6. Consider these two utility functions: U(x, y) = ln(x)+ln(y) and U(x, y) (xy) 0.5. If...

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6. Consider these two utility functions: U(x, y) = ln(x)+ln(y) and U(x, y) (xy) 0.5. If two utility functions are equivalent, then the demand functions derived from them are identical. Two utility functions are equivalent if you can transform one of them and get the other one. The transformation must be performed by a function that transforms one set of numbers into 1 another set without changing their order. So, for example, the square function could be used, because it does not change the order of numbers that are squared (as long as the numbers are not negative). If w is larger than Z then w is larger than 22. These kinds of transformation are called monotonic transformations. (a) Demonstrate these utility functions are equivalent using monotonic transformations. (b) Demonstrate that two utility functions' equivalence directly by de- riving their demand functions. 7. The Lump Sum Principle: Suppose that the government subsidizes hous- ing expenditures of low-income families by providing a dollar-for-dollar subsidy to a family's housing expenditure. The Marschkes qualify for this subsidy and spend a total of $500 per month on housing: they spend $250 of their own and receive a government subsidy of $250. Recently, a new policy has been proposed that would provide each low income family with a lump sum transfer of $250 which can be used for housing or other goods. Using a graph, demonstrate whether the Marschkes would prefer the cur- rent program, the proposed program, or would be indifferent between the two. Please draw clearly. 6. Consider these two utility functions: U(x, y) = ln(x)+ln(y) and U(x, y) (xy) 0.5. If two utility functions are equivalent, then the demand functions derived from them are identical. Two utility functions are equivalent if you can transform one of them and get the other one. The transformation must be performed by a function that transforms one set of numbers into 1 another set without changing their order. So, for example, the square function could be used, because it does not change the order of numbers that are squared (as long as the numbers are not negative). If w is larger than Z then w is larger than 22. These kinds of transformation are called monotonic transformations. (a) Demonstrate these utility functions are equivalent using monotonic transformations. (b) Demonstrate that two utility functions' equivalence directly by de- riving their demand functions. 7. The Lump Sum Principle: Suppose that the government subsidizes hous- ing expenditures of low-income families by providing a dollar-for-dollar subsidy to a family's housing expenditure. The Marschkes qualify for this subsidy and spend a total of $500 per month on housing: they spend $250 of their own and receive a government subsidy of $250. Recently, a new policy has been proposed that would provide each low income family with a lump sum transfer of $250 which can be used for housing or other goods. Using a graph, demonstrate whether the Marschkes would prefer the cur- rent program, the proposed program, or would be indifferent between the two. Please draw clearly.

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6 a To demonstrate that the utility functions Ux y lnx lny and Ux y zy05 are equivalent using monotonic transformations we can apply the exponential function to the second utility function Applying th... View the full answer