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Mathematical Economics Exercises Exercises for Section 3: Inequality Constraints This section includes the topics of non-negative variables,...
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ECONOMICS 350, MATHEMATICAL ECONOMICS, INEQUALITY CONSTRAINTS

Mathematical Economics
Exercises
Exercises for Section 3: Inequality Constraints
This section includes the topics of non-negative variables, inequality constraints, constraint qualification,
Lagrange, and Kuhn Tucker. We need to have covered Topic 17 (Solution Methods #1 and #2) before
these exercises can be done.
Solve the following exercises before looking at the answers. Then check the answers, and redo the
exercise if your answer is incorrect. You should also consider repeating exercises on another day and/or
repeating exercises with a self-imposed time deadline.
If you have the Dixit textbook, work through Examples 3.1 and 3.2.
1. Simple problems treating non-negativity constraints as inequality constraints (Method #1)
Solve the following problems treating non-negativity constraints as inequality constraints. Remember
x, 20, x2 2 0 can be written -x, SO, -x2 50.
a. max F(X,, X2) = 2x, + 3x2 subject to 2.x, + 5x2 &lt;10, x, 20, x, 20
b. max F(X,, X2) = x x2.&quot; subject to 2x, + 5x2 &lt;10, x, 20, x, 20
C.
max F(X, X2) = 2x, + 4x2 subject to xx, &lt;10, x, 20, x, 20
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