Question

please help with questions e, f, g, h, i, j. i have included answers for a-d

2. Pat's utility function over consumption today (C) and consumption in the future (C) is given by function U(CC) = 6 She has an income of M = $8.400 that she can allocate between today's consumption and savings. Pat's budget line is (1 + r) + = 8.400(1+r) For any rate of interest r. answer the following questions a) How much wil Pat consume today? b) Depict her savings function on a graph with Savings on the horizontal axis and on the vertical axis. Jim's utility function over consumption today (C1) and in the future (CZ) is U(.) = min . ) He also has an income of M = $8.400 c) For any , what is Jim's optimal consumption pattern today and in the future? d) Draw his Savings function and compare it to Pat's. 04. Fill in the following tables Suppose the interest rate decreases from t = 0.5 to e) Pat C C 2 -0.5 Savings Utility 1) Jim C C 2 Savings Utility r=0.5 0.4 g) How much income does Pat need to enjoy his old Utility level at the new interest rate of 0.47 h) What are her savings with this additional income? What is the Substitution Effect of the interest rate decrease? What is the income effect? D Repeat parts g) toil) for Jim and compare your answers.

Answer 1

E) Pat

Interest rate	C1	C2	Saving	Utility
r1 = .5	4200	6300	4200
r2 =.4	4200	5880	4200

C2 = (1+r)4200

.

F) Jim

Interest rate	C1	C2	Saving	Utility
.5	5040	5040	3360
.4	4900	4900	3500

C1 = C2 = 8400(1+r)/(2+r)

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G) pat

Old Utility U1 ( when r= .5)

U1 = C1*C2 = 4200*6300

Then at new r = .4

Let new income M"

Then C1 = M"/2

So C2 = (1+r)C1

= 1.4*M"/2

= .7M"

So,( M"/2)*(.7M") = 4200*6300

M" = $ 8694.83

so income needed = 8694.83

.

h)

New savings = M" - C1

= M" - M"/2

= M"/2

=$ 4347.413

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It's mandatory to answer only four parts