Econ 519: David Reiley
Due Monday, 31 July 2006
Summer Problem Set
These problems come from the text by Simon & Blume. Note that you can check
your answers to many of these problems in the back of the book. However, you
should attempt each problem independently, and check your answer only after
you have either solved the problem or struggled with the problem unsuccessfully
for at least 15 minutes.
I recognize that 105 problems is quite a lot. If it's any consolation, I have
actually omitted some problems that previous students felt were too long and
tedious. I have attempted to retain only those problems whose marginal educational
benefit exceeds their marginal cost.
I estimate that each problem will take you 15 minutes on average, though that
figure could be much higher if some of the material is unfamiliar to you from
previous classes. If you struggle for more than 30 minutes on a problem, feel
free to email me (or your classmates) for help during the summer. At 15 minutes
per problem, it should take you a total of around 30 hours to complete the problem
set. At half an hour per day during the next two months, I hope that's not too
daunting. This work will prepare you quite well for the fastpaced course in
August.

Problem 2.1.
 Problem 2.3. Note that the (2) refers to equation (2) on page 12.
 Problem 2.4.
 Problem 2.5.
 Problem 2.8.
 Problem 2.9.
 Problem 2.10(b). The proof of Theorem 2.2 can be found in Example 2.6.
 Problem 2.11(b,d,f,h,j,l).
 Problem 2.12.
 Problem 2.13.
 Problem 2.14.
 Problem 2.16.
 Problem 2.17.
 Problem 2.18. You are asked to describe for what values of x the function
is continuous, and for what values of x it is differentiable.
 Problem 2.19. On separate graphs, plot both the function and its first derivative.
Label the point where the second derivative does not exist. Is this a C^{1}
function? Is this a C^{2} function?
 Problem 2.20(omit k, l, m).
 Problem 2.22.
 Problem 2.23.
 Problem 2.24.
 Problem 3.2.
 Problem 3.3. Graph the functions in question 3.1, using whatever technique
you like, and then label the regions of convexity and concavity.
 Problem 3.5.
 Problem 3.7(d,e,f).
 Problem 3.8.
 Problem 3.9(e,f,g,h).
 Problem 3.10.
 Problem 3.12.
 Problem 3.13.
 Problem 3.15. You are asked to demonstrate the truth of the three properties
in Theorem 3.7 for this specific function, and then graph the average and
marginal cost functions as in Figure 3.19.
 Problem 3.16.
 Problem 3.18.
 Problem 4.1(d,e).
 Problem 4.2.
 Problem 4.3(d,e).
 Problem 4.4(d).
 Problem 4.5(e,f,g).
 Problem 4.7.
 Problem 4.8.
 Problem 4.9.
 Problem 5.2(a,b).
 Problem 5.4.
 Problem 5.5(a,b,c).
 Problem 5.6.
 Problem 5.8.
 Problem 5.16.
 Problem 5.17.
 Problem A4.1.
 Problem A4.2.
 Problem A4.3.
 Problem A4.4.
 Problem A4.5.
 Problem A5.1.
 Problem A5.2.
 Problem A5.3.
 Problem 6.3.
 Problem 6.4.
 Problem 7.1.
 Problem 7.2.
 Problem 7.3.
 Problem 7.7.
 Problem 7.8.
 Problem 7.10 (omit d,e).
 Problem 7.11 (omit c).
 Problem 7.12.
 Problem 7.13 (omit c).
 Problem 7.14.
 Problem 7.15.
 Problem 7.16 (omit c,d).
 Problem 7.18.
 Problem 7.20 (omit e).
 Problem 7.21.
 Problem 7.22.
 Problem 7.23.
 Problem 7.25.
 Problem 7.30.
 Problem 8.1.
 Problem 8.2.
 Problem 8.3.
 Problem 8.4. Two examples will suffice.
 Problem 8.5.
 Problem 8.6.
 Problem 8.7.
 Problem 8.9.
 Problem 8.10.
 Problem 8.11. You are asked to multiply all four of the matrices together,
and demonstrate that you get the row echelon form.
 Problem 8.15.
 Problem 8.16.
 Problem 8.18.
 Problem 8.19 (omit d,e,f).
 Problem 8.22.
 Problem 8.23. You are asked to prove the three statements involving permutation
matrices and scalar numbers.
 Problem 8.26.
 Problem 8.27. Don't worry about the case for general k; just prove these
statements for k=2.
 Problem 8.31.
 Problem 8.38. You may find it unfamiliar to write matrices in block form.
Believe it or not, it will come in handy in econometrics class to be able
to understand this notation.
 Problem 8.39. The first part of this question is poorly worded. Instead
of saying "show that the matrix D exists," it should say "show
that the matrix D is welldefined." That is, I want you to check to make
sure the dimensions of the matrix work out correctly.
 Problem 9.1.
 Problem 9.2.
 Problem 9.3.
 Problem 9.4.
 Problem 9.7.
 Problem 9.8.
 Problem 9.9 (omit d,e).
 Problem 9.10.
 Problem 9.11.