Luis is a fan of loud music that he plays on his stereo system. His utility function is defined by equation:

U(q, y) = 10q − 1/2q^2 + y

where q is the number of hours of music he plays, and y is his consumption of all other goods. Each hour of music he plays costs him $2 in electricity, but his income is large enough that he could always afford to play music 10 hours a day if he so wished.

(a) Find Luis’ demand for hours of music as a function of the price of electricity

(b) Luis has a roommate, Maria, who has the same utility function as Luis. She doesn’t have a stereo system, nor does she pay the electricity bill, but she listens to the music. How many hours of music maximizes social surplus?

(c) Maria moves out, and Gordon moves in with Luis. Gordon’s utility function is defined by the equation:

U(q, y) = −2q − 1/2q^ 2 + y Now which allocation maximizes total surplus, and what (Pigouvian) tax/subsidy enables this allocation to be attained?