Here is a question we did in class...Why in the answer do we take the derivatve? How do we know to take the derivative? What in the problem would have set us off to look for the derivative and set to 0?(adsbygoogle = window.adsbygoogle || []).push({});

Consider an economy that is composed of identical individuals who live for two periods. These individuals have preferences over consumption in periods 1 and 2 given

by U = ln(C1) + ln(C2). They receive an income of 100 in period 1 and an income of 50

in period 2. They can save as much of their income as they like in bank accounts,

earning an interest rate of 10% per period. They do not care about their children, so

they spend all their money before the end of period 2. Each individual’s lifetime budget constraint is given by C1+ C2/(1 + r) = Y1+ Y2/(1+ r). Individuals choose consumption in each period by maximizing lifetime utility subject to this lifetime budget constraint.

here is part a. and the answer

a. What is the individual’s optimal consumption in each period? How much saving

does he or she do in the first period?

Individuals solve

max U = ln(C1) + ln(C2) subject to C1+ C2/(1.1) = 100 + 50/(1.1).

Rearrange the budget constraint C2= 110 + 50 – 1.1C1 and plug into the maximand: max U = ln(C1) + ln(160 – 1.1C1).

Then take the derivative and set it equal to zero:1/C1= 1.1/(160 – 1.1C1), or 2.2C1

= 160.

So C1

≈ 72.7, and savings 100 – C1≈ 27.3. The optimal consumption in the second period is then 50 + 1.1(100 – C1) = 80

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# Confused on when to take derivative

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