<p>So the firm's problem is, letting $L=Nl$</p>

<p>$\max_{L} Y-Lw\implies w=(1-\alpha)AL^{-\alpha}, \pi(w)=\alpha AL^{1-\alpha}$</p>

<p>Consumer's problem: substitute out c and only choose l, taking $\pi$ and $w$ as given</p>

<p>$\max_l u(l, wl+1/(N\pi))\implies -\gamma/(1-l)+w/(wl+1/(N\pi))=0$</p>

<p>Now substitute in the values for w and profit from the firm into the consumer's FOC and you will solve for labor supply (=labor demand as we are in eq) in terms of exogenous parameters ($\gamma, N,\alpha, A)$.</p>

CC BY-SA 3.0
2016-09-12T17:28:06.910Z
2016-09-12T17:28:06.910Z
VCG
<p>I know that $f'(l)=w$. But if i have that the aggregate production is $Y=AL^{1-α}$  with $L=N*l$ (The number of workers, $N$, multiplied by the labor force). So basically I want to find an expression for $w$ (the wage.).</p>

<hr>

<p><strong>Full problem</strong>:</p>

<p>Consider a one period economy, with aggregate technology given by: $Y=AL^{1-α}$ ,$0&lt;α&lt;1$. $L$ denotes the aggregate labor. The economy is integrated by $N$ identical agents, that offers labor force for a remuneration $w$. Also each person receives an Nth part of the earnings $π$ that generates the aggregate production. The objective of each agent is:</p>

<p>$\max \qquad γ\ln(1-l) + \ln(c)$. </p>

<p>$\text{subject to} \qquad c = wl + \frac{1}{Nπ(w)}$ </p>

CC BY-SA 3.0
2016-09-10T01:44:39.903Z
What is $f(\cdot)$?
Kun
CC BY-SA 3.0
2016-09-10T01:49:34.673Z
@Kun The exercise doesn't  gives you the production function a single one. Also it doesn't says anything about if the firms are all equal or  the number of  firms.
neto333
CC BY-SA 3.0
2016-09-10T02:01:23.383Z
Do you guys think that something is missing in the exercise?
neto333
CC BY-SA 3.0
2016-09-10T02:13:55.823Z
Giving us the entire text of the problem would be helpful.
VCG
CC BY-SA 3.0
2016-09-10T02:25:05.840Z
Consider a one period economy, with aggregate technology given by: $Y=AL^{1-α}$ ,$0<α<1$. L denotates the aggregate labor. The economy is integrated by N identical agents, that offers labor force for a remuneration w. Also each person receives an Nth part of the earnings $π$ that generates the aggregate production. The objetive of each agent is: max $γln(1-l)+ln(c)$. subjet to $c=wl+1/Nπ(w)$
neto333
CC BY-SA 3.0
2016-09-10T02:51:50.817Z
thats all the info that i have
neto333
CC BY-SA 3.0
2016-09-11T16:48:05.370Z
Are you maximizing over $l$?
FooBar
<self-study>
Marginal productivity of aggregate labor relation to wage
neto333
# Marginal productivity of aggregate labor relation to wage

(Asked by: username_0 on 2016-09-10)

I know that $f'(l)=w$. But if i have that the aggregate production is $Y=AL^{1-α}$ with $L=N\*l$ (The number of workers, $N$, multiplied by the labor force). So basically I want to find an expression for $w$ (the wage.).

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**Full problem**:

Consider a one period economy, with aggregate technology given by: $Y=AL^{1-α}$ ,$0<α<1$. $L$ denotes the aggregate labor. The economy is integrated by $N$ identical agents, that offers labor force for a remuneration $w$. Also each person receives an Nth part of the earnings $π$ that generates the aggregate production. The objective of each agent is:

$\max \qquad γ\ln(1-l) + \ln(c)$.

$\text{subject to} \qquad c = wl + \frac{1}{Nπ(w)}$

**Tags:** self-study
> **Comments:**
> **username_1**: What is $f(\cdot)$?  
> **username_0**: @Kun The exercise doesn't  gives you the production function a single one. Also it doesn't says anything about if the firms are all equal or  the number of  firms.  
> **username_0**: Do you guys think that something is missing in the exercise?  
> **username_2**: Giving us the entire text of the problem would be helpful.  
> **username_0**: Consider a one period economy, with aggregate technology given by: $Y=AL^{1-α}$ ,$0<α<1$. L denotates the aggregate labor. The economy is integrated by N identical agents, that offers labor force for a remuneration w. Also each person receives an Nth part of the earnings $π$ that generates the aggregate production. The objetive of each agent is: max $γln(1-l)+ln(c)$. subjet to $c=wl+1/Nπ(w)$  
> **username_0**: thats all the info that i have  
> **username_3**: Are you maximizing over $l$?  

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## 1 answers

### Answer by username_2 on 2016-09-12. Score: 2

So the firm's problem is, letting $L=Nl$

$\max\_{L} Y-Lw\implies w=(1-\alpha)AL^{-\alpha}, \pi(w)=\alpha AL^{1-\alpha}$

Consumer's problem: substitute out c and only choose l, taking $\pi$ and $w$ as given

$\max\_l u(l, wl+1/(N\pi))\implies -\gamma/(1-l)+w/(wl+1/(N\pi))=0$

Now substitute in the values for w and profit from the firm into the consumer's FOC and you will solve for labor supply (=labor demand as we are in eq) in terms of exogenous parameters ($\gamma, N,\alpha, A)$.


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