<p>I'll guess that, since you're not yet in college but you're doing something this "advanced," you're not doing a homework problem, and that you're asking for a hint.</p>

<p>Since B doesn't care about A, you should be able to find B's consumption <span class="math-container">$(C_B, l_B)$</span> using standard method (maximizing utility w.r.t. budget constraint, etc.)</p>

<p>Now there are two cases.</p>

<ul>
<li><span class="math-container">$C_B \geq 1$</span>. Then what would the problem for A turn out to be?</li>
<li><span class="math-container">$C_B &lt; 1$</span>. Then think about how much should A transfer to B? Should he transfer nothing? 0.1? Up until what point would the increase in the transfer stop making A better off?</li>
</ul>

CC BY-SA 4.0
2019-09-27T03:10:26.677Z
The problem, though, is that I am not supposed to find B's consumption using standard method. This is the wording of the part b of the same question: 'Suppose A is able to insist that B does not reduce his labour supply when he
receives the transfer. How large should it be then, and how long should A work?' - suggesting that in part a, B does reduce his labour - I'm not sure then, how that works in terms of setting up equations? Thanks
Iso1510
CC BY-SA 4.0
2019-09-26T15:35:55.507Z
2019-09-26T15:35:55.507Z
Art
<p>I have been stuck on this question for about two days and can find no way out (apologies if the question seems really simple as I haven't started university yet). I would strongly prefer it if this can be solved using the Lagrange multiplier. Thanks.</p>

<p>There are two individuals, A and B, in an economy. Each derives utility from his
consumption, C, and the fraction of his time spent on leisure, l, according to the
utility function:
U = ln(C) + ln(l)
However, A is made very unhappy if B’s consumption falls below 1 unit, and he
makes a transfer, G, to ensure that it does not. B has no concern for A. A faces a
wage rate of 10 per period, and B a wage rate of 1 per period.
(a) For what fraction of the time does each work, and how large is the transfer G?</p>

<microeconomics>
Constrained optimisation with transfer
Iso1510
# Constrained optimisation with transfer

(Asked by: username_0 on 2019-09-26)

I have been stuck on this question for about two days and can find no way out (apologies if the question seems really simple as I haven't started university yet). I would strongly prefer it if this can be solved using the Lagrange multiplier. Thanks.

There are two individuals, A and B, in an economy. Each derives utility from his
consumption, C, and the fraction of his time spent on leisure, l, according to the
utility function:
U = ln(C) + ln(l)
However, A is made very unhappy if B’s consumption falls below 1 unit, and he
makes a transfer, G, to ensure that it does not. B has no concern for A. A faces a
wage rate of 10 per period, and B a wage rate of 1 per period.
(a) For what fraction of the time does each work, and how large is the transfer G?

**Tags:** microeconomics


---

## 1 answers

### Answer by username_1 on 2019-09-26. Score: 1

I'll guess that, since you're not yet in college but you're doing something this "advanced," you're not doing a homework problem, and that you're asking for a hint.

Since B doesn't care about A, you should be able to find B's consumption $(C\_B, l\_B)$ using standard method (maximizing utility w.r.t. budget constraint, etc.)

Now there are two cases.

* $C\_B \geq 1$. Then what would the problem for A turn out to be?
* $C\_B < 1$. Then think about how much should A transfer to B? Should he transfer nothing? 0.1? Up until what point would the increase in the transfer stop making A better off?

> **Comments:**
> **username_0**: The problem, though, is that I am not supposed to find B's consumption using standard method. This is the wording of the part b of the same question: 'Suppose A is able to insist that B does not reduce his labour supply when he receives the transfer. How large should it be then, and how long should A work?' - suggesting that in part a, B does reduce his labour - I'm not sure then, how that works in terms of setting up equations? Thanks  

---

