Appendix 2 – Calculation of GDP per hour
Let 
be hours worked per week, and 
the hourly wage of employed people in age-sex group 
, as shown in Table 3. Let 
be GDP per hour of employed people in age-sex group , the first quantity we are trying to find. We assume that
(1) 
where 
is an unknown constant. Let 
be the number of employed people in age-sex group in 2001, as shown in the first two columns of Table 2. Let 
be GDP in 2001, which was $120,509 million, according to the Statistics New Zealand (series SNCQ.S1NB15). By definition,
(2) 
(where the 52 appears because there are 52 weeks in the year.)
Substituting in Equation 1 gives
(3) 
which can be solved to give an equation for ,
(4) 
and hence an equation for ,
(5) 
Let 
be the imputed GDP per hour, and 
the imputed hourly wage, of people not currently in employment. We simply assume that
(6) 
