Question

Furiosa has individual preferences for gasoline (G) and water (W), which can be represented by the...

Furiosa has individual preferences for gasoline (G) and water (W), which can be represented by the following utility function: U(G,W) = 7G4W5 + 31.9

Furiosas budget line can generally be written as I=pgG+pwW. Find Furiosas demand for gasoline as a function of income and prices. Put another way, what is G*(I,pg,pw)?
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Answer #1

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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