2.1 The Production Sector In each region a representative firm produces at time a single good using a j, t Cobb-Douglas technology. The firm hires labour and rents physical capital. Both factors are region specific. With representing output, physical capital, effective units of labour, a scaling factor and the share of physical capital in value added, a region A specific production function is: (1) Firms are assumed to be perfectly competitive and factor demands follow from profit maximization: (2) (3) where and are the rental rates of capital and wages, and is the output price. Labour is distinguished by four skill levels, high-skilled, medium-skilled and workers, plus non-working individuals denoted by the binary index of skills Therefore, firms also disaggregate their demand for labour into a demand qual. Lj,t for skills based on a constant-elasticity-of-substitution (CES) function: (4) where is the wage rate for a specific type of skills, and and are respectively wqual share of skill levels and substitution-elasticity parameters. It follows from optimization that the wage rate of the labour input is composite firm’s aggregate related to market wages by the following expression: wqual (5) 2.2 Household Behaviour
2.1 The Production Sector In each region j, a representative firm produces at time t a single good using a Cobb-Douglas technology. The firm hires labour and rents physical capital. Both factors are region specific. With representing output, physical capital, effective units of labour, A a scaling factor and the share of physical capital in value added, a region specific production function is: (1) Firms are assumed to be perfectly competitive and factor demands follow from profit maximization: (2) (3) where and are the rental rates of capital and wages, and is the output price. Labour is distinguished by four skill levels, high-skilled, medium-skilled and workers, plus non-working individuals denoted by the binary index of skills qual. Therefore, firms also disaggregate their demand for labour Lj,t into a demand for skills based on a constant-elasticity-of-substitution (CES) function: (4) where wqual is the wage rate for a specific type of skills, and and are respectively share of skill levels and substitution-elasticity parameters. It follows from optimization that the composite wage rate of the firm’s aggregate labour input is related to market wages wqual by the following expression: (5) 2.2 Household Behaviour