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  2. Contract curve - Wikipedia

    en.wikipedia.org/wiki/Contract_curve

    By varying the weighting parameter b, one can trace out the entire contract curve: If b = 1 the problem is the same as the previous problem, and it identifies an efficient point at one edge of the lens formed by the indifference curves of the initial endowment; if b = 0 all the weight is on person 2's utility instead of person 1's, and so the ...

  3. Lagrange multiplier - Wikipedia

    en.wikipedia.org/wiki/Lagrange_multiplier

    For example, in economics the optimal profit to a player is calculated subject to a constrained space of actions, where a Lagrange multiplier is the change in the optimal value of the objective function (profit) due to the relaxation of a given constraint (e.g. through a change in income); in such a context is the marginal cost of the ...

  4. Offer curve - Wikipedia

    en.wikipedia.org/wiki/Offer_curve

    When it produces at point B, it can trade with the other country and consume at point S. We now look at our Offer curve and draw a ray at the level 5 Y for 7 X. When full specialization occurs, K then produces at point A, trades and then consumes at point T. The price has reduced to 1 Y for 1 X, and the economy is now at equilibrium.

  5. Gradient - Wikipedia

    en.wikipedia.org/wiki/Gradient

    Further, a point where the gradient is the zero vector is known as a stationary point. The gradient thus plays a fundamental role in optimization theory, where it is used to minimize a function by gradient descent. In coordinate-free terms, the gradient of a function () may be defined by:

  6. Demand curve - Wikipedia

    en.wikipedia.org/wiki/Demand_curve

    The usual method is to collect data on past prices, quantities, and variables such as consumer income and product quality that affect demand and apply statistical methods, variants on multiple regression. The issue with this approach, as outlined by Baumol, is that only one point on a demand curve can ever be observed at a specific time.

  7. Hessian matrix - Wikipedia

    en.wikipedia.org/wiki/Hessian_matrix

    The second-derivative test for functions of one and two variables is simpler than the general case. In one variable, the Hessian contains exactly one second derivative; if it is positive, then is a local minimum, and if it is negative, then is a local

  8. Saddle point - Wikipedia

    en.wikipedia.org/wiki/Saddle_point

    A saddle point (in red) on the graph of z = x 2 − y 2 (hyperbolic paraboloid). In mathematics, a saddle point or minimax point [1] is a point on the surface of the graph of a function where the slopes (derivatives) in orthogonal directions are all zero (a critical point), but which is not a local extremum of the function. [2]

  9. Descent direction - Wikipedia

    en.wikipedia.org/wiki/Descent_direction

    In optimization, a descent direction is a vector that points towards a local minimum of an objective function :.. Computing by an iterative method, such as line search defines a descent direction at the th iterate to be any such that , <, where , denotes the inner product.