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Math Methods for Economists 

Fall 2016 Final

1. Evaluate the indefinite integral.  Please show all intermediate steps.

2. Evaluate the definite integral.  Please show all intermediate steps.  Hint: set u =  and then apply the integration by parts rule.  

3. Find solutions to the values of x, y, and z using the matrix inversion technique shown in this course.  Please show all intermediate steps.

4. Partially differentiate the following equation with respect to x and y:

5. Without substituting u or v into Z, please find the total derivative of Z with respect to x.

6. Determine the critical points of functions.  Determine whether each critical point corresponds to local maxima, minima, or a saddle-point. Clearly distinguish the first-order conditions and the second-order conditions.

7. Given the constraint, find the stationary points for the following function and evaluate the second order conditions.  Use the Lagrange technique.

 subject to