Rachel Spends Her Income,Y,on Rock Shows (R)and Sunglasses (S)with Prices

Rachel spends her income,Y,on Rock Shows (R)and Sunglasses (S)with prices pR and pS.Rachel's preferences are given by the Cobb-Douglas utility function
U(X,Y)= R.⁸S.²
a.Write out the Lagrangian for Rachel's utility-maximization problem.
b.Use the Lagrangian to derive Rachel's optimal choice,(R*,S*).
c.For a given utility level,U₀,derive Rachel's Expenditure function E(pR,pS,U₀).
d.Use the Expenditure function to derive Rachel's compensated demand for Rock Shows.

Correct Answer:

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a.The Lagrangian is
L = R.⁸S.² + [Y - pR...

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