Im confused about endogeneity and how to approach this problem in a case of one equation and multiple equations that are jointly determined (simultaneous)

**One equation**

D = Endogenous, Z1 = instrument, E = error

Equation: Y = D + X2 + X3 + E

The first stage: D = Z1 + X2 + X3 + E

Reduced form: Y = Z1 + X2 + X3 + E

The first stage is OLS regression of endogneous on all exogenous and IV. It is used to check whether the IV a good instrument (high t-value). The fitted values are substituted in the second stage. I get this part.

Question 1: But: what does the reduced form tell us (in non-mathematical language)? What is the function of the reduced form?

**simultaneous equation (2 equations)**

For example supply and demand.

Demand equation: Qd = D1(price) + X2 + X3 + X4 + E

Supply equation: Qs = D1(price) + X2 + E

X3 does not appear in the supply equation (Use it as IV), hence supply is identified.

First stage: D1(price) = X3 + X4 + E

Reduced form: Qs = X3 + X4 + X2 + E

Question 2: is the first stage correctly specified?

Question 3: is the reduced form correctly specified?

In general, I do not know how to specify the model in case of simultaneous equations, like supply and demand. That is the reason for asking question 2 and 3.

If someone can explain the above I would really appreciate that!!

I posted this question on stackexchange to. But I get the feeling there are more people around here that can help. If I receive an answer on stackexchange I will post it here