Joe Grad has just arrived at the big U. He has a fellowship that covers his tuition

Question:

Joe Grad has just arrived at the big U. He has a fellowship that covers his tuition and the rent on an apartment. In order to get by, Joe has become a grader in intermediate price theory, earning $100 a month. Out of this $100 he must pay for his food and utilities in his apartment. His utilities expenses consist of heating costs when he heats his apartment and air-conditioning costs when he cools it. To raise the temperature of his apartment by one degree, it costs $2 per month (or $20 per month to raise it ten degrees). To use air-conditioning to cool his apartment by a degree, it costs $3 per month. Whatever is left over after paying the utilities, he uses to buy food at $1 per unit.

(a) When Joe first arrives in September, the temperature of his apartment is 60 degrees. If he spends nothing on heating or cooling, the temperature in his room will be 60 degrees and he will have $100 left to spend on food. If he heated the room to 70 degrees, he would have ________ left to spend on food. If he cooled the room to 50 degrees, he would have ________ left to spend on food. On the graph below, show Joe’s September budget constraint (with black ink).

(b) In December, the outside temperature is 30 degrees and in August poor Joe is trying to understand macroeconomics while the temperature outside is 85 degrees. On the same graph you used above, draw Joe’s budget constraints for the months of December (in blue ink) and August (in red ink).

(i) His favorite temperature for his apartment would be 65 degrees if it cost him nothing to heat it or cool it.

(ii) Joe chooses to use the furnace in December, air-conditioning in August, and neither in September.

(iii) Joe is better off in December than in August.

(d) In what months is the slope of Joe’s budget constraint equal to the slope of his indifference curve? _________.

(e) In December Joe’s marginal rate of substitution between food and degrees Fahrenheit is -____In August, his MRS is ______

(f) Since Joe neither heats nor cools his apartment in September, we cannot determine his marginal rate of substitution exactly, but we do know that it must be no smaller than -_____. and no larger than 3.