derivatives of the functions with respect to the variables , and represents the × matrix of partial derivatives of the functions with respect to the parameters . (The derivatives in and are evaluated at the initial values of and .) Note that if one wants just the comparative static effect of one exogenous variable on one endogenous variable, Cramer's Rule can be used on the totally differentiated system of equations . Stability The assumption that the equilibrium is stable matters for two reasons. First, if the equilibrium were unstable, a small parameter change might cause a large jump in the value of , invalidating the use of a linear approximation. Moreover, Paul A. Samuelson's correspondence principle states that stability of equilibrium has qualitative implications about the comparative static effects. In other words, knowing that the equilibrium is stable may help us predict whether each of the coefficients in the vector is positive or negative. Specifically, one of the n necessary and jointly sufficient conditions for stability is that the determinant of the n×n matrix B have a particular sign; since this determinant appears as the denominator in the expression for , the sign of the determinant influences the signs of all the elements of the vector of comparative static effects. An example of the role of the stability assumption Suppose that the quantities demanded and supplied of a product are determined by the following equations: where is the quantity demanded, is the quantity supplied, P is the price, a and c are intercept parameters determined by exogenous influences on demand and supply respectively, b < 0 is the reciprocal of the slope of the demand curve, and g is the reciprocal of the slope of the supply curve; g > 0 if the supply curve is upward sloped, g = 0 if the supply curve is vertical, and g < 0 if the supply curve is backward-bending. If we equate quantity supplied with quantity demanded to find the equilibrium price , we find that This means that the equilibrium price depends positively on the demand intercept if g – b > 0, but depends negatively on it if g – b < 0. Which of these possibilities is relevant? In fact, starting from an initial static equilibrium and then changing a, the new equilibrium is relevant only if the market actually goes to that new equilibrium. Suppose that price adjustments