A consumer maximises the following two-period utility function 1 u(c2) 1+p)² V = max- subject to the following 2-period budget constraint, C2 +r* (1+r)² Y2 = Ao ++r*(1+r)²' By choosing consumption at each period, c, and c2. r denotes the real interest rate, p is the time preference rate, A, is initial wealth and y, and y, represents incomes in period 1 and period 2 respectively. (a) Use the Lagrangian method to obtain the first order conditions for the utility maximisation problem and obtain the Euler equation. (b) Assume utility function has the form of u(c,) = 0.2 and r = 0.3. Obtain the equations/solutions for maximal c, and c2 by substituting the Euler equation back into the two-period budget constraint for the situations of either A, = -50 or A, = 50. Explain the results. = 200, yz = 300, p =

A consumer maximises the following two-period utility function 1 u(c2) 1+p)² V = max- subject to the following 2-period budget constraint, C2 +r* (1+r)² Y2 = Ao ++r*(1+r)²' By choosing consumption at each period, c, and c2. r denotes the real interest rate, p is the time preference rate, A, is initial wealth and y, and y, represents incomes in period 1 and period 2 respectively. (a) Use the Lagrangian method to obtain the first order conditions for the utility maximisation problem and obtain the Euler equation. (b) Assume utility function has the form of u(c,) = 0.2 and r = 0.3. Obtain the equations/solutions for maximal c, and c2 by substituting the Euler equation back into the two-period budget constraint for the situations of either A, = -50 or A, = 50. Explain the results. = 200, yz = 300, p =

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter17: Capital And Time

Section: Chapter Questions

Problem 17.1P

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