Question 2 (20 marks) Assume that a consumer's utility over two years is a function of consumption during the two years.
Posted: Wed May 11, 2022 7:46 pm
- Question 2 20 Marks Assume That A Consumer S Utility Over Two Years Is A Function Of Consumption During The Two Years 1 (162.95 KiB) Viewed 23 times
years is a function of consumption during the two years. Let the
consumer’s utility function be U(C1, C2) = ln C1 + β ln C2, where
C1 is consumption during the 1st year, and C2 is the consumption
during the 2nd year. The consumer’s income is Y1 during the 1st
year and Y2 during the 2nd year. Let R denote the annual interest
rate (0 < R < 20%), at which the consumer can choose to
borrow or lend across the two years. The consumer’s budget
constraint is C1 + C2 1 + R = Y1 + Y2 1 + R . We aim to find out
the values of C1 and C2, at which the consumer’s utility is
maximised. (1) Write down the Lagrangian function, which can be
used to maximise the consumer’s utility function subject to the
budget constraint. (2) Use the 1st order condition to derive the
values of C1 and C2, at which the consumer’s utility is maximised
subject to the budget constraint. (3) Derive the Lagrange
multiplier when the utility function achieves its maximum under the
budget constraint.
Question 2 (20 marks) Assume that a consumer's utility over two years is a function of consumption during the two years. Let the consumer's utility function be U(C1, C2) = In C1 + B In C2, 3 where Ci is consumption during the 1st year, and C2 is the consumption during the 2nd year. The consumer's income is Yį during the 1st year and Y2 during the 2nd year. Let R denote the annual interest rate (0 < R<20%), at which the consumer can choose to borrow or lend across the two years. The consumer's budget constraint is C2 Ci + Y2 =Y1 + 1+R 1+R We aim to find out the values of Cį and C2, at which the consumer's utility is maximised. (1) Write down the Lagrangian function, which can be used to maximise the consumer's utility function subject to the budget constraint. (2) Use the 1st order condition to derive the values of Cị and C2, at which the consumer's utility is maximised subject to the budget constraint. (3) Derive the Lagrange multiplier when the utility function achieves its maximum under the budget constraint.