Introduction to Factor Markets: Study Guide (Microeconomics 5.1)

Two kinds of market

So far the course has studied product markets: markets for goods and services such as bread, cement or phone plans. Firms sell and households buy. Unit 5 turns to factor markets (also called resource markets): markets for the inputs firms use to make those products.

In a factor market the roles are reversed. Households own the factors of production and sell their services. Firms buy them. A nurse sells hours of work to a hospital; a landowner rents a field to a farmer; a saver lends money that a firm uses to buy machines.

Factors and their prices

Each factor of production earns its own kind of payment, called its factor price.

Factor	Example	Factor price (payment to the owner)
Labour	hours of work by a picker, nurse or engineer	wage (per hour, day or year)
Capital	machines, buildings, tools used in production	interest (the price of using funds to buy capital)
Land	fields, sites and natural resources	rent

Factor prices do two jobs. They are incentives: a higher wage in one job draws workers towards it. They also carry information: a high price for a factor tells firms it is scarce, so they should use it carefully. This topic and the next three use labour as the main example, because the labour market is the one you will be asked about most. The same ideas apply to capital and land.

Derived demand

A firm does not want workers for their own sake. It hires a picker because the picker produces strawberries, and the strawberries can be sold. The demand for labour is therefore a derived demand: it is derived from the demand for the product the labour helps to make.

This explains the three things every hiring decision depends on:

1. Productivity of the factor. How much extra output does one more worker add? This is the marginal product (MP) from Topic 3.1.
2. The price of the output. What is that extra output worth? For a price taker, each unit sells for the market price P. For a firm with market power, the useful measure is marginal revenue (MR).
3. The cost of the factor. How much does one more worker add to the firm’s costs?

The first two combine into the benefit of hiring; the third is the cost. This is the familiar marginal benefit versus marginal cost comparison from Unit 1, applied to inputs instead of outputs.

Marginal revenue product

Marginal revenue product (MRP) is the extra total revenue a firm earns from hiring one more unit of a factor.

MRP = ΔTR ÷ ΔL (change in total revenue ÷ change in the number of workers)

Because each extra worker adds MP units of output, and each extra unit adds MR to revenue, MRP can also be found as:

MRP = MP × MR

Two cases matter:

How the firm sells its output	Marginal revenue	MRP
Perfectly competitive output market (price taker)	MR = P, the same for every unit	MRP = MP × P, also called the value of the marginal product
Imperfectly competitive output market (monopoly, oligopoly, monopolistic competition)	MR < P, because the firm must cut its price to sell more	MRP = MP × MR, which is less than MP × P

Either way, MRP falls as more workers are hired. With capital fixed, diminishing marginal returns make MP fall. For a firm with market power, MR also falls as output rises, so MRP falls even faster.

Marginal resource cost

Marginal resource cost (MRC), also called marginal factor cost (MFC), is the extra total cost of hiring one more unit of a factor.

MRC = ΔTC ÷ ΔL

Fixed costs do not change when one more worker is hired, so only the extra labour cost matters. If the firm can hire as many workers as it wants at the market wage (it is a wage taker), every extra worker adds exactly the wage to total cost. Then MRC = wage, and MRC is a horizontal line on a graph. (In Topic 5.4 you will meet a firm that must raise the wage to attract more workers; its MRC is above the wage.)

Worked example 1: pickers at Saltmere Strawberry Farm

Question. Saltmere Strawberry Farm is a fictional farm with a fixed amount of land and equipment. It sells strawberries in a perfectly competitive market at $4 per kilogram. It hires pickers at the market wage of $60 per day, and its fixed costs are $200 per day.

Pickers per day (L)	Total product (kg per day)
0	0
1	30
2	55
3	75
4	90
5	100
6	105

(a) Calculate the marginal product and MRP of each picker. (b) Check the MRP of the 3rd picker using total revenue. (c) Calculate total cost and the MRC of each picker. (d) Should the farm hire the 5th picker? Explain using MRP and MRC.

(a) MP = change in total product. MRP = MP × P, because Saltmere is a price taker (MR = P = $4).

L	TP (kg)	MP (kg)	MRP = MP × $4
1	30	30	$120
2	55	25	$100
3	75	20	$80
4	90	15	$60
5	100	10	$40
6	105	5	$20

(b) Total revenue = $4 × total product. With 2 pickers, TR = 4 × 55 = $220. With 3 pickers, TR = 4 × 75 = $300. MRP of the 3rd picker = 300 − 220 = $80, the same as 20 × $4.

(c) Total cost = $200 + $60 × L: $200, $260, $320, $380, $440, $500, $560. Each picker raises total cost by $60, so MRC = $60 for every picker. MRC equals the wage, because the farm pays the same market wage however many pickers it hires.

(d) No. The 5th picker adds $40 to revenue (MRP) but $60 to cost (MRC). Hiring that picker would lower profit by $20 per day.

Check. The MRP column falls steadily, which fits diminishing marginal returns: the land and equipment are fixed, so each extra picker has less to work with.

