Reference no: EM132207631
Question: There are two individuals, Kirk and Dirk, who each live for two periods. Both individuals derive utility from consumption, and their utility functions are the same. Both face lifetime budget constraint. Assume b=(1+r)=1, where b is the subjective discount factor, and r is the real interest rate. Both receive endowments: Kirk receives 100 in period 1 and 0 in period 2, which Dirk receives 0 in period 1 and 100 in period 2. Kirk also has initial wealth equal to 50, while Dirk has no initial wealth.
a) State the optimality conditions that must hold if both Kirk and Dirk maximize their respective utility subject to their respective budget constraints.
b) Find current consumption (c) and future consumption (cf) for Kirk and Dirk
c) Find current period saving for Kirk and Dirk.
d) Suppose Kirk's current income y goes down by 30. Find his new consumption plan and current saving. Find his marginal propensity to consume (MPC) and save (MPS).
e) Suppose Kirk's permanent income goes down by 30, i.e. both y and yf decline by 30. Find his new consumption plan and current saving. Find his marginal propensity to consume (MPC) and save (MPS).
f) Now let's look at Dirk. Suppose Dirk is facing borrowing constraints, so that he cannot borrow. Find Dirk's consumption plan (c and cf) and his current saving. Discuss how (if at all) his consumption plan and saving differ from those you obtained for him under no borrowing constraints in part b and c.
g) Continue to assume that Dirk faces borrowing constraints. Suppose Dirk's current income y goes up by 30. Find his new consumption plan and current saving. Find his marginal propensity to consume (MPC) and save (MPS).
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