A household lives for two periods, t= 1,2. In period t, she receives income I 20...

 

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A household lives for two periods, t= 1,2. In period t, she receives income I 20 and decides how much to consume, C- Her utility function is given by: U(C₁,C₂) Inc₁ + In c₂ (i) Suppose that at t = 1, she can either borrow or save at market interest rate r. However, she must pay back all debts at t = 2. Formulate her bud- get constraints as equality or inequality constraints (explain). Write out her constrained optimization problem, find a candidate solution, and prove that it solves the problem stated. (ii) Now suppose instead that at t = 1, she can save at market interest rate r, but cannot borrow. She must still pay back all debts at t = 2. Formulate her budget constraints as equality or inequality constraints (explain). Write out her constrained optimization problem, find a candidate solution, and prove that it solves the problem stated. Constramts: C₂ 1₂ + (Hr). (= A household lives for two periods, t= 1,2. In period t, she receives income I 20 and decides how much to consume, C- Her utility function is given by: U(C₁,C₂) Inc₁ + In c₂ (i) Suppose that at t = 1, she can either borrow or save at market interest rate r. However, she must pay back all debts at t = 2. Formulate her bud- get constraints as equality or inequality constraints (explain). Write out her constrained optimization problem, find a candidate solution, and prove that it solves the problem stated. (ii) Now suppose instead that at t = 1, she can save at market interest rate r, but cannot borrow. She must still pay back all debts at t = 2. Formulate her budget constraints as equality or inequality constraints (explain). Write out her constrained optimization problem, find a candidate solution, and prove that it solves the problem stated. Constramts: C₂ 1₂ + (Hr). (=

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ANSWER i When the household can either borrow or save at market interest rate r her budget constraint at time t1 is given by C1 B1 I1 where B1 is the ... View the full answer