A city with too many patricians won't have enough workers. Don't devote all of your effort to encouraging patrician villas. If you're too successful, your labor force might shrink too quickly. Remember, patricians don't work. When you do see patrician villas replacing plebeian apartments, check in with your Labor Advisor. If you have a shortage of workers, create new low-income housing before lack of services makes the new villas devolve back to plebeian housing.
In times of labor shortage, tell your Trade Advisor to temporarily turn off any farms or industries that have built up surpluses. This frees up workers for other sectors with more immediate labor needs, and buys you some time to attract new immigrants. Don't forget to turn the industries back on when immigrants start to arrive!
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