Exercises: Labour demand, labour supply and wage determination

Explain why the demand curve for labour is downward sloping and the supply curve of labour is upward sloping. Refer to the hourly wage rate on the vertical axis and the number of workers on the horizontal axis.

In a Galway town, the weekly demand and supply for part-time shop assistants are given by $Q_d = 600 - 20W$ and $Q_s = 100 + 30W$, where $W$ is the hourly wage in euro and $Q$ is the number of workers.

1. a) Calculate the equilibrium hourly wage.

1. b) Calculate the equilibrium number of workers employed.

State which of the following would shift the demand curve for labour and which would shift the supply curve of labour in the Irish construction sector, and state the direction of the shift in each case:

1. a) A boom in demand for new houses.

1. b) More people qualify as electricians through apprenticeships.

1. c) Workers return to Ireland from Australia and enter the labour force.

1. d) The price of the houses being built rises.

The labour market for hospitality workers in Killarney is described by $Q_d = 900 - 40W$ and $Q_s = 200 + 30W$, where $W$ is the hourly wage in euro and $Q$ is the number of workers.

1. a) Find the equilibrium wage and employment.

1. b) A fall in tourist numbers reduces demand to $Q_d = 690 - 40W$. Find the new equilibrium wage and employment.

1. c) Calculate the change in total hourly wage bill (wage × employment) between the two equilibria.

A Cork firm hires labour in a competitive market at a wage of €15 per hour. Each worker produces output that sells at €5 per unit. The marginal physical product (MPP) of each additional worker is: worker 1: 8 units, worker 2: 7, worker 3: 6, worker 4: 5, worker 5: 4, worker 6: 3 (units per hour).

1. a) Calculate the marginal revenue product (MRP) of each worker.

1. b) How many workers will the firm hire? Explain your answer.

1. c) If the wage rises to €20, how many workers will the firm hire?

Explain how each of the following would affect the equilibrium wage and employment of software developers in Dublin. Use a labour market diagram described in words.

1. a) The Government increases the number of university places in computer science, with the effect appearing five years later.

1. b) A large multinational technology company opens a new European headquarters in Dublin.

1. c) Both (a) and (b) occur together. What can you say with certainty and what is uncertain?

A firm in Limerick sells its output in a perfectly competitive market at €10 per unit. Its marginal physical product of labour is $MPP = 20 - 2L$, where $L$ is the number of workers. The wage is €40 per hour.

1. a) Derive the firm's MRP schedule and explain why it is the firm's demand curve for labour.

1. b) Calculate the profit-maximising number of workers.

1. c) The price of output falls to €5. Calculate the new number of workers hired and comment on the link between product demand and labour demand (derived demand).

1. d) Explain why the market demand curve for labour may be less than the sum of individual firms' demand curves when all firms in the industry change output.

Demand for nurses in a region is $Q_d = 5{,}000 - 50W$ and supply is $Q_s = 1{,}000 + 50W$, where $W$ is the hourly wage in euro.

1. a) Calculate the equilibrium wage and employment.

1. b) Calculate the wage elasticity of labour demand at equilibrium and interpret it.

1. c) The Government wishes to raise nurse employment to 3,500. Calculate the wage that would be needed on the supply side and discuss whether a wage subsidy or a training programme is more appropriate. Justify your answer.

Evaluate the view that "automation will reduce wages for all workers in Ireland". In your answer, use labour demand and supply analysis, distinguish between low-skilled and high-skilled labour, and refer to the concepts of substitutes and complements in production and to the elasticity of labour demand.