Question 1: Consumption-Savings

Consider a consumer with a lifetime utility function (, +1) = ln() + n(+1)

The period t and t + 1 budget constraints are

+ =

+1 = +1 + (1 + )

a. Derive the lifetime budget constraint.

b. Derive the Euler equation. Explain the economic intuition of the equation.

c. Using the Euler equation and lifetime budget constraint, solve for the period t consumption function = (, +1, ).

d. Use your answer to part (c) to find the MPC. (Hint: MPC = c/y )

e. Using your answer to part (c), how would the optimal consumption in period t change if +1 decreases? Explain the economic intuition behind this result

f. Using your answer to part (c), How would the optimal consumption in period t change if increases? Explain the economic intuition behind this result

g. Suppose = 100, +1 = 200, r = 5%, and = 0.8, solve for the optimal consumption in t and t+1. (find ^otp, t+1^otp )

h. How would the optimal consumption in period t change if increases to 150? Is this consistent with your findings from part (d)? Explain.