<p>Under what constraints is <span class="math-container">$u_1+u_2$</span> maximized? The exercise may be about the First Welfare Theorem: a competitive equilibrium is Pareto efficient. In this case, maximizing the sum may be designed to highlight that the equilibrium you found also maximizes the sum of utilities. </p>

<p>In general, the maximum of a sum of functions need not equal the maximum of any of these functions. </p>

CC BY-SA 4.0
2018-11-11T12:02:14.840Z
The constraints are their budget constraints and then we have the economy  resource constraints for each of the two goods. The utilities have the form aln(goodi)+bln(goodi) where i=1,2 for the two agents. I set up a new lagrangian with u1+u2 -lambda1(bc1) -lambda2 (bc2) but obviusly i get the same result as before and no new hindsight.. Thank you, Sander.
ceins
CC BY-SA 4.0
2018-11-11T01:32:35.163Z
2018-11-11T01:32:35.163Z
Sander Heinsalu
<p>I derived the Walrasian equilibrium for an economy of two consumers with their respective utility functions (u1, u2) and initial endowments but later on I am asked to maximize (u1+u2).</p>

<p>Does anyone know how this changes the problem ? Like, what is the difference in both approaches when it comes to the optimal allocations ?</p>

<microeconomics><utility><walrasian>
What is the difference between solving for utility maximization separately or aggregately?
ceins
# What is the difference between solving for utility maximization separately or aggregately?

(Asked by: username_0 on 2018-11-10)

I derived the Walrasian equilibrium for an economy of two consumers with their respective utility functions (u1, u2) and initial endowments but later on I am asked to maximize (u1+u2).

Does anyone know how this changes the problem ? Like, what is the difference in both approaches when it comes to the optimal allocations ?

**Tags:** microeconomics, utility, walrasian


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## 1 answers

### Answer by username_1 on 2018-11-11. Score: 1

Under what constraints is $u\_1+u\_2$ maximized? The exercise may be about the First Welfare Theorem: a competitive equilibrium is Pareto efficient. In this case, maximizing the sum may be designed to highlight that the equilibrium you found also maximizes the sum of utilities.

In general, the maximum of a sum of functions need not equal the maximum of any of these functions.

> **Comments:**
> **username_0**: The constraints are their budget constraints and then we have the economy  resource constraints for each of the two goods. The utilities have the form aln(goodi)+bln(goodi) where i=1,2 for the two agents. I set up a new lagrangian with u1+u2 -lambda1(bc1) -lambda2 (bc2) but obviusly i get the same result as before and no new hindsight.. Thank you, username_1.  

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