An individual has the utility function: U(x1,x2,x3) = ln x1 + ln x2 + 0.5ln x3....

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An individual has the utility function: U(x1,x2,x3) = ln x1 + ln x2 + 0.5ln x3....

An individual has the utility function: U(x₁,x₂,x₃) = ln x₁ + ln x₂ + 0.5ln x_3. The price of good x₁ is p_1, the price of good x₂ is p₂ = 1 and the price of good x₃ is p3. The individual’s income is I. Derive the Marshallian demand functions (x₁* , x₂*, x₃* ).

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Answer 1

Answer #1

The utility function is given as , and the budget constraint is . The Lagrangian function would be as . The FOCs would be as below.

or or or or .

or or or .

Comparing the first two FOCs, we have or or , and comparing the second and third FOC, we have or , which are the required utility maximizing combination of goods.

Since , we have or .

Putting it in the last FOC, we have or or or , and since and , we have and or and or and .

Hence, the Marshallian demand functions are .

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Answer 2

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An individual has the utility function: U(x1,x2,x3) = ln x1 + ln x2 + 0.5ln x3....

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An individual has the utility function: U(x1,x2,x3) = ln x1 + ln x2 + 0.5ln x3....