(b) Show how technological progress might affect the labour market in this model.
(a) The labour market, in the classical theory, does not work differently from any other market. The quantity of the good under examination (labour) is a function of its price: the real wage. Real because there is no money illusion: employers (employees) are only interested in the real cost (purchasing power) of the wage. Equilibrium exists where the upward-sloping supply curve meets the downward sloping demand curve.
Employers derive labour demand from the production function. Total production is determined by the amount of capital and labour employed, and by the technology used. Assuming for the moment capital and technology to be fixed, we can represent output as a function of labour as in figure 14.1 (a). From the production function we now derive the marginal productivity of labour - figure 14.1 (b) - which is downward sloping because, by employing one more unit of labour, total output increases but less than proportionally.
Since marginal productivity of labour (MPL) represents the increase in production that firms get from using one more unit of labour, employers decide to hire an extra worker if and only if the extra revenue that they get (marginal revenue) is at least equal to the extra cost (marginal cost): when MPL is equal to the real wage (wage / price).
Marginal Revenue = Marginal Productivity of Labour x Price
Marginal Cost = Wage
Firms hire workers until profits are maximised: Marginal Revenue = Marginal Cost
Therefore: MPL x Price = Wage
or: MPL = Real Wage
If the real wage goes up from (w/p)0 to (w/p)1 firms will reduce the quantity of labour demanded from L0 to L1.
Supply of labour is derived from the analysis of how individuals decide to spend their time between labour and leisure. Since the wage rate is the opportunity cost of leisure, an increase in the real wage raise the cost of not working. Therefore, individuals would decide to supply more labour and to substitute away from leisure: the supply curve is upward sloping.
Since leisure also has a psychological and social 'remuneration', although not economic, the response of each individual to increases in the real wage is more complex and could also lead to a downward sloping supply curve: if your wage went up to £1,000,000 per hour, you would probably supply only one hour of work per week or per month, (decreasing labour supply) and dedicate the rest of the time to leisure activities. Unfortunately, this eventuality is rare and, for the sake of simplicity, the classical model considers only the upward sloping part of the supply curve (figure 14.1 - b).
(b) Technological progress implies the introduction of new machines capable of producing more output per unit of time and labour. In figure 14.1 (a), the production function, after a technological breakthrough, shifts upwards. The effect on the labour