hiring with discounting
– Suppose an extra worker creates $5,000 of incremental revenue one year from now (MRP in year 1), and $5,000 each subsequent year for three years. Discount rate = 8%.
– DMRP = 5,000/(1.08) + 5,000/(1.08)^2 + 5,000/(1.08)^3 ≈ $4,629 + $4,287 + $3,969 = $12,885.
– If total marginal cost (wages + benefits + training pro-rated) is ≤ $12,885 on a present-value basis, hiring is justified.
Graphical intuition (brief)
– The MRP curve typically slopes downward (due to diminishing MPP and, sometimes, falling MR if output expansion reduces price).
– A firm’s demand for a factor is a derived demand: it derives from the product’s demand. The firm hires where the factor’s price equals MRP.
When MRP analysis can mislead
– If the product’s demand is highly elastic or your incremental output is large relative to market size, MR will drop as output expands and a simple MPP × current price overstates MRP.
– If there are complementarities—e.g., the extra worker yields large gains only when paired with new technology—ignoring interactions will misstate MPP.
– Public policy, taxes, subsidies, and regulation can alter effective costs and revenues.
Conclusion
MRP is a core tool for incremental decision-making: it turns physical productivity estimates into dollar terms and gives a clear rule — pay up to the marginal revenue the input produces. Its correct application requires careful estimation of MPP and MR, attention to timing (discounting), and awareness of real-world frictions like bargaining and market power. Use pilots, sensitivity analysis, and ongoing monitoring to make MRP-based decisions practical and robust.
Sources
– Investopedia. “Marginal Revenue Product (MRP).” https://www.investopedia.com/terms/m/marginal-revenue-product-mrp.asp
– Britannica. “John Bates Clark.” https://www.britannica.com/biography/John-Bates-Clark
– Britannica. “Knut Wicksell.” https://www.britannica.com/biography/Knut-Wicksell
If you’d like, I can:
– Run a worked multi-year DMRP calculation for a specific hire or capital purchase,
– Draft a small survey or pilot-test plan to estimate MPP for your business, or
– Create an Excel template that calculates MRP and sensitivity break-evens. Which would help most?