2. Let U=U(x,y) be the utility function of the agent. x and y_represent the goods. Assume positive marginal utilities. Let Px, Py be the prices and I the income. a. State the agent's utility maximization problem. b. Present the Lagrangian function. c. Derive and interpret the first order condition. In your analysis, you must include the Lagrange multiplier. d. Present a graphical interpretation of the optimality condition (include indifferent curves and budget sets). 3 دیا e. Present the second-order condition and describe the conditions under which one could secure a maximum. f. Solve the previous questions but assuming: (i) U(x,y)=xy where a+b<1, (ii) U(x,y)=ax+by, (iii) U(x,y)=Min{x,y}. ax. apx g. Now, using the general formulation U=U(x,y), express the comparative-static derivative as the sum of income and substitution effects.
2. Let U=U(x,y) be the utility function of the agent. x and y_represent the goods. Assume positive marginal utilities. Let Px, Py be the prices and I the income. a. State the agent's utility maximization problem. b. Present the Lagrangian function. c. Derive and interpret the first order condition. In your analysis, you must include the Lagrange multiplier. d. Present a graphical interpretation of the optimality condition (include indifferent curves and budget sets). 3 دیا e. Present the second-order condition and describe the conditions under which one could secure a maximum. f. Solve the previous questions but assuming: (i) U(x,y)=xy where a+b<1, (ii) U(x,y)=ax+by, (iii) U(x,y)=Min{x,y}. ax. apx g. Now, using the general formulation U=U(x,y), express the comparative-static derivative as the sum of income and substitution effects.
Chapter3: Preferences And Utility
Section: Chapter Questions
Problem 3.13P
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