<p>In The Classic economy, we consider the following macroeconomic model</p>
<p><span class="math-container">$$Y=F(K,N)$$</span> where <span class="math-container">$F_N&gt;0$</span>, <span class="math-container">$F_K&gt;0$</span>, <span class="math-container">$F_{KK}, F_{NN}&lt;0$</span> and <span class="math-container">$F_{NK}&gt;0$</span></p>
<p><span class="math-container">$$F_N(K/N)=w/p$$</span>
The labor supply function is <span class="math-container">$$N^s=N^s(w/p, r-\pi)$$</span> where <span class="math-container">$N_{w/p}&gt;0, N_{r-\pi}&gt;0$</span></p>
<p><span class="math-container">$$N=N^s$$</span>
<span class="math-container">$$I=I(r-\pi), I’&lt;0$$</span>
<span class="math-container">$$C=C(Y-T), 0&lt;C’&lt;1$$</span>
<span class="math-container">$$Y=C+I+G$$</span>
<span class="math-container">$$M/p= m(r,Y)$$</span>
where <span class="math-container">$m_r&lt;0, m_Y&gt;0$</span></p>
<p>where Y is real GDP; K is the capital stock, N is employment, w is the money wage, Ns is the supply of labor, p is the price level, r is the interest rate, <span class="math-container">$\pi$</span> is the anticipated inflation rate, I is investment, C is consumption, G is government expenditure, T is net taxes. The endogenous variables are Y;N;w=p;r;p;C and I: The exogenous variables are M;K;G;T;: Let dK = 0.</p>
<p>Is this system dichotomous?</p>
<p>—-</p>
<p>I consider the supply side block</p>
<p>By the labor demand function, <span class="math-container">$$d(w/p)= F_{NK} dK+ F_{NN} dN$$</span></p>
<p>By the labor market clearing condition,</p>
<p><span class="math-container">$$dN=N_1^sd(w/p)+N_2^s(dr-d\pi)$$</span></p>
<p>By the output supply</p>
<p><span class="math-container">$$dY= F-N+dN+F_KdK$$</span></p>
<p>When I combine these three equations under the assumption <span class="math-container">$dK=0$</span></p>
<p><span class="math-container">$$dN= \frac{N_2^s}{1-N_1^s F_{NN}}(dr-d\pi)$$</span></p>
<p><span class="math-container">$$dY= \frac{N_2^s}{1-N_1^s F_{NN}}\frac{w}{p}(dr-d\pi)$$</span></p>
<p>Next consider the demand side block</p>
<p><span class="math-container">$$dC=C’(dY-dT)$$</span></p>
<p><span class="math-container">$$dC= c’ \frac{N_2^s}{1-N_1^s F_{NN}}\frac{w}{p}(dr-d\pi)-C’dT$$</span></p>
<p>Investment demand</p>
<p><span class="math-container">$$dI= I’(dr-d\pi)$$</span></p>
<p>Good market equilibrium condition</p>
<p>$$dY=dC+dI+dG$</p>
<p><span class="math-container">$$[(1-C’)\frac{N_2^s}{1-N_1^s F_{NN}}\frac{w}{p}-I’](dr-d\pi)=-C’dT+dG$$</span></p>
<p>Dichotomous system means that the nominal variables does not affect the real variables. For example, the change in M doesn’t effect C.</p>
<p>But I cannot interpret this model. Is this system dichotomous? How can I explain this?</p>

