It is January, and Joe Grad, whom we met in Chapter 5, is shivering in his apartment when the phone rings. It is Mandy Manana, one of the students whose price theory problems he graded last term. Mandy asks if Joe would be interested in spending the month of February in her apartment. Mandy, who has switched majors from economics to political science, plans to go to Aspen for the month and so her apartment will be empty (alas). All Mandy asks is that Joe pay the monthly service charge of $40 charged by her landlord and the heating bill for the month of February. Since her apartment is much better insulated than Joe’s, it only costs $1 per month to raise the temperature by 1 degree. Joe thanks her and says he will let her know tomorrow. Joe puts his earmuffs back on and muses. If he accepts Mandy’s offer, he will still have to pay rent on his current apartment but he won’t have to heat it. If he moved, heating would be cheaper, but he would have the $40 service charge. The outdoor temperature averages 20 degrees Fahrenheit in February, and it costs him $2 per month to raise his apartment temperature by 1 degree. Joe is still grading homework and has $100 a month left to spend on food and utilities after he has paid the rent on his apartment. The price of food is still $1 per unit.
(a) Draw Joe’s budget line for February if he moves to Mandy’s apartment and on the same graph, draw his budget line if he doesn’t move.
(b) After drawing these lines himself, Joe decides that he would be better off not moving. From this, we can tell, using the principle of revealed preference that Joe must plan to keep his apartment at a temperature of _________.
(c) Joe calls Mandy and tells her his decision. Mandy offers to pay half the service charge. Draw Joe’s budget line if he accepts Mandy’s new offer. Joe now accepts Mandy’s offer. From the fact that Joe accepted this offer we can tell that he plans to keep the temperature in Mandy’s apartment ____.