What makes a factor market perfectly competitive
Firms buy factors of production (labour, capital and land) in factor markets. This topic looks at the labour market, with other inputs held fixed.
A labour market is perfectly competitive when:
- Many firms hire this type of worker, and each hires only a tiny share of the total.
- Many workers offer the same skills, so one worker is a perfect substitute for another.
- Workers and firms have good information about wages and jobs, and workers can move freely between employers.
The result is that the market sets the wage. Market demand for labour (the sum of all firms’ demand) and market supply of labour cross at one wage. Each firm is a wage taker: it can hire one more worker, or a hundred more, at that wage. If it offered less, its workers would leave for other firms. It has no reason to offer more, because it can already hire all it wants.
So, for one firm:
- The firm’s labour supply curve is horizontal at the market wage.
- The marginal resource cost (MRC), sometimes called marginal factor cost, is the extra cost of hiring one more worker. For a wage taker, MRC = wage, and it stays the same however many workers the firm hires.
A firm’s position in its labour market does not depend on its position in its output market. A firm can be a monopoly when it sells, yet one of hundreds of employers when it hires electricians, drivers or accountants. It then takes the wage like any other small employer.
The hiring rule: MRP = MRC = wage
Each extra worker adds to the firm’s revenue and to its costs.
- Marginal revenue product (MRP) of labour = change in total revenue ÷ change in labour = ΔTR ÷ ΔL. It is also MP × MR: the extra output of the worker multiplied by the extra revenue from each unit of that output.
- Marginal resource cost (MRC) = change in total labour cost ÷ change in labour. For a wage taker, MRC = W.
The firm compares the two, one worker at a time:
- MRP > W: the worker adds more revenue than cost, so hiring them raises profit. Hire.
- MRP < W: the worker costs more than they bring in, so hiring them lowers profit. Do not hire.
- MRP = W: profit is unchanged; this is where the firm stops.
The profit-maximising quantity of labour is where MRP = MRC = W. Because MP eventually falls (diminishing marginal returns), MRP eventually falls too. That is why there is a stopping point.
This rule also explains why the firm’s MRP curve is its labour demand curve. At each wage, the firm hires the quantity where its downward-sloping MRP equals that wage. A lower wage means more workers hired: a movement along the MRP curve, not a shift.
Notice two things in Figure 1. The firm’s horizontal supply line is not the market supply curve; it is what one tiny employer faces. And only the falling part of MRP matters for the decision: the bakery would never stop at worker 1 just because MRP is rising there.
MRP and VMP: when the output market matters
The value of the marginal product (VMP) of labour is MP × P: the extra output multiplied by the price at which it sells.
- If the firm sells its output in a perfectly competitive market, it is a price taker, so MR = P for every unit. Then MRP = MP × MR = MP × P = VMP.
- If the firm has market power in its output market (monopoly, oligopoly or monopolistic competition), it must lower its price to sell more, so MR < P. Then MRP < VMP (in a table, from the second worker on, once some output is already being sold), and the MRP curve falls faster.
Always use MRP, not VMP, for the hiring decision. MRP is the revenue the firm really gains. A firm with output market power therefore hires fewer workers at a given wage than VMP would suggest (see Worked example 2).
Using more than one input
Firms use labour and capital (machines, buildings, equipment). Let W be the wage and r the price (rental) of one unit of capital.
Least-cost rule. To make any given output as cheaply as possible, the last dollar spent on each input must add the same output:
MP_L ÷ W = MP_K ÷ r
If MP_L ÷ W is larger, a dollar spent on labour adds more output than a dollar spent on capital. The firm can make the same output more cheaply by shifting spending towards labour and away from capital. As it does, MP_L falls and MP_K rises, until the ratios are equal.
Profit-maximising rule. Being least-cost is not enough: the firm might be making the cheapest possible version of the wrong amount of output. To maximise profit it also hires each input until its MRP equals its price:
MRP_L = W and MRP_K = r, which means MRP_L ÷ W = MRP_K ÷ r = 1
A firm that meets the profit-maximising rule also meets the least-cost rule. The reverse is not true.