CC BY-SA 4.0
2020-11-09T19:23:56.433Z
Is there any reason why this system should be dichotomous? I did not take time to completely work through the model but inflation and prices are popping out almost everywhere and both depend on money supply
1muflon1
CC BY-SA 4.0
2020-11-09T19:26:40.833Z
Yes, Iam asking for the reason why  this system is dichotomous? @1muflon1
studentp
CC BY-SA 4.0
2020-11-09T19:28:46.260Z
I think you misunderstood me. This system does not look dichotomous, but you seem to think it should be. I am asking if you have any reason to suspect it should be dichotomous, because here money does not look neutral at all
1muflon1
CC BY-SA 4.0
2020-11-09T19:30:42.577Z
No no, I have no idea about the system. Okay, you have said that, since the equations include price and money supply changes prices, money supply affects real variables indirectly. I understand right?@1muflon1
studentp
CC BY-SA 4.0
2020-11-09T19:53:18.153Z
the money wont be neutral in model as long as there is any nominal rigidity, to me the formulation of the model looks like it should include some, I will try to have a close look at it later, but just from the look of it this looks like a model where money is not neutral
1muflon1
<self-study><money><classical-economics>
Question on Dichotomous system
studentp
# Question on Dichotomous system

(Asked by: username_0 on 2020-11-09)

In The Classic economy, we consider the following macroeconomic model

$$Y=F(K,N)$$ where $F\_N>0$, $F\_K>0$, $F\_{KK}, F\_{NN}<0$ and $F\_{NK}>0$

$$F\_N(K/N)=w/p$$
The labor supply function is $$N^s=N^s(w/p, r-\pi)$$ where $N\_{w/p}>0, N\_{r-\pi}>0$

$$N=N^s$$
$$I=I(r-\pi), I’<0$$
$$C=C(Y-T), 0<C’<1$$
$$Y=C+I+G$$
$$M/p= m(r,Y)$$
where $m\_r<0, m\_Y>0$

where Y is real GDP; K is the capital stock, N is employment, w is the money wage, Ns is the supply of labor, p is the price level, r is the interest rate, $\pi$ is the anticipated inflation rate, I is investment, C is consumption, G is government expenditure, T is net taxes. The endogenous variables are Y;N;w=p;r;p;C and I: The exogenous variables are M;K;G;T;: Let dK = 0.

Is this system dichotomous?

—-

I consider the supply side block

By the labor demand function, $$d(w/p)= F\_{NK} dK+ F\_{NN} dN$$

By the labor market clearing condition,

$$dN=N\_1^sd(w/p)+N\_2^s(dr-d\pi)$$

By the output supply

$$dY= F-N+dN+F\_KdK$$

When I combine these three equations under the assumption $dK=0$

$$dN= \frac{N\_2^s}{1-N\_1^s F\_{NN}}(dr-d\pi)$$

$$dY= \frac{N\_2^s}{1-N\_1^s F\_{NN}}\frac{w}{p}(dr-d\pi)$$

Next consider the demand side block

$$dC=C’(dY-dT)$$

$$dC= c’ \frac{N\_2^s}{1-N\_1^s F\_{NN}}\frac{w}{p}(dr-d\pi)-C’dT$$

Investment demand

$$dI= I’(dr-d\pi)$$

Good market equilibrium condition

$$dY=dC+dI+dG$

$$[(1-C’)\frac{N\_2^s}{1-N\_1^s F\_{NN}}\frac{w}{p}-I’](dr-d\pi)=-C’dT+dG$$

Dichotomous system means that the nominal variables does not affect the real variables. For example, the change in M doesn’t effect C.

But I cannot interpret this model. Is this system dichotomous? How can I explain this?

**Tags:** self-study, money, classical-economics

> **Comments:**
> **username_1**: Is there any reason why this system should be dichotomous? I did not take time to completely work through the model but inflation and prices are popping out almost everywhere and both depend on money supply  
> **username_0**: Yes, Iam asking for the reason why  this system is dichotomous? @username_1  
> **username_1**: I think you misunderstood me. This system does not look dichotomous, but you seem to think it should be. I am asking if you have any reason to suspect it should be dichotomous, because here money does not look neutral at all  
> **username_0**: No no, I have no idea about the system. Okay, you have said that, since the equations include price and money supply changes prices, money supply affects real variables indirectly. I understand right?@username_1  
> **username_1**: the money wont be neutral in model as long as there is any nominal rigidity, to me the formulation of the model looks like it should include some, I will try to have a close look at it later, but just from the look of it this looks like a model where money is not neutral  

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## 0 answers

