A university has a small dorm with four rooms, in which three sophomores, A, E, and J, and a freshman, C, are residing. Not being equipped with gas/electricity meters for individual rooms, the dorm has charged each resident $20/month for the heating cost in lump sum manner during winter. The total payment of $80/month covers only a half of the full heating cost; the university has subsidized the dorm to cover the remainder. However, the university, facing tight budget, decides to abolish this subsidy starting next month and so the dorm is in need for some measures to avoid deficits.

There are potentially better ways to sustain the budget of the dorm than simply charging extra $20/month each, since residents can reduce total heating cost by lowering the preset room temperatures. Room temperature can be individually adjusted by each resident and, we assume that, dorm director can fully monitor preset temperature of each room. Moreover, when residents are chilled, new sweatshirts, upon purchase, will protect them against the cold. A sweatshirt costs $10. Residents are heterogeneous in terms of liquidity (cash reserves in hand) and each resident may or may not have enough cash to buy her own sweatshirt.

Unfortunately, the residents are not unified. The followings are the remarks by the residents in the recent round table discussion.

A: I cannot think of adjusting the room temperature, which is just comfortably set for me. Summer or winter, I grow up wearing T-shirt only in home; my long-sleeves are for outside use only. I have strong desire to light-clothing in home and so it does not make sense to buy a sweatshirt

E: I am ready to reduce the preset temperature in my room. I hope that the others show such commitments too. I am also keen to discuss and negotiate more individually.

J: I am fine to set an ambitious temperature target of my room. I should be able to handle it well with a thermal blanket which is stored in the closet now. However, this should not be a unilateral measure because it allows free riders. We must work together to reduce the total heating cost.

C: I get hot easily. Moreover, mine is a sun-flooded room on the second floor. I believe that the heating cost of my room is not as high as others. In addition, unlike others, I was not a beneficiary of the university's subsidy last year. Three sophomores are primarily responsible for the temperature cut and cost reduction.

You, as an agent for the dorm director, have advisory authority for this matter. Propose a plan to sustain the dorm's budget, while taking the circumstances and remarks as given. Describe how your plan works for each of the residents and explain how you mediate and convince them. When you need further assumptions for accurate reasoning, explicitly mention them.