U(G,W) = 7G4W5 + 31.9
MUG = U/G = 28G3W5
MUW = U/W = 35G4W4
MRSG,W = MUG/MUW
= 28G3W5/35G4W4
= 4W/5G
At Optimal choice
MRSG,W = Pg / Pw
4W/5G = Pg /Pw
W = (Pg /Pw)(5G/4)
Budget line
PgG + PwW = I
Put W = (Pg /Pw)(5G/4) in budget line
PgG + PwW = I
PgG + Pw(Pg/Pw)(5G/4) = I
PgG + 5PgG/4 = I
(4PgG + 5PgG)/4 = I
9PgG/4 = I
9PgG = 4I
G = 4l/9Pg
Demand function for gasoline is
G*(I,Pg,Pw) = 4I/9Pg
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