Melanie inherited $25,000, and she needs to decide how much to spend now and how much tosave for period 2. For every dollar she saves, she earns an additional 20% in interest to spend inperiod 2. If Melanie's total utility is maximized by having $12,000 in period 2, how much will shechoose to spend now?$15,000$13,000$12,000$10,000

Answered: Melanie inherited $25,000, and she…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Melanie inherited $25,000, and she needs to decide how much to spend now and how much to
save for period 2. For every dollar she saves, she earns an additional 20% in interest to spend in
period 2. If Melanie's total utility is maximized by having $12,000 in period 2, how much will she
choose to spend now?
$15,000
$13,000
$12,000
$10,000

Expert Solution

Step 1

Answer:

Correct option: $15,000

Explanation:

Melanie income in period 1 = $25,000

Now suppose that she saves X$ in period 1 so that she will get $12000 in period 2. She will also get 20% interest on $X.

$X + X \times \frac{20}{100} = 12, 000 X + 0.2 X = 12, 000 1.2 X = 12, 000 X = \frac{12, 000}{1.2} = 10, 000$

If Melanie saves $10,000 today then she will have $12,000 in period 2 (including interest). So the remaining amount she will spend in period 1.

$R e m a i n i n g a m o u n t = T o t a l a m o u n t - A m o u n t s a v e d f o r p e r i o d 2 R e m a i n i n g a m o u n t = 25, 000 - 10, 000 R e m a i n i n g a m o u n t = $ 15, 000$

After saving $10,000 for future consumption she will be left with $15,000 and it will be her current consumption.

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