Cobb-Douglas utility function
Let the utility function be
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Let the price of good xbe pand the price of good ybe qand the income be I.
Applying the method of Lagrange multiplier, find the utility maximizing consumption bundle (x∗,y∗).
Also determine the value of Lagrange multiplier λ∗.
2. Quasi-linear utility function
Let the utility function be
u(x,y)=x+0.1lny.
Let the price of good xbe $1per unit and the price of good ybe $pper unit and the income be I.
Applying the method of Lagrange multiplier, find the utility maximizing consumption bundle (x∗,y∗).
Also determine the value of Lagrange multiplier
Hint: It is useful to note that dlnydy=1y.
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