Production and Productivity

Aggregate Production Function

The aggregate production function is a fundamental concept in macroeconomics, relating total output to the inputs used in production. It is typically expressed as:

• Y = A F(K, N), where:

• Y: Real output produced

• A: Total factor productivity (TFP), measuring the effectiveness of capital and labour utilization

• K: Capital stock (quantity of capital used)

• N: Number of workers employed

Other inputs, such as materials, are often ignored for simplicity, focusing on capital and labour as primary factors.

Properties of the Production Function

Total factor productivity (TFP) reflects improvements in technology or efficiency. It may also capture productivity embodied in capital and labour, such as advanced machinery or skilled workers.

Constant Returns to Scale

A production function exhibits constant returns to scale if increasing all inputs by a factor b results in output increasing by the same factor:

• Example: Doubling all inputs doubles output.

Cobb-Douglas Production Function

The Cobb-Douglas function is a common form:

• If , then

Doubling only one input (e.g., labour) increases output by less than double due to the constraint imposed by the fixed input.

Marginal Product of Labour (MPN)

The marginal product of labour measures the increase in output from a small increase in labour, holding capital constant:

• MPN is positive but declines as N increases, reflecting diminishing marginal productivity.

Marginal Product of Capital (MPK)

MPK measures the increase in output from a small increase in capital, holding labour constant:

• MPK also declines as K increases.

Supply (Productivity) Shocks

A supply shock, such as an increase in TFP, shifts the production function upward, allowing more output for any combination of inputs. Both MPN and MPK curves shift up.

Growth Accounting

Growth accounting decomposes output growth into contributions from TFP, capital, and labour:

• Assume Cobb-Douglas:

• Growth rate approximation:

• TFP growth is calculated as:

GDP per Capita and Labour Productivity

GDP per capita is determined by the fraction of the population in the labour force and output per worker:

• Growth in GDP per capita depends on growth in labour productivity and labour force participation.

• Labour productivity:

Unemployment

Employment States

The labour market consists of three main statuses:

• Employed: Worked during the past week

• Unemployed: Did not work but actively sought work in the past four weeks

• Out of the labour force: Did not work and did not seek work

• Labour force = employed + unemployed

Labour Market Flows

The labour market is dynamic, with workers moving between employment, unemployment, and out of the labour force. Most unemployment spells are short, but most unemployed at a given time are long-term unemployed.

Types of Unemployment

• Frictional unemployment: Due to search and matching processes

• Structural unemployment: Long-term, caused by skill mismatches or technological change

• Cyclical unemployment: Due to economic downturns

Natural Rate of Unemployment

The natural rate (\bar{u}) is the rate prevailing at full employment, caused by frictional and structural factors. Cyclical unemployment is the difference between actual and natural rates.

Unemployment Demographics

• Higher rates among males, youth, and less educated individuals

Labour Supply

Labour Supply and Real Wages

Labour supply responds to real wages through two effects:

• Substitution effect: Higher wages increase labour supplied

• Income effect: Higher wages decrease labour supplied, as leisure is a normal good

• For temporary wage changes, substitution dominates; for permanent changes, income effect dominates

Labour Supply Curve

The labour supply curve relates labour supplied to the current real wage, holding other factors constant. Changes in wealth or expected future wages shift the curve.

Aggregate Labour Supply

• Higher real wages increase aggregate labour supply via intensive (more hours) and extensive (more workers) margins

Classical Labour Market Equilibrium

In the classical model, real wages adjust to equate labour supply and demand, resulting in full employment and market-clearing wage.

Labour Demand

Labour Demand and Marginal Product

Firms demand labour based on the marginal product of labour (MPN) and the real wage:

• Profit-maximizing firms hire until

• MPN curve is downward sloping due to diminishing returns

Impact of Technology on Labour Demand

Technological improvements generally increase TFP and shift labour demand outward, though effects may differ for skilled and unskilled workers.

Skill-Biased Technological Change

• Recent changes have increased productivity of skilled workers more than unskilled

• Wage inequality has grown, especially among males

Summary Table: Labour Market Statuses and Flows

Additional info: Table summarizes monthly flows between employment states in Canada, illustrating labour market dynamics.