a) Find out Mr. A’s optimal consumption levels (i.e. C1*, C2*) and optimal savings (i.e. S1*, S2*) in terms of interest rate r. b) Show clearly the results in part a) in a suitable diagram (with C1 as x-axis and C2 as y-axis). c) Is Mr. A a saver ? or a borrower ? d) If r is equal to 0 (i.e. saving gives no returns), will Mr. A still choose to save when he is young (i.e. is S1 still bigger than 0) ? Why ? e) Suppose that Mr. A is not allowed to save (i.e. S1 = 0). What are his optimal consumption levels ? Show his optimal consumption levels in the same diagram you prepare for part a) (with a suitable indifference curve). f) If r increases, what will happen to your results in part a) (i.e. C1*, C2*, S1* and S2*) ? Use the diagram you prepare for part a) to show the effects of changing r on these results. g) Compare Mr. A’s well-beings (indicated by indifference curve) before and after the change in r. Is an increase in r good or bad for his well-being ?
2. Mr. A has the following utility function and budget constraints:
Max 0.1Ln(C1) + 0.7Ln(C2)
Subject to S1 + C1 = 100
C2 + S2 = (1 + r)S1
where C1 and C2 are consumption level at young and that at old respectively. Likewise, S1 and S2 are saving at young and saving at old respectively.
a) Find out Mr. A’s optimal consumption levels (i.e. C1*, C2*) and optimal savings (i.e. S1*, S2*) in terms of interest rate r.
b) Show clearly the results in part a) in a suitable diagram (with C1 as x-axis and C2 as y-axis).
c) Is Mr. A a saver ? or a borrower ?
d) If r is equal to 0 (i.e. saving gives no returns), will Mr. A still choose to save when he is young (i.e. is S1 still bigger than 0) ? Why ?
e) Suppose that Mr. A is not allowed to save (i.e. S1 = 0). What are his optimal consumption levels ? Show his optimal consumption levels in the same diagram you prepare for part a) (with a suitable indifference curve).
f) If r increases, what will happen to your results in part a) (i.e. C1*, C2*, S1* and S2*) ? Use the diagram you prepare for part a) to show the effects of changing r on these results.
g) Compare Mr. A’s well-beings (indicated by indifference curve) before and after the change in r. Is an increase in r good or bad for his well-being ?
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