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PLEASE COMPLETE THE ANSWER :)
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IV. Utility Maximization 11 You spend your entire income on two goods, good 1 and good 2. Your preferences are represented by the utility function U = 2x1 + 4x20.5 for X1 > 0 and x2 > 0. 1. Using the necessary conditions and the above information, write the two first-order conditions that your choice of xl and x2 must satisfy to maximize your utility. (Note: You are not being asked to solve for xl and x2in this question.) 2. Use your results in part 1 to find your Marshallian demand functions for the two goods. Simplify your answers. You do not need to show that the soc for a maximum utility is satisfied. 3. What values of pı will ensure that the quantity demand of good 1 is positive? 4. Let t be the proportion change in all prices and income. Demonstrate that your Marshallian demand functions for the two goods are homogeneous of degree 0 in prices and income. 5. Is good 1 normal or inferior? How about good 2? Show the basis for your answer. 6. Find your indirect utility function. Simplify your answer. 7. Find you expenditure function. Show and briefly discuss how you arrived at your answer. 8. Use Shephard's Lemma to find your Hicksian demand functions for the two goods.
IV. Utility Maximization 11 You spend your entire income on two goods, good 1 and good 2. Your preferences are represented by the utility function U = 2x1 + 4x20.5 for X1 > 0 and x2 > 0. 1. Using the necessary conditions and the above information, write the two first-order conditions that your choice of xl and x2 must satisfy to maximize your utility. (Note: You are not being asked to solve for xl and x2in this question.) 2. Use your results in part 1 to find your Marshallian demand functions for the two goods. Simplify your answers. You do not need to show that the soc for a maximum utility is satisfied. 3. What values of pı will ensure that the quantity demand of good 1 is positive? 4. Let t be the proportion change in all prices and income. Demonstrate that your Marshallian demand functions for the two goods are homogeneous of degree 0 in prices and income. 5. Is good 1 normal or inferior? How about good 2? Show the basis for your answer. 6. Find your indirect utility function. Simplify your answer. 7. Find you expenditure function. Show and briefly discuss how you arrived at your answer. 8. Use Shephard's Lemma to find your Hicksian demand functions for the two goods.