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Economic equilibrium; Empirical ... an input–output model is a quantitative economic model that represents the ... Then solving the system of linear equations ...
By solving the above linear programming problem, the optimal numbers of production days for the three firms are found to be 2, 0, and 8, respectively; and the corresponding total output is 280. Next, we transform this linear programming problem into a general equilibrium problem, with the following assumptions:
Now substituting in for , and solving we obtain the symmetric (same for each firm) output quantity in Equilibrium as =. This equilibrium value describes the optimal level of output for firms 1 and 2, where each firm is producing an output quantity of q ∗ {\displaystyle q^{*}} .
The Nash equilibrium occurs when both firms are producing the outputs which maximize their own profit given the output of the other firm. In terms of the equilibrium properties, we can see that P2 is satisfied: in a Nash equilibrium, neither firm has an incentive to deviate from the Nash equilibrium given the output of the other firm.
The Nash Equilibrium in the Bertrand model is the mutual best response; an equilibrium where neither firm has an incentive to deviate from it. As illustrated in the Diagram 2, the Bertrand-Nash equilibrium occurs when the best response function for both firm's intersects at the point, where P 1 N = P 2 N = M C {\displaystyle P_{1}^{N}=P_{2}^{N ...
With advances in computing power and the development of input–output tables, it became possible to model national economies, or even the world economy, and attempts were made to solve for general equilibrium prices and quantities empirically.
The Stackelberg model can be solved to find the subgame perfect Nash equilibrium or equilibria (SPNE), i.e. the strategy profile that serves best each player, given the strategies of the other player and that entails every player playing in a Nash equilibrium in every subgame.
Walras's law is a consequence of finite budgets. If a consumer spends more on good A then they must spend and therefore demand less of good B, reducing B's price. The sum of the values of excess demands across all markets must equal zero, whether or not the economy is in a general equilibrium.