Question 6 (a) Jan.08.2024 Solve the utility maximization problem subject to px + qy = m,...

Transcribed Image Text:

Question 6 (a) Jan.08.2024 Solve the utility maximization problem subject to px + qy = m, where 0<a< subject to the budget constraint: x + aln in y (b) Suppose a consumer who can borrow or lend at an annual rate of interest r 20 anticipates receiving positive income y this year and y, next year. (The consumer ignores the future more than one year ahead.) The same consumer chooses the levels of consumption c, this year and c, next year in order to maximize the utility function: U(c₁, c₂) = In in c₂ + In In ln C₂ c₁ + ir (i) provide an economic interpretation for expressing y for money. 3₁ + 01:23 ||| 1 ir (ii) Write out the Lagrangian for the constrained maximization problem. 147 (iii) Show that the Lagrangian is concave as a function of (₁, ₂). (iv) Write out the first-order conditions for a constrained maximum. O id. 6989830 (Hint: think about time value Solving complete (7 marks) (2 marks) (v) Find the utility maximizing expenditures in both periods, as well as the Lagrange multiplier A, all as functions of the parameter triple (r, y₁, y₂) (2 marks) (5 marks) (4 marks) (6 marks) Question 6 (a) Jan.08.2024 Solve the utility maximization problem subject to px + qy = m, where 0<a< subject to the budget constraint: x + aln in y (b) Suppose a consumer who can borrow or lend at an annual rate of interest r 20 anticipates receiving positive income y this year and y, next year. (The consumer ignores the future more than one year ahead.) The same consumer chooses the levels of consumption c, this year and c, next year in order to maximize the utility function: U(c₁, c₂) = In in c₂ + In In ln C₂ c₁ + ir (i) provide an economic interpretation for expressing y for money. 3₁ + 01:23 ||| 1 ir (ii) Write out the Lagrangian for the constrained maximization problem. 147 (iii) Show that the Lagrangian is concave as a function of (₁, ₂). (iv) Write out the first-order conditions for a constrained maximum. O id. 6989830 (Hint: think about time value Solving complete (7 marks) (2 marks) (v) Find the utility maximizing expenditures in both periods, as well as the Lagrange multiplier A, all as functions of the parameter triple (r, y₁, y₂) (2 marks) (5 marks) (4 marks) (6 marks)

Answer rating: 100% (QA)

The image youve provided contains a series of questions related to utility maximization problems in economics Lets address each part of the question in the order they are presented a Solve the utility ... View the full answer