How is the wage rate determined in a perfectly competitive labour market?
Similar to a goods market, wage rate in a labour market is determined by the intersection of demand for labour and supply of labour. The rate at which the demand equals the supply is called the equilibrium wage rate. Corresponding hours of labour are demanded and supplied in the labour market at the equilibrium wage rate.
The demand for labour is derived from the value of marginal product of labour (VMPL). We know that a particular firm will employ labour up to a point where marginal cost of employing the last unit of labour hired equals the marginal benefit earned by the firm by hiring that unit of labour.
Labour is supplied by those households, who need to trade-off between working hours (labour) or leisure. The supply of labour is a positive function of wage up to a point beyond which the supply curve becomes backward bending supply curve.
The intersection of demand for labour and the supply of labour occur at the wage rate w. Here, the equilibrium takes place at E where DLDL equals SLSL and the equilibrium units of labour supplied and demanded is L.