The town of Dogville, where twenty-some men, women, and children all live and struggle together in poverty and depression. Major factors of their difficult and dull lives are the minimalist set design and bleak lighting. But what showed me that they were living in poverty was the costume design. Classic Great Depression chic, with raggedy pants and skirts, dirty button-downs and blouses, and broken down shoes to bring it all together. Fashion and shopping aren't a priority of a citizen of Dogville, mostly because it isn't necessary.
When Grace, a fugitive on the run from her mobster father, stumbles her way into town she is dressed in a high-end fur coat, heels, jewelry, and makeup. This helps to show that she is an outsider in the town, and doesn't belong there. Grace is allowed to stay for two weeks to prove she is worth their while. She performs manual labor and numerous jobs for the townspeople, all in her aristocratic getup. Not until she has fully become a member of the community that she changes into the common rags of the women, which is so in that season.
The costume design in Dogville is a representation of how these people live and what they worry about. The women are more preoccupied with keeping the town maintained and raising the children than to go on a shopping spree, considering that most of the residents have never left the town. The men are too busy with bringing in some sort of income and utilizing Grace to all their "needs" to go out and buy a new pair of slacks. Clothing is a material to keep them warm and covered up, not much else. Even Grace becomes dirty and unkept as her stay in the town progresses.
After being sodomized and tortured, Grace is given a few days off. She decides to wash herself and her clothes, which the other residents don't do very often or at all. She finally has time to take care of herself and not being used for other peoples' tasks and games. Grace is still a member of the higher class back home, and her personality shows that at times. This decision to clean herself shows us that she is still the same Grace as she was the night she showed up in this hell-hole of a town.
When the mobsters and Grace's father show back up in the town square, Grace is dressed back into her fur and heels, fitting in well with her father's suit and hat. The moment she is back into her own outfit, Grace is once again not just a lone wolf mentally, but also physically. The costume design in Dogville may not seem like a big contribution to the film's mies-en-scene, but since it fits with the simplistic production design and overall aesthetic of the film, I would say it is a very important part.