ECONOMICS : MATHEMATICS FOR ECONOMISTS III

GAME THEORY, ECON 159, PROBLEM SET 9 (i) If the n firms sustain a cartel that charges the monopoly price of 60 in each period, then the cartel output in each period is: Q=100 −pm=100 −60 =40.

Practice Exam Game Theory1 Consider the following game in normal form:

A concave function has an absolute maximum when plotted on a graph, while a convex function gives an absolute minimum when plotted on a graph. It is easy to check for concavity and convexity in functions of single independent variable by just checking the second order derivative. If the second order derivative is negative, the function is concave and if positive, the function is said to be convex. In functions of two independent variables, there is a corresponding test which also use...

The Jacobian matrix can help to test whether there exists functional linear dependence in a set of ݊ functions in ݊ variables. It is a matrix of the first order partial derivatives. If the functions are linearly dependent, the determinant of the Jacobian matrix is 0.

In our lecture two, we were able to see how a LPP can be solved using the graphical method. In this lecture we will learn how to a LPP can be solved using the simplex method. Steps • Formulate the problem in the standard way. • Convert the inequalities into equations through the addition of a slack variable if the inequality is of a less than type (≤). • A slack variable represents unused capacity in the constraint. E.g. 4X1+6X2≤180 Labour hours constraint 4X1+6X2 + S1 ...

In our lecture one, we were able to see how a LPP can be formulated in a standard way. In this section we will see how a LPP can be solved using the graphical method. Graphical methods of solving Linear programming can only be used for problems with TWO unknowns or decision variables. Problems with THREE OR MORE unknowns must be solved by techniques such as the simplex method. Graphical methods are the simplest to use and should be used wherever possible. Graphical method can be used t...