Appendix A - The Simulation Model
Firms
A representative firm produces output of a single good according to a Cobb-Douglas production function. Output, Y, in period j is given by
where A is a constant exogenous technology parameter,[14] Kj is the capital stock, and Lj is aggregate labour consisting of the sum of the labour of all generations: 
where Li,j is the labour of workers of age i in year j.
The optimal capital stock, Kj, is determined by the first order condition that the marginal product of capital (net of depreciation, δ) is equal to the cost of capital, rj.
That is, 
, which gives
And investment, Ij, is given by
Competitive firms equate the price of labour, wj, to the marginal product of labour:
The wage of each worker is given by
where wi,j is the wage of a worker of age i in year j, αi is a weight equal to the wage for age i divided by the average of wages for all age groups which are given by the data.
Notes
- [14]The technology parameter is constant, implying zero technical progress. The reason, as also given in Kulish et al. (2006), is that the leisure to consumption ratio would eventually decline to zero with continual productivity-induced rises in real wages. See Auerbach and Kotlikoff (1987) for a further discussion. It would be possible to specify a non-standard utility function that could deal with this problem in the presence of technical progress, but this is not pursued here.
