Suppose a household has the following lifetime utility function: U = c1/2 + ẞc¹/2t+1 A) Find expressions for the partial derivatives of lifetime utility, U, with respect to period t and period t+1 consumption. Is marginal utility of consumption in both periods always positive? B) Find expressions for the second derivatives of lifetime utility with respect to period t and t+1 consumption, i.e., a 2 and 320_Are these second derivatives always negative for aede any positive values of period t and t+1 consumption? C) Derive an expression for the indifference curve associated with lifetime utility level U. (i.e., derive an expression for C++1 as a function of U, and c). What is the slope of the indifference curve? How does the magnitude of the slope vary with the value of c
Suppose a household has the following lifetime utility function: U = c1/2 + ẞc¹/2t+1 A) Find expressions for the partial derivatives of lifetime utility, U, with respect to period t and period t+1 consumption. Is marginal utility of consumption in both periods always positive? B) Find expressions for the second derivatives of lifetime utility with respect to period t and t+1 consumption, i.e., a 2 and 320_Are these second derivatives always negative for aede any positive values of period t and t+1 consumption? C) Derive an expression for the indifference curve associated with lifetime utility level U. (i.e., derive an expression for C++1 as a function of U, and c). What is the slope of the indifference curve? How does the magnitude of the slope vary with the value of c
Chapter4: Utility Maximization And Choice
Section: Chapter Questions
Problem 4.3P
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