Monetary policy - a long post
This is quite a long post on monetary policy. I can't suggest what Canada or Quebec would or should do but I can list the options.
From the ECB's website:
The ECB is the central bank for Europe's single currency, the euro. The ECB’s main task is to maintain the euro's purchasing power and thus price stability in the euro area. The euro area comprises the 15 European Union countries that have introduced the euro since 1999.
The ECB is a joint operation between the 15 EU nations that use the Euro and sets its monetary policy taking into account the interests of those nations. Things like inflation are calculated across the entire 15 nations. Other countries use the Euro but aren't necessarily included in the statistics that are used to determine monetary policy.
If Quebec obtained independence then three things could happen.
1) Canada could set monetary policy taking into account only the interests of Canada. Independent Quebec could issue its own currency and set its own monetary policy according to its needs.
2) Canada could set monetary policy according to its own needs. Independent Quebec could use the Canadian dollar but wouldn't have any say in Canadian monetary policy. If Canada sets interest rates higher than Quebec would like then Quebec's economy suffers. If Canada sets interest rates lower then Quebec risks an overheating economy and excess inflation.
3) The current situation could continue. Interest rates are set taking into account the interests of both Canada and Quebec - the two countries would be treated as one big economy. Occassionally interest rates would be out of sync with Quebec (just as they could be today) but less so than if Quebec was excluded from the economic statistics. Conversely, Canada would have to accept that sometimes monetary policy would be 'wrong' for Canada.
A Quebec currency tied to a basket of the US, Canadian (and maybe Euro) currencies is similar to option 2 but Quebec gets some of the flexibility of option 1 by being able to adjust the basket.
Would Canada accept the loss of soveriegnty that sharing monetary policy with Quebec would entail? Would the Canadian people want to suffer unnecesarily high interest rates or unnecesarily high inflation?
This issue has come up between New Zealand and Australia. Australia would let New Zealand use the Australian dollar but isn't prepared to let New Zealand have a say in monetary policy. New Zealand would consider adopting the Australian dollar but only if it gets a say.