Three

roommateslong dash$$Tinker$,$

$$Evers$,$ and

Chancelong dash$$share

an apartment. It is really cold outside and they are considering turning up the thermostat in the apartment by$1,2,3,$ or $4$ degrees. Their individual marginal benefits from making it warmer in the apartment are as$$ follows:

Tinker

Evers

Chance

$1$ degree

$$$$1515$

$$$$1212$

$$$$99$

$2$ degrees

$$$$1212$

$$$$99$

$$$$66$

$3$ degrees

$$$$99$

$$$$66$

$$$$33$

$4$ degrees

$$$$66$

$$$$33$

$$$$0$

Part $2$

They know that each time they raise the temperature in the apartment by $1$ degree, their heating bill goes up by

$$$$3030.$

Part $3$

To maximize social$$ benefit, they should raise the temperature by

$$

$$

$1$ degree

$3$ degrees

$2$ degrees

$4$ degrees

$.$