Atticus really doesn't discuss the economy with his children much in the story (as was the case with most parents of the time). But Maycomb was hit particularly hard by the Great Depression because, according to Atticus,
... professional people were poor because the farmers were poor. As Maycomb county was farm country, nickels and dimes were hard to come by for doctors and dentists and lawyers.
Atticus often accepted trade for his services, as in the case of Walter Cunningham. Cunningham had no money since his farm land "was mortgaged to the hilt." Dr. Reynolds often accepted "a bushel of potatoes for the delivery of a baby."
Atticus seemed to supply his children with the necessities of life, but there is little evidence that they were spoiled with excessive gifts like the ones Dill received from his parents. However, they never complained about the things they didn't have, either. The family never ate at restaurants (assuming Maycomb had any) and there was no movie theatre or other entertainment distractions on which to spend money in the sleepy little town. Most of the Finch's neighbors seem to live fairly comfortably, but few of them work, so we can only assume that their homes are paid for. The children received gifts at Christmas and on birthdays, but little else is said about Atticus' own expenditures; he is able to afford Calpurnia, who probably receives a fair wage. When Tom Robinson's supporters shower Atticus with gifts of food following the trial, he tearfully told Calpurnia that they must desist.
... tell them they must never do this again. Times are too hard...