Worked example 1: Halden Bakery hires bakers
Question. Halden Bakery sells bread in a perfectly competitive market at $3 per loaf. It hires bakers in a perfectly competitive labour market at $60 per day. Other inputs are fixed.
| Bakers | Total product (loaves per day) |
|---|---|
| 0 | 0 |
| 1 | 30 |
| 2 | 70 |
| 3 | 100 |
| 4 | 125 |
| 5 | 145 |
| 6 | 160 |
| 7 | 170 |
(a) Calculate MP and MRP for each baker. (b) How many bakers does Halden hire? (c) Show that hiring a sixth baker would lower profit. (d) The market wage falls to $45. How many bakers does Halden hire now?
(a) MP = change in total product. MRP = MP × $3, because the bakery is a price taker (so here MRP = VMP).
| Baker | MP (loaves) | MRP ($ per day) |
|---|---|---|
| 1st | 30 | 90 |
| 2nd | 40 | 120 |
| 3rd | 30 | 90 |
| 4th | 25 | 75 |
| 5th | 20 | 60 |
| 6th | 15 | 45 |
| 7th | 10 | 30 |
(b) Compare each MRP with MRC = W = $60. Bakers 1 to 4 have MRP above $60. The 5th has MRP = $60 = W. The 6th has MRP $45 < $60. Halden hires 5 bakers, where MRP = MRC = W.
(c) The 6th baker adds $45 of revenue but costs $60. Profit changes by 45 − 60 = −$15 per day. So hiring them lowers profit.
(d) At W = $45, the 6th baker’s MRP ($45) now equals the wage, and the 7th’s ($30) is below it. Halden hires 6 bakers. The lower wage moves the bakery down along its MRP (labour demand) curve.
Check. Units: MRP is in dollars per day, MP in loaves. Comparing MP (20 loaves) with the wage ($60) would mix units. Notice also that the 2nd baker has a higher MP than the 1st (specialisation); the decision is made on the falling part of MRP.
Worked example 2: Tidewell Kayaks has market power when it sells
Question. Tidewell Kayaks is the only kayak builder on its island, so it faces a downward-sloping demand curve: to sell Q kayaks per day it charges P = 120 − 4Q dollars. It hires boat-builders from a large regional labour market at a market wage of $100 per day.
| Workers | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| Kayaks per day (Q) | 0 | 5 | 9 | 12 | 14 | 15 |
(a) Calculate the price, total revenue, MRP and VMP for each worker. (b) How many workers does Tidewell hire? (c) How many would it hire if it wrongly used VMP? Why is that wrong?
(a) Price from P = 120 − 4Q; TR = P × Q; MRP = ΔTR; VMP = MP × P at the new output.
| Workers | Q | P ($) | TR ($) | MP | MRP ($) | VMP ($) |
|---|---|---|---|---|---|---|
| 1 | 5 | 100 | 500 | 5 | 500 | 500 |
| 2 | 9 | 84 | 756 | 4 | 256 | 336 |
| 3 | 12 | 72 | 864 | 3 | 108 | 216 |
| 4 | 14 | 64 | 896 | 2 | 32 | 128 |
| 5 | 15 | 60 | 900 | 1 | 4 | 60 |
Check one value with MRP = MP × MR. From 2 to 3 workers, MR per kayak = (864 − 756) ÷ 3 = $36, and 3 × 36 = $108. ✓
(b) MRC = W = $100. The 3rd worker’s MRP ($108) is above $100; the 4th worker’s ($32) is far below. Tidewell hires 3 workers.
(c) The 4th worker’s VMP is $128, which is above $100, so a VMP rule would say 4 workers. But to sell the 4th worker’s 2 extra kayaks, Tidewell must cut the price on all its kayaks from $72 to $64. Total revenue rises by only $32, not $128. Hiring the 4th worker would change profit by 32 − 100 = −$68 per day.
