<blockquote>
  <p>income is total profit plus wage income, and the two are fixed in proportions</p>
</blockquote>

<p>I.e. <span class="math-container">$y_t = w_t + \pi_t$</span> and  <span class="math-container">$w_t = \alpha y_t$</span> and  <span class="math-container">$\pi_t = (1-\alpha)y_t$</span>, where <span class="math-container">$\alpha$</span> and <span class="math-container">$(1-\alpha)$</span> are the fixed proportions.</p>

<p>For <span class="math-container">$y_{t+1}$</span> we have <span class="math-container">$y_{t+1}=(1+g_y)y_t$</span> and <span class="math-container">$w_{t+1} = \alpha y_{t+1} = \alpha (1+g_y)y_t = (1+g_y)\alpha y_t = (1+g_y) w_t$</span> and <span class="math-container">$\pi_{t+1} = (1-\alpha) y_{t+1} = (1-\alpha)(1+g_y)y_t = (1+g_y)(1-\alpha) y_t = (1+g_y) \pi_t.$</span></p>

<p>I.e. <span class="math-container">$g_y = g_w = g_{\pi}$</span></p>

CC BY-SA 4.0
2020-04-25T11:11:30.283Z
Hey, thank you so much. Now I see what was meant! Is this the only solution path?
randomname
CC BY-SA 4.0
2020-04-25T06:40:44.480Z
2020-04-25T06:40:44.480Z
Grada Gukovic
<p>I am trying to understand the R&amp;D model and how to calculate the growth rate of wage in this model. </p>

<p>There is no equation given, but it’s stated that : <em>household income must equal total consumption. as income is total profit plus wage income, and the two are fixed in proportions, wages grow at the same rate as output <span class="math-container">$g_w=g_y$</span></em></p>

<p>I tried to write down the equation of this statement, however, I don‘t really think it’s right: <span class="math-container">$\pi+w= C_t$</span>.</p>

<p>Can anyone help with the equation and it’s intuition?</p>

<p>Addition: the R&amp;D model introduces final good producers that sell their good in a competitive market and intermediate goods producers that produce either a produced intermediate good or “ideas” that are sold to the final good producers and used to produce the final good. The intermediate good and “ideas” are substitutes.</p>

CC BY-SA 4.0
2020-04-23T21:29:15.703Z
Can you show the R&D model for context? It will make the question more clear
Brennan
<macroeconomics><economic-growth><endogenous-growth><balanced-growth>
Wage Growth Rate in the R&D Model
randomname
# Wage Growth Rate in the R&D Model

(Asked by: username_0 on 2020-04-23)

I am trying to understand the R&D model and how to calculate the growth rate of wage in this model.

There is no equation given, but it’s stated that : *household income must equal total consumption. as income is total profit plus wage income, and the two are fixed in proportions, wages grow at the same rate as output $g\_w=g\_y$*

I tried to write down the equation of this statement, however, I don‘t really think it’s right: $\pi+w= C\_t$.

Can anyone help with the equation and it’s intuition?

Addition: the R&D model introduces final good producers that sell their good in a competitive market and intermediate goods producers that produce either a produced intermediate good or “ideas” that are sold to the final good producers and used to produce the final good. The intermediate good and “ideas” are substitutes.

**Tags:** macroeconomics, economic-growth, endogenous-growth, balanced-growth
> **Comments:**
> **username_1**: Can you show the R&D model for context? It will make the question more clear  

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## 1 answers

### Answer by username_2 on 2020-04-25. Score: 1 | Accepted answer

> income is total profit plus wage income, and the two are fixed in proportions

I.e. $y\_t = w\_t + \pi\_t$ and $w\_t = \alpha y\_t$ and $\pi\_t = (1-\alpha)y\_t$, where $\alpha$ and $(1-\alpha)$ are the fixed proportions.

For $y\_{t+1}$ we have $y\_{t+1}=(1+g\_y)y\_t$ and $w\_{t+1} = \alpha y\_{t+1} = \alpha (1+g\_y)y\_t = (1+g\_y)\alpha y\_t = (1+g\_y) w\_t$ and $\pi\_{t+1} = (1-\alpha) y\_{t+1} = (1-\alpha)(1+g\_y)y\_t = (1+g\_y)(1-\alpha) y\_t = (1+g\_y) \pi\_t.$

I.e. $g\_y = g\_w = g\_{\pi}$

> **Comments:**
> **username_0**: Hey, thank you so much. Now I see what was meant! Is this the only solution path?  

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