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behavior budget constraint Chapter choice variables comparative statics analysis comparative statics results conditions for profit constant constrained optimization constrained utility maximization consumer consumption convex cost function Cramer's rule critical point decreasing demand function determinant economic envelope theorem equal to zero equals zero equilibrium conditions equilibrium values EXERCISES Section exogenous variables expression Figure find the derivative firm's first-order conditions graph Hessian matrix homogeneous implicit function theorem increase independent variable indifference curve indirect objective function input markets inverse isocost isoquant labor Lagrange multiplier Lagrangian objective function linear marginal cost marginal product marginal revenue mathematical maximum minimization minimum money income negative obtain optimization models optimum values output market parameters partial derivatives price-searcher price-taker principal minors production function profit function quantity demanded rate of output relationship second derivative second-order conditions slope solve total cost total differential total revenue utility function wage rate