Labour Demand in Macroeconomics: Theory, Technological Change, and Wage Inequality

Labour Demand

Overview of Labour Demand

Labour demand is a central concept in macroeconomics, describing how firms decide the quantity of labour to employ based on economic conditions, technology, and wages. This section explores the standard production model, the effects of technological change, and the implications for different types of workers.

• Labour demand refers to the number of workers firms are willing to hire at different wage levels.

• It is derived from the firm's goal to maximize profit, given the productivity of labour and the cost of hiring workers.

• Technological change and shifts in the economy can alter the demand for labour, sometimes benefiting skilled workers more than unskilled workers.

Simplifying Assumptions in the Standard Model

To analyze labour demand, economists often use a simplified model with the following assumptions:

• The short run: Capital stock is fixed, but the amount of labour is variable.

• All workers are identical (homogeneous labour).

• Wages are determined in a competitive market.

• Firms hire workers to maximize profit.

Marginal Product of Labour and Real Wage

The decision to hire an additional worker depends on the marginal benefit and marginal cost:

• Marginal Product of Labour (MPN): The additional output produced by employing one more worker.

• Marginal Revenue Product of Labour (MRPN): The extra revenue from hiring one more worker, calculated as:

$MRPN = P \times MPN$

• P: Price of output

• MPN: Marginal product of labour

• The cost to the employer is the nominal wage (W).

• In real terms, the cost is the real wage (w):

$w = \frac{W}{P}$

Labour Demand Curve

The labour demand curve shows the relationship between the real wage and the quantity of labour demanded:

• The MPN curve is downward sloping due to diminishing marginal returns to labour.

• Profit-maximizing firms hire workers up to the point where:

$MPN = w$

• If $MPN > w$, hire more workers.

• If $MPN < w$, reduce the workforce.

• The optimal number of workers is where $MPN = w$.

Aggregate Labour Demand

Aggregate labour demand is the sum of all firms' labour demands in the economy. It has the same shape and properties as the individual firm's labour demand curve.

Example: Labour Demand Function

Suppose the marginal product of labour is given by:

$MPN = a - bN$

• b > 0 ensures the curve is downward sloping.

• Setting $MPN = w$ and solving for $N$ gives the labour demand curve:

$a - bN = w$

$N^D = \frac{a}{b} - \frac{w}{b}$

• This curve is downward sloping in $w$.

• An increase in $a$ (e.g., due to higher productivity) shifts the curve up.

Technological Change and Labour Demand

Technological progress can affect labour demand in several ways:

• The standard model assumes technology and labour are complements, so technological improvement increases labour demand.

• However, technology can also substitute for labour, especially with advances in robotics and AI.

• Historically, technology has not led to higher unemployment rates; instead, it has shifted labour to new sectors and increased overall productivity.

Labour Reallocation: The Hot Dog Parable

This parable illustrates how technological improvement in one sector can lead to labour reallocation and higher total output:

• Suppose 120 workers are split between two industries: buns and wieners.

• Initially, it takes 2 workers to produce either a bun or a wiener, so 60 in each sector yields 30 hotdogs.

• After a technological improvement, only 1 worker is needed to produce a wiener.

• Now, 30 workers can produce 30 wieners, and 60 can still produce 30 buns, so only 90 workers are needed for 30 hotdogs.

• Alternatively, reallocating all 120 workers can produce 40 hotdogs (80 buns, 40 wieners).

Wage Inequality and Skill-Biased Technological Change

Technological change can affect different groups of workers unequally:

• Between 1980 and 2000, real wages in Canada became more unequal, with skilled workers seeing wage growth and unskilled workers' wages stagnating.

• Since 2000, wage differentials have stabilized, and women's wages have grown faster than men's.

• Skill-biased technological change increases the productivity of skilled workers more than unskilled workers, often due to computerization and automation.

• There has been a decline in routine jobs, especially in the US, as technology replaces repetitive tasks.

• The workforce may respond slowly to these changes, leading to temporary mismatches in skills and employment.

Summary Table: Effects of Technological Change on Labour Demand

Type of Technological Change	Effect on Labour Demand	Effect on Wage Inequality
General Productivity Increase	Shifts labour demand curve up (higher demand at each wage)	May benefit all workers
Labour-Substituting (e.g., automation)	Reduces demand for routine/unskilled labour	Increases wage inequality
Skill-Biased	Increases demand for skilled labour	Raises skilled/unskilled wage gap

Additional info: The above table summarizes the main effects of different types of technological change on labour demand and wage inequality, as discussed in the lecture notes.