What would a control variable be for the population distribution in canada?

I don't understand control variables, I am doing a study on population distribution in canada and I don't understand what a control variable for that would be..|||Population distribution can be measured by the rate of job development and the amount of immigration and the birth and mortality rates. So if we were to try to determine the optimal immigration needed to meet the job growth rate due to an improving economy and a diminished birth rate and and increased mortality rate we would need to use a control variable



Thus using immigration rate as the control variable we can make a mathematical equation that can help us determine the optimal immigration policy that politicians would need to implement to keep the Canadian economy functioning effectively across all age groups.



Optimum control (or immigration) policies corresponding to the target sets where



T1= [xm, xM] = [ 2.8 x 10^7, 2.9 x 10^7 ]



and



T2 = [xm, xM] = [ 2.9 x 10^7, 3.0 x 10^7]



respectively showing the detailed transition from high to low immigration rates. Note that the immigration rate corresponding to the target set T2 remains at its maximum admissible value

for a longer period of time compared to that of target set T1 because the lower and the upper boundaries of the set T2 are above those of T1.



It appears from this result that optimum immigration policy is to keep the immigration rate

(actual number = rate x X2) at its highest admissible level during the early period of the planning horizon and then rapidly reduce to zero. This translates into maximum 500,000 (approximately) annually during the early period. In control theory this kind of phenomenon is known as bang-bang control. This shows that once the lower limit of the target set is met there is no reason for

further immigration unless humanitarian concerns are added to our cost function. This is entirely due to the population goal and the maximum immigration rate used in our example. If there is no specified target, we have already seen at the beginning of this subsection that population will continue to increase with the increase of immigration rate.



This is because the target is far from the initial population and the error is large which encourages maximum admissible immigration rate for reaching the lower boundary as quickly as possible. The speed of approach is dependent on the maximum admissible immigration rate uM. Once the total population exceeds the lower boundary, the growth slows down and the optimum immigration policy seems to maintain the population in the neighborhood of the target set. In contrast, if the population exceeds the upper boundary the optimum policy seems to pull it down by cutting down the immigration rate.



We conclude from these results that control theory provides a promising tool for determining the optimum immigration policy seeking specified targets. In fact one can add to the cost function as many factors as one desires, including humanitarian factors, to reflect the concerns of the society and use the optimization methodology proposed here to determine the optimum policy. This technique can be used by the Department of Immigration as an intelligent tool for determining the optimum immigration policy.





The question is what should be the intake rate (immigration rate) so as to satisfy the manpower demand and at the same time keep the unemployment rate low. In addition to humanitarian factors, it is reasonable to tie the immigration rate with availability of jobs and job creation rate. Otherwise one can expect many social and political problems.



We have demonstrated that by use of modern Systems and Optimal Control theory, it is possible to formulate optimum immigration and job creation strategies while maintaining population level close to certain pre-specified target sets.



Using the basic data (birth, death and transition rates etc.) from Stat.Canada, we found the

numerical results (population) based on our model in close agreement with the actual population.



Based on the model constructed above, we have formulated a control problem with the objective of reaching a specified population target set (fixed as well as variable) by use of immigration rate as the control variable. Optimal control theory is used to determine the optimum immigration policy as

illustrated by numerical results.