in the market occur according to where > 0 is the speed of adjustment parameter and is the time derivative of the price — that is, it denotes how fast and in what direction the price changes. By stability theory, P will converge to its equilibrium value if and only if the derivative is negative. This derivative is given by This is negative if and only if g – b > 0, in which case the demand intercept parameter a positively influences the price. So we can say that while the direction of effect of the demand intercept on the equilibrium price is ambiguous when all we know is that the reciprocal of the supply curve's slope, g, is negative, in the only relevant case (in which the price actually goes to its new equilibrium value) an increase in the demand intercept increases the price. Note that this case, with g – b > 0, is the case in which the supply curve, if negatively sloped, is steeper than the demand curve. Without constraints Suppose is a smooth and strictly concave objective function where x is a vector of n endogenous variables and q is a vector of m exogenous parameters. Consider the unconstrained optimization problem . Let , the n by n matrix of first partial derivatives of with respect to its first n arguments x1,...,xn. The maximizer is defined by the n×1 first order condition . Comparative statics asks how this maximizer changes in response to changes in the m parameters. The aim is to find . The strict concavity of the objective function implies that the Jacobian of f, which is exactly the matrix of second partial derivatives of p with respect to the endogenous variables, is nonsingular (has an inverse). By the implicit function theorem, then, may be viewed locally as a continuously differentiable function, and the local response of to small changes in q is given by Applying the chain rule and first order condition, (See Envelope theorem). Application for profit maximization Suppose a firm produces n goods in quantities . The firm's profit is a function p of and of m exogenous parameters which may represent, for instance, various tax rates. Provided the profit function satisfies the smoothness and concavity requirements, the comparative statics method above describes the changes in the firm's profit due to small changes in the tax rates. With constraints A