Interpretation. Figure 2 shows the logic the firm uses. Pickers 1 to 3 add more to revenue than to cost, picker 4 exactly covers the cost, and pickers 5 and 6 add less. Now imagine the wage changes. At $100 a day only the first 2 pickers are worth hiring; at $40 a day, 5 are. A lower wage means more workers are worth hiring. This is why the firm’s MRP curve is its demand curve for labour. You will use this rule formally, and practise finding the profit-maximising number of workers, in Topic 5.3.

Worked example 2: a firm that sets its own price

Question. Ferncastle Tiles is a fictional firm that makes hand-painted tiles. Its tiles are distinctive, so it faces a downward-sloping demand curve: to sell Q boxes a day, it must charge P = $100 − Q per box, on every box. Its daily output with each number of workers is:

Workers (L)	0	1	2	3	4	5
Boxes per day (Q)	0	10	18	24	28	30

(a) Find the price, total revenue and MRP for each number of workers. (b) Compare MRP with MP × P. Explain the difference for the 2nd worker. (c) The wage is $200 per day. Which workers add more to revenue than to cost?

(a)

L	Q	MP	P = 100 − Q	TR = P × Q	MRP = ΔTR	MP × P
0	0	–	100	0	–	–
1	10	10	90	900	900	900
2	18	8	82	1,476	576	656
3	24	6	76	1,824	348	456
4	28	4	72	2,016	192	288
5	30	2	70	2,100	84	140

All money values are in dollars per day (prices in dollars per box).

(b) From the 2nd worker on, MRP is less than MP × P. Take the 2nd worker:

1. The 8 extra boxes sell at $82 each: 8 × 82 = $656. This is MP × P.
2. To sell 18 boxes instead of 10, Ferncastle must cut the price from $90 to $82 on the first 10 boxes too. That loses 10 × $8 = $80.
3. MRP = 656 − 80 = $576, matching the change in total revenue (1,476 − 900).

So MRP = MP × MR, not MP × P. A firm with market power gains less from each extra worker than the price of the output suggests.

(c) MRC = $200 for each worker (the market wage). Workers 1, 2 and 3 have MRP of $900, $576 and $348, all above $200. The 4th worker’s MRP is $192, below $200. So the first 3 workers add more to revenue than to cost.

Interpretation. MRP falls for two reasons here: MP falls (diminishing returns) and MR falls (the price must be cut to sell more). Ferncastle’s demand curve for labour is therefore steeper than a price taker’s would be.

The labour market: demand and supply

Add up the demand for a type of labour by all the firms that hire it and you get the market demand for labour. Add up all the people willing to do that job and you get the market supply of labour.

Why labour demand slopes down. The quantity of labour demanded is negatively related to the wage, other things constant. Each firm’s demand is its MRP curve, and MRP falls as more workers are hired. When the wage falls, workers whose MRP was below the old wage become worth hiring, so firms hire more. When the wage rises, fewer workers are worth hiring.

Why labour supply slopes up. The quantity of labour supplied is positively related to the wage, other things constant. A higher wage:

• raises the opportunity cost of leisure, so people choose to work more hours;
• draws workers into this market from other occupations and from outside the labour force.

Equilibrium. The market wage settles where quantity demanded equals quantity supplied (W* and Q* in Figure 3). Above W*, there is a surplus of labour: more people want jobs than firms want to fill, so the wage tends to fall. Below W*, there is a shortage, so firms compete for workers and the wage tends to rise.

Movement, not shift. A change in the wage causes a movement along the demand and supply curves: a change in quantity demanded or supplied. Things other than the wage, such as the price of the product, workers’ productivity or immigration, shift the curves. That is Topic 5.2.

Common misconceptions

• “In factor markets, households are the buyers.” Households sell factor services; firms buy them. It is the reverse of a product market.
• “MRP is the marginal product.” MP is measured in units of output (kilograms, boxes). MRP is measured in dollars: it is MP turned into revenue.
• “MRP = total product × price.” That is total revenue. MRP uses the change in output (MP) or the change in total revenue.
• “MRP always equals MP × P.” Only for a price taker in the output market. A firm with market power must cut its price to sell more, so its MRP = MP × MR is lower (Worked example 2).
• “MRC includes fixed costs.” Fixed costs do not change when one more worker is hired. MRC is the change in total cost.
• “A higher wage shifts the labour demand curve left.” A wage change moves the market along the curve. Only a change in a determinant other than the wage shifts it.
• “Firms demand labour because they need workers.” Firms demand labour only for the output it produces and the revenue that output brings: it is a derived demand.

Where this leads

You now have the two measures that drive every hiring decision: MRP (the benefit of a worker) and MRC (the cost). Next, Topic 5.2, Changes in Factor Demand and Factor Supply, explains what shifts the labour demand and supply curves. Then Topic 5.3 puts MRP and MRC together to find the number of workers a profit-maximising firm hires. Test yourself with the practice questions, then use the revision notes and the checklist to consolidate. For the product-market topic just before this one, see Topic 4.5, Oligopoly and Game Theory.