Discriminating monopoly

  1. (10 Marks) Create and work with a function of two variables, create a linear constraint
    with two variables.
    NOTE: Each student must create and work with their own unique func- tions.
    (a) (2 marks) Set up the Lagrangian function.
    (b) (2 marks) Find the critical values of your function (including the critical value for the
    Lagrangian multiplier).
    (c) (2 marks) Find the maximum/minimum value of your function.
    (d) (4 marks) Determine whether or not your solution is a minimum or a maximum of the
    function and explain how you came to that conclusion.
  2. (10 marks) Suppose there exists a discriminating monopolist which has the inverse
    demand functions are P1 = a1 − b1Q1 and P2 = a2 − b2Q2. Find the profit function and
    find an expression for the optimal value of profit in terms of a1, a2, b1 and b2. Be sure to
    explain your steps as much as possible.

Sample Solution