The analysis of model (8.32) was carried out on the basis of a single equation, namely, (8.35). Since only one endogenous variable can fruitfully be incorporated into one equation, the inclusion of P* means the exclusion of Q*. As a result, we were compelled to find (dP*fdYo) first and then to infer (dQ*fdYo) in a subsequent step. Now we shall show how P* and Of can be studied simultaneously. As there are two endogenous variables, we shall
accordingly set up a twoequation system. First, letting Q = Qd — Q, in (8.32) and rearranging, we can express our market model as
which is in the form of (8.24), with n— 2 and m = 1. It becomes of interest, once again, to check the conditions of the implicitfunction theorem. First, since the demand and supply functions are both assumed to possess continuous derivatives, so must the functions F1 and F1. Second, the endogenousvariable Jacobian (the one involving P and Q) indeed turns out to be nonzero, regardless of where it is evaluated, because
3F] 
9F> 
im  
ÖP 
HQ 
BP  
dF2 
3F2 
dS dP  
dP 
»Q 
Hence, if an equilibrium solution (P\ Q*) exists (as we must assume in order to make it meaningful to talk about comparative statics), the implicitfunction theorem tells us that we can write the implicit functions even though we cannot solve for P* and Q* explicitly. These functions are known to have continuous derivatives. Moreover, (8.38) will have the status of a pair of identities in some neighborhood of the equilibrium state, so that we may also write From these, (dP*jdY^) and {dQ* jdY$) can be found simultaneously by using the implicitfunction rule (8.28'). )n the present context, with F1 and F2 as defined in (8.41), and widi two endogenous variables P* and 0* and a single exogenous variable Yfj, the implicitfunction rule takes tlie specific form

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