Labour demand, labour supply and wage determination

The demand for labour

A firm does not hire workers for their own sake. It hires them to produce goods or services it can sell. For this reason the demand for labour is a derived demand: it comes from the demand for the product the labour helps to make. If more people want coffee, cafés want more baristas.

Recall from the production theory section that the marginal physical product (MPP) of labour is the extra output from hiring one more worker. Because of the law of diminishing returns, MPP falls as more workers are added to a fixed amount of capital (Aoife's café has only one coffee machine).

Output is only useful to the firm if it can be sold, so we convert MPP into money:

A firm is profit-maximising when it hires workers up to the point where the extra revenue from the last worker equals the extra cost:

where $W$ is the wage (the marginal cost of labour for a firm that is a wage taker). Hire a worker whose MRP is above the wage and profit rises. Hire one whose MRP is below the wage and the firm loses money on that worker. This is exactly the MC = MR rule, applied to labour.

Since MRP falls as MPP falls, the MRP curve slopes downward. It is the firm's demand curve for labour: at each wage, it shows how many workers the firm will hire. The market demand curve is downward sloping for the same reason: a lower wage makes it profitable to hire workers whose MRP is lower.

When MPP is given as a formula

Sometimes MPP is given as an equation. Suppose a firm sells at €5 per unit and $MPP = 30 - 3L$, where $L$ is the number of workers. Then $MRP = 5(30 - 3L) = 150 - 15L$. If the wage is €45, set $MRP = W$: $150 - 15L = 45$, so $15L = 105$ and $L = 7$. If the wage rises to €60, then $150 - 15L = 60$ gives $L = 6$. Check: at $L = 7$, $MRP = 150 - 105 = 45$ ✓.

What shifts the demand for labour?

A change in the wage causes a movement along the demand curve. A change in anything else that alters MRP shifts the curve:

• The price of the product: higher price raises MRP, so demand shifts right. Lower price shifts it left.

• Productivity (MPP): better training or better technology raises MPP, so demand shifts right.

• The price of other inputs: if machines become cheaper and are substitutes for workers, demand for workers shifts left. If the input is a complement (a worker needs it to be productive), demand shifts right.

The supply of labour

On the other side of the market are workers. A person decides how many hours to offer by weighing the wage against the opportunity cost of working: the leisure, study time or unpaid work they give up.

At a higher wage:

• more people find it worth entering the labour force (a student in Limerick may take a part-time job at €16 an hour but not at €11);

• people already in work may offer more hours;

• workers in other jobs or other counties move into this occupation.

So the supply curve of labour slopes upward: a higher wage gives a larger quantity of labour supplied. For a single occupation such as electricians, the movement of workers from other jobs is the strongest reason.

What shifts the supply of labour?

• Population and migration: more people of working age, or workers returning from abroad, shifts supply right.

• Skills and training: more people qualifying in an occupation (for example through apprenticeships) shifts supply of that occupation right.

• Wages in other occupations: if pay rises in a rival occupation, workers leave and supply shifts left.

• Non-wage factors: better working conditions, childcare, or a shorter commute make a job more attractive, shifting supply right.

• Taxes and welfare: higher income tax or generous benefits can reduce the incentive to work.

Equilibrium wage and employment

Put the two curves together. At the equilibrium wage $W^*$, the quantity of labour demanded equals the quantity supplied, at $Q^*$ workers. Above $W^*$ there are more people seeking work than jobs (a surplus of labour: unemployment in that market). Below $W^*$ firms cannot find enough workers (a shortage), so employers bid wages up.

Read the widget with "price" as the wage and "quantity" as the number of workers: it shows what happens when the demand curve shifts right.

Shifts of both curves at once

When demand and supply both shift, one effect is certain and the other depends on the size of the shifts.

• Demand right, supply right: employment definitely rises; the wage may rise, fall or stay the same.

• Demand right, supply left: the wage definitely rises; employment is uncertain.

• Demand left, supply left: employment definitely falls; the wage may rise, fall or stay the same.

Elasticity of labour demand and policy

How much does employment fall when wages rise? That depends on the wage elasticity of demand for labour:

If $|E_w| > 1$, demand is elastic: a small rise in wages causes a large fall in employment. If $|E_w| < 1$, it is inelastic.

For the Sligo market above, at $W = 10$ and $Q = 550$ with $Q_d = 800 - 25W$, $\frac{dQ}{dW} = -25$. So $E_w = -25 \times \frac{10}{550} = -0.45$. Demand is inelastic: a 10% rise in the wage reduces employment by only about 4.5%.

Labour demand is more elastic when:

• workers can easily be replaced by machines (good substitutes);

• the demand for the final product is elastic (a firm cannot pass on higher costs);

• labour is a large share of total costs;

• there is plenty of time to adjust (in the long run firms can reorganise).

Substitutes and complements: the automation debate

Technology can be a substitute for some workers and a complement to others. Self-checkout machines substitute for supermarket cashiers: demand for routine, low-skilled labour shifts left and may be elastic. Data analytics tools complement skilled analysts, raising their MPP, so their demand shifts right. The effect of automation on "wages in Ireland" therefore depends on the type of labour, and on whether displaced workers can retrain and move to growing occupations (supply side).

Government policy: demand side or supply side?

If the Government wants more employment in an occupation:

• a wage subsidy lowers the cost to the employer, shifting labour demand to the right. It acts quickly but costs the Exchequer money and may subsidise jobs that would have existed anyway;

• a training programme increases the supply of qualified workers (a right shift in supply) and may raise their MPP, so demand shifts right too. It takes longer but builds lasting skills.

Which is better depends on the cause of the shortage. If employers cannot find qualified people, training addresses the cause. If firms cannot afford to hire, a subsidy helps.

How useful are MPP and MRP?

For an employer, MRP is a hiring rule. It shows how many workers to take on at a given wage, which jobs are worth creating and what the most is that a worker is worth paying. For an employee, MRP gives a case in a pay negotiation. A worker who can show that their training or skills raise MPP, or that the product sells at a higher price, has an argument for higher pay, because a firm will pay up to MRP and no more. It also shows why workers who are more productive tend to earn more.

There are limits. MPP is hard to measure when people work in teams (in a café, who produced the coffee: the barista or the person at the till?). Many jobs, such as nurses or teachers, produce output that is not sold, so MR is hard to define. Wages are also affected by bargaining power, trade unions, the National Minimum Wage and discrimination, so actual pay does not always equal MRP.

Back to the start: Aoife hires assistants until the extra revenue of the last one (MRP) equals the wage, and she needs to pay at least the wage that makes people value the job above the leisure or other job they give up. Where all the cafés, shops and workers in Galway meet is the equilibrium wage.

Summary