Source: NYU Introduction to Microeconomics, Class Notes (pp. 360–362)
Difficulty: Intermediate | Prerequisites: Basic supply and demand, production functions, marginal analysis.
This topic sits at the intersection of production theory and market structure. You have already learned how firms decide how much output to produce; now the question flips: how many workers (or units of any input) should a firm hire? The answer depends on what each additional worker adds to revenue, which is where the value of the marginal product comes in. Understanding factor demand is essential before you move into wage determination, monopsony, and labour-market policy topics later in the course.
A profit-maximising firm hires workers until the value of the last worker's output equals the wage. The total product curve shows output rising at a decreasing rate (diminishing marginal product), and the value of the marginal product (VMP) curve is the firm's demand curve for labour. When the firm has market power in its product market, the relevant measure becomes marginal revenue product (MRP), which falls even faster because marginal revenue itself declines with output.
Total product (TP)
The total quantity of output produced as the number of workers (or another variable input) increases, holding all other inputs constant. Think of it as the factory's total output at each staffing level.
Marginal product (MP)
The additional output produced by hiring one more worker. In simple terms, this means the extra units you get from the last person you brought on.
Diminishing marginal product
The principle that, beyond some point, each additional worker adds less output than the previous one. Think of it as crowding: the tenth cook in the same kitchen does not add as much as the third.
Value of the marginal product (VMP)
The marginal product of labour multiplied by the market price of the output: VMP = MP × P. In simple terms, this is the dollar value of what one extra worker produces. For a price-taking firm, VMP is the demand curve for labour.
Marginal revenue product (MRP)
The marginal product of labour multiplied by marginal revenue: MRP = MP × MR. This is the term used when the firm has product-market power (it is a monopolist or oligopolist), because it must lower price to sell more, so MR < P. Think of it as VMP's less optimistic cousin: it accounts for the fact that selling extra output pushes revenue per unit down.
Demand shifters for labour
Factors that shift the entire labour-demand curve left or right, rather than moving along it. Key shifters include changes in the output price, technological change, and changes in the prices or quantities of other inputs.
The total product (TP) curve plots output on the vertical axis against workers on the horizontal axis.
It rises steeply at first, then flattens as diminishing marginal product sets in.
The slope of the TP curve at any point is the marginal product of labour.
Diminishing MP is the reason the TP curve is concave (curving downward) rather than a straight line.
To translate physical output into a hiring decision, the firm multiplies MP by the price it receives for output.
For a competitive (price-taking) firm: VMP = MP × P. Because MP declines with each worker, VMP slopes downward.
The VMP curve is the firm's demand curve for labour. The firm hires workers up to the point where VMP equals the wage.
If VMP > wage, the firm profits from hiring another worker.
If VMP < wage, the last worker costs more than they bring in.
A competitive firm sells all output at the market price, so VMP = MP × P is the right measure.
A monopolist (or any firm with market power) faces a downward-sloping demand curve for its product. To sell more, it must cut price, so marginal revenue is less than price.
For a monopolist: MRP = MP × MR. Two forces pull the curve down: diminishing MP and falling MR.
MRP therefore lies below VMP at every employment level. The monopolist hires fewer workers than an otherwise identical competitive firm would.
Output price: if the price of the good rises, each worker's output is worth more, shifting labour demand right.
Technological change: an improvement that raises MP shifts labour demand right (each worker is more productive). A technology that substitutes for workers shifts it left.
Prices or availability of complementary and substitute inputs can also shift the labour-demand curve.
VMP = MP \times PMRP = MP \times MRDiagram notes from the lecture:
Total product curve: output (vertical) vs workers (horizontal), concave shape.
VMP curve: dollars (vertical) vs workers (horizontal), downward-sloping. This is the labour demand curve for a competitive firm.
MRP curve: same axes, but lies below VMP because MR < P for a monopolist.
The VMP framework is how firms in practice decide staffing levels. A restaurant owner asking "should I schedule one more server tonight?" is implicitly comparing that server's VMP to their hourly wage. Agricultural economists use the same logic to study how changes in crop prices affect farmworker employment across regions.
Students often think diminishing marginal product means total output is falling. It does not. Total output still rises; it just rises more slowly.
Students sometimes confuse VMP and MRP. VMP uses the output price; MRP uses marginal revenue. They are the same only for a perfectly competitive firm.
A common error is thinking that a firm hires where MP is maximised. The hiring rule is where VMP (or MRP) equals the wage, not where MP peaks.
Some students assume that a higher output price means the firm hires at a different point on the same demand curve. It does not: a price change shifts the entire VMP curve.
⚠️ You will almost certainly be asked to derive or graph the VMP curve from a total product function. Know the steps: compute MP, then multiply by P.
⚠️ Be ready to explain why a monopolist hires fewer workers than a competitive firm, using the VMP vs MRP distinction.
⚠️ Demand-shifter questions often appear as "what happens to labour demand if the output price rises?" Make sure you shift the curve, not move along it.
True or false: Diminishing marginal product means total output is decreasing.
False. Total output still increases; it just increases at a decreasing rate.
Fill in the blank: VMP = MP × ______.
Price (P).
True or false: The MRP curve lies above the VMP curve for a monopolist.
False. MRP lies below VMP because MR < P.
Fill in the blank: A firm hires workers until VMP equals the ______.
Wage.
True or false: A rise in the output price causes a movement along the labour demand curve.
False. It shifts the entire labour demand curve rightward.
Q: A competitive firm sells its output at $10 per unit. If the marginal product of the fifth worker is 12 units, what is the VMP of the fifth worker? Should the firm hire the fifth worker if the wage is $100?
A: VMP = 12 × $10 = $120. Since $120 > $100 (the wage), the firm should hire the fifth worker.
Q: Explain why a monopolist's labour demand curve lies below that of an identical competitive firm.
A: The monopolist must lower its output price to sell additional units, so its marginal revenue is less than the price. MRP = MP × MR, while the competitive firm uses VMP = MP × P. Since MR < P, MRP < VMP at every level of employment.
Q: Name two factors that shift the labour demand curve to the right.
A: An increase in the output price and a productivity-enhancing technological change both shift labour demand rightward.
Q: What is the difference between a movement along the labour demand curve and a shift of the curve?
A: A change in the wage causes a movement along the curve (the firm adjusts the quantity of labour demanded). A change in output price, technology, or other input prices shifts the entire curve.
This material connects directly to wage determination and labour-market equilibrium: once you know the demand side (VMP/MRP), adding the supply side gives you the equilibrium wage. It also links to the monopoly and market-structure material you have already covered, because the VMP vs MRP distinction depends on whether the firm is a price-taker or a price-setter. Later in the course, monopsony (a single buyer of labour) builds on this framework by asking what happens when the firm also has market power on the input side.
Labour demand, factor demand, derived demand, total product curve, marginal product of labour, diminishing returns, diminishing marginal product, value of the marginal product, VMP, marginal revenue product, MRP, labour demand curve, hiring rule, profit-maximising employment, demand shifters, output price effect, technology and labour demand, competitive firm labour, monopolist labour demand, factor markets, input markets.