# Question on Dichotomous system

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 $$N_{w/p}>0, N_{r-\pi}>0$$

$$N=N^s$$ $$I=I(r-\pi), I’<0$$ $$C=C(Y-T), 0 $$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?

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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?

• 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
Nov 9 '20 at 19:23
• Yes, Iam asking for the reason why this system is dichotomous? @1muflon1
– 1190
Nov 9 '20 at 19:26
• 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
Nov 9 '20 at 19:28
• 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
– 1190
Nov 9 '20 at 19:30
• 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
Nov 9 '20 at 19:53