Interpretation. Tidewell is a monopoly when it sells but a perfect competitor when it hires: it pays the market wage of $100, and its MRC is $100 for every worker.
Worked example 3: Lakemoor Print chooses labour and machines
Question. Lakemoor Print sells boxes of labels for $2 each in a competitive market. It pays W = $40 per worker per day and rents machines at r = $60 per machine per day. Both input markets are perfectly competitive.
| Units of input | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| MP of labour (boxes) | 60 | 50 | 40 | 30 | 20 | 10 |
| MP of capital (boxes) | 120 | 90 | 60 | 45 | 30 | 15 |
(a) Lakemoor has $400 a day to spend on inputs. Which combination of workers and machines makes the most output for that budget? (b) What combination maximises profit? (c) Explain why the answer to (a) is not the profit-maximising choice.
(a) MP per dollar:
| Unit | MP_L ÷ W | MP_K ÷ r |
|---|---|---|
| 1st | 1.5 | 2 |
| 2nd | 1.25 | 1.5 |
| 3rd | 1 | 1 |
| 4th | 0.75 | 0.75 |
| 5th | 0.5 | 0.5 |
| 6th | 0.25 | 0.25 |
The ratios are equal at 4 workers and 4 machines (0.75 each), and the cost is 4 × 40 + 4 × 60 = $400. The only other combination in the table costing $400 is 1 worker and 6 machines, where the ratios (1.5 and 0.25) are far apart. So 4 workers and 4 machines is the least-cost choice for this budget.
(b) MRP = MP × $2. MRP_L of the 5th worker = 20 × 2 = $40 = W. MRP_K of the 5th machine = 30 × 2 = $60 = r. The 6th of each would add less than it costs. Profit is maximised at 5 workers and 5 machines, spending $500 a day.
(c) At 4 and 4, MRP_L ÷ W = 60 ÷ 40 = 1.5 and MRP_K ÷ r = 90 ÷ 60 = 1.5. The ratios are equal (least-cost) but both are above 1: each extra dollar on either input still brings back $1.50 of revenue. Lakemoor should expand both inputs until each ratio falls to 1. At 5 and 5, both MP ratios are 0.5 and both MRP ratios are 1, so both rules hold.
Common misconceptions
- “The firm hires until MP is as high as possible.” It hires until MRP falls to the wage. The best number of workers is usually well past the peak of MP.
- “Compare MP with the wage.” MP is in units of output; the wage is in dollars. Convert first: MRP = MP × MR.
- “MRP always equals MP × P.” Only when the firm sells in a perfectly competitive output market. With market power, MR < P, so MRP < VMP.
- “A wage taker’s MRC rises as it hires more.” For a wage taker, every extra worker costs the same market wage, so MRC = W and is constant.
- “A firm that is a monopoly in its output market must set wages.” Output market power and labour market power are separate. Many monopolies hire in competitive labour markets.
- “A fall in the wage shifts the firm’s labour demand curve.” A wage change is a movement along the MRP curve. Changes in output price or productivity shift it (Topic 5.2).
- “If MP per dollar is equal for every input, profit is maximised.” That only guarantees least cost. Profit needs MRP = price for each input as well.
Where this leads
Here the firm could hire as many workers as it wanted at one wage. Next, in Topic 5.4, Monopsonistic Markets, one employer faces the whole upward-sloping supply of labour, so hiring one more worker means raising the wage for everyone, and MRC rises above the wage. Test yourself with the practice questions, then use the revision notes and the checklist to consolidate.
Quick questions
Can a monopoly be a wage taker?
Yes. A firm can be the only seller of its product and still be one of many employers hiring a common type of worker. It then sells as a monopoly but hires as a perfect competitor, at the market wage.
Why does the firm hire the worker whose MRP exactly equals the wage?
That worker adds as much revenue as cost, so profit is the same with or without them. By convention we say the firm hires up to the point where MRP = MRC, so that worker is included.