AP Syllabus focus: ‘Marginal revenue product equals MP times MR, and VMPL equals MPL times price in perfectly competitive output markets.’
Factor-demand calculations connect a worker’s (or any input’s) productivity to the firm’s revenue. This page focuses on computing marginal revenue product (MRP) and value of the marginal product of labor (VMPL) and interpreting what each measures.
Core Measures for Factor Demand
Marginal Revenue Product (MRP)
Marginal revenue product (MRP): The additional revenue a firm earns from employing one more unit of an input (such as one more worker), holding other inputs constant.
MRP is a revenue concept, not a physical output concept. It combines how much extra output the input creates with how much extra revenue each additional unit of output generates.
In general, you compute MRP using the input’s marginal product and the firm’s marginal revenue from selling output.
= marginal product of the input (extra units of output per extra unit of input)
= marginal revenue (extra dollars of total revenue per extra unit of output)
= marginal product of labour (extra units of output per extra worker)
= output price (dollars per unit of output)
The key distinction is that MR depends on the firm’s output market conditions, while P is simply the market price.
VMPL (Value of the Marginal Product of Labor)
This figure plots (i.e., VMPL) against labor, showing a downward-sloping VMPL curve as diminishing marginal product sets in. The label highlights that VMPL converts marginal physical output into dollars using the output price. This graph is also commonly interpreted as the firm’s labor-demand curve when the output market is perfectly competitive. Source
Value of the marginal product of labor (VMPL): The dollar value of the extra output produced by one more worker, calculated as the worker’s marginal product times the output price.
VMPL translates extra physical output into dollars using price, so it is especially convenient when the firm is a price taker in the output market.
Perfectly Competitive Output Markets: When VMPL = MRP
In a perfectly competitive output market, a firm faces a perfectly elastic demand curve for its product, so selling one more unit does not require lowering the price. As a result, marginal revenue equals price (so ). That makes the two calculations coincide:
MRP uses
VMPL uses
If output is perfectly competitive, , so MRP and VMPL are the same measure
This is exactly why the syllabus highlights that VMPL equals in perfectly competitive output markets: it is a direct, price-based way to express the revenue contribution of the marginal worker.
Imperfect Output Markets: Why MRP and VMPL Can Differ
If the firm has output market power (for example, a downward-sloping demand curve for output), then selling additional output typically requires lowering the price on at least some units sold. In that case:
over the relevant range
This graph shows a downward-sloping demand curve with a marginal revenue curve that lies below it. Because selling more output requires lowering price on units sold, the marginal revenue from an extra unit is less than the price, so . That wedge is exactly why can be smaller than in imperfectly competitive output markets. Source
MRP = will be lower than VMPL =
Using VMPL as if it were MRP would overstate the extra revenue created by the marginal worker
So, when computing the revenue effect of hiring, the correct “revenue per extra unit of output” term is MR, not necessarily P.
Reading and Computing from Information You’re Given
AP-style prompts may provide information in different forms. Your task is to identify the needed components and combine them correctly.
If you are given (or ) and told the firm is a perfect competitor in output, use price to get VMPL, which will also equal MRP
If you are given (or can infer it from a demand/revenue relationship) and , use MRP =
Keep units consistent:
or : units of output per unit of input
: dollars per unit of output
: dollars per unit of output
MRP/VMPL: dollars per unit of input
FAQ
Write demand as $P(Q) = a - bQ$, then total revenue is $TR = P \cdot Q = aQ - bQ^2$.
Differentiate: $MR = \frac{dTR}{dQ} = a - 2bQ$.
So $MR$ has the same intercept as demand but twice the slope.
$MP$ is generic: marginal product of any input (labour, capital, land).
$MPL$ is the specific case for labour, used when the input being varied is the number of workers.
Yes. $VMPL$ moves one-for-one with $P$ because $VMPL = MPL \times P$.
Recalculate using the new $P$, holding $MPL$ fixed unless the prompt indicates productivity also changed.
Mixing “per worker” and “per unit of output.”
Check that $MPL$ is in units of output per worker and that $P$ or $MR$ is in £ (or $) per unit of output, so the product is £ (or $) per worker.
Yes, if $MP$ is negative (e.g., severe congestion so an extra worker reduces output).
Then $MRP = MP \times MR$ is negative, meaning the marginal worker reduces revenue rather than adding to it.
Practice Questions
(2 marks) State the formula for marginal revenue product and define marginal revenue product.
1 mark: Correct formula: .
1 mark: Correct definition: additional revenue from employing one more unit of an input, ceteris paribus.
(6 marks) Explain how to calculate in a perfectly competitive output market and compare with when the firm has market power in the output market.
1 mark: States .
1 mark: Explains that in perfect competition .
1 mark: Concludes that therefore , so .
1 mark: States in imperfect competition (over the relevant range).
1 mark: Uses in imperfect competition.
1 mark: Correct comparison: when .
