How are each of the seven deadly sins demonstarted in the story?
Prince Prospero exhibits the deadly sin of pride. Despite the fact that his country has lost half its inhabitants, he thinks that, because of his wealth and resources, he will be able to protect himself from the plague sweeping the kingdom:
When his dominions were half depopulated, he summoned to his presence a thousand hale and light-hearted friends from among the knights and dames of his court, and with these retired to the deep seclusion of one of his castellated abbeys.
They weld the gates shut so that no one can get in or out. "With such precautions, [he believed,] the courtiers might bid defiance to contagion." He proudly thinks that, even when others cannot, he can escape death. He is, of course, wrong. I think we can also use this example to demonstrate his greed. Rather than stay and try to help his countrymen as best he can, and as a good leader ought, Prospero cares only about saving his own life and the lives of his friends. He feels that "The external world can take care of itself." He cares about his own, and that's it.
While the disease rages on outside the abbey, those inside feel "[...] it was folly to grieve or to think." This sounds a lot like sloth. The Prince is quite reluctant to make any effort to help his kingdom, and he is happy to hide out in his well-stocked fortress. His unwillingness to help and his ability to sit back and do nothing while his kingdom is decimated is quite slothful.
Further, in that "amply provisioned" abbey,
The prince had provided all the appliances of pleasure. There were buffoons, there were improvisatori, there were ballet-dancers, there were musicians, there was Beauty, there was wine.
This sounds like gluttony. The courtiers certainly indulge heartily while they dance and eat and drink without regard for much of anything else.
The human "dreams" that stalk the rooms at least provide the suggestion of lust.
There were much glare and glitter and piquancy and phantasm [...]. There were arabesque figures with unsuited limbs and appointments. There were delicious fancies such as the madman fashions. There were much of the beautiful, much of the wanton, much of the bizarre, something of the terrible, and not a little of that which might have excited disgust.
The use of the word "wanton," especially, hints at the lustiness of the scene.
When the Prince first spots the Red Death masked figure at the party, he cowers from it. However, then, "Prince Prospero, maddening with rage and the shame of his own momentary cowardice, rushed hurriedly through the six chambers [...]. He bore aloft a drawn dagger [...]." In other words, his fear turned to terrible rage––or anger––when he is faced with the possibility of his own demise.
Envy is tough. Perhaps it is, like lust, hinted at only. The Prince believes himself to be quite powerful, as I mentioned when discussing pride, and the one thing in the story more powerful than he is Death itself. Perhaps, then, if his prideful attempt to thwart death is one side of the coin, envy of Death's power is the other side.
One could easily align the color of each of the seven rooms in Poe's "The Masque of the Red Death" with the seven deadly sins. (This being said, remember that reader-response is how one aligns imagery with other ideas. What this means is that a reader justifies a text through their own filter and lens and makes judgements based upon their own understanding and beliefs.)
1. Blue- Gluttony- Gluttony is where one consumes more than the person requires to survive, or even live comfortably. The color blue can represent the vastness of the sky. Therefore the vastness of the sky represents the vastness of one who is gluttonous.
2. Purple-Pride- The color purple has been historically used to represent royalty. Here, a person who is prideful rejects God's grace and only raises up him/herself.
3. Green- Envy- The representation of one being envious as historically stated "green with envy."
4. White- Sloth- Represented by the color white because white is void of color and a person who is considered a sloth does nothing.
5. Orange- Lust- Orange, as a derivative of red, can be used to represent lust. When one is lustful, they tend to become red-hot: skin will flush, temperature will rise, and they (sometimes) will be unable to control the physical desires of the body.
6. Violet- Anger- Here one can refer back to the fact that some physically turn violet with anger. The color ones face takes on when angry can resemble the color violet.
7. Black- Greed- Greed can be represented by the color black given the pit it will put people in based upon their ignoring of God. Like pride, one can only become greedy when ignoring the fact that God will provide. A person filled with greed is not satisfied with the necessitates. Instead, the person takes from others so that they can have more.