ECONOMICS 207 SPRING 2008 PROBLEM SET 10 KEY
For this laboratory exercise, consider the following matrices and vectors. You may want to tear this page off so it is easy to view. [ ] [ ] -5 2 0 1 1 4 3 A = , B = , C = 1 -1 -1 2 3 2 2 -4 2 1 [ ] 1 -4 2 3 6
ECONOMICS 207 SPRING 2008 PROBLEM SET 4 KEY
Problem 1. Solve the following equations for x. a. 8x2 22x + 15 = 0 8x2 22x + 15 = 0 (2x 3)(4x 5) = 0 x = 3/2 or x = 5/4
b. 15x2 145x + 90 = 0 15x2 145x + 90 = 0 3x2 29x + 18 = 0 (x 9)(3x 2) = 0 x = 9 or x = 2/3
ECONOMICS 207 SPRING 2008 PROBLEM SET 3
Problem 1. Do the following problems from the book. a. Section 2.1 1) 1d 2) 1f 3) 2f 4) 3c 5) 4d b. Section 2.2 1) 2b 2) 2c 3) 3a 4) 3b 5) 3e 6) 4d 7) 4e 8) 4f c. Section 2.4 1) 4a 2) 4d d. Section 2.5 1) 1b 2) 1e 3
ECONOMICS 207 SPRING 2008 PROBLEM SET 1 KEY
Problem 1. Do the following problems from the book. a. Section 1.2 1) 4a 2) 4b 3) 4c 4) 13a b. Section 1.3 1) 1b 2) 2a 3) 4a 4) 4c 5) 9a 6) 12a 7) 12c 8) 15c 9) 15f c. Section 1.4 1) 2b 2) 3a 3) 3c 4) 5b 5) 6f d
ECONOMICS 207 SPRING 2008 PROBLEM SET 2 KEY
Problem 1. Do the following problems from the book. a. Section 2.3 1) 2a 2) 2d 3) 2e b. Section 2.3 1) 3a 2) 3b 3) 4a c. Section 3.1 1) 1a 2) 1b 3) 1c d. Section 3.2 1) 1 2) 2 e. section 4.2 1) 1a 2) 3a 3) 6
Dat
ECONOMICS 207 SPRING 2008 PROBLEM SET 5 KEY
Problem 1. Solve the following systems of equations for x1 and x2 using the method of substitution. a. cfw_ x1 = 125, x2 = 32
- 3/5 100x1 2/3 x2 - 32 = 0
1/3 - 180x1 x2 2/5 - 225 = 0
From the second equation,
1/
ECONOMICS 207 SPRING 2008 PROBLEM SET 6 KEY
Problem 1. Find the derivatives of each of the following functions with respect to x. a. f ( x ) = 4x2 e2x
3 +4x
f ( x ) = 8xe2x
3 +4x 3 +4x
+ 4x2 e2x
3 +4x
(6x2 + 4)
3 +4x
= 8xe2x
+ 8x2 (3x2 + 2)e2x
b. f ( x )
ECONOMICS 207 SPRING 2008 PROBLEM SET 9 KEY
Problem 1. For each of the following problems, nd the critical points. For each critical point state whether the function is at a relative maximum, relative minimum, or otherwise. Also nd the points of inection
ECONOMICS 207 SPRING 2008 PROBLEM SET 11 KEY
Problem 1. Consider the following matrix and vector. [ ] 1 5 P = , p = 1 6 a. Use elementary row operations to nd both the inverse set of operations.
[ ] 7 , 9 of P and solve the equation Px=p in one
First augm
ECONOMICS 207 SPRING 2008 PROBLEM SET 14 KEY
For your information, the Hessian matrix in the profit maximization problem written as (x1 , x2 ) = pf (x1 , x2 ) - w1 x1 - w2 x2 is given by 2 (x1 , x2 ) 2 (x1 , x2 ) x1 x1 x1 x2 H(x1 , x2 ) = 2 (x , x ) 2 (x
ECONOMICS 207 SPRING 2008 PROBLEM SET 15
For your information, the Hessian matrix in the profit maximization problem written as (x1 , x2 ) = pf (x1 , x2 ) - w1 x1 - w2 x2 is given by 2 (x1 , x2 ) 2 (x1 , x2 ) x1 x1 x1 x2 H(x1 , x2 ) = 2 (x , x ) 2 (x , x
ECONOMICS 207 SPRING 2008 PROBLEM SET 13 KEY
Problem 1. The cost function for a firm is a rule or mapping that tells the minimum total cost of production of any output level produced by the firm for a fixed level of input prices. If the variable y represe
ECONOMICS 207 SPRING 2008 PROBLEM SET 12 KEY
Problem 1. Consider the following matrix and vector. [ ] [ ] 1 1 2 P = , p = , 3 7 2 a. Use elementary row operations to nd both the inverse of P and solve the equation Px=p in one set of operations. Augment ma
ECONOMICS 207 SPRING 2008 PROBLEM SET 7 KEY
Problem 1. Find the second derivative of each of the following functions with respect to x a. f (x) = 5x3 - 4x2 + 15x + 10 f (x) = 15x2 - 8x + 15 f (x) = 30x - 8
b. f (x) = 200x5/6 + 3x-4 + 30x-1/3 f (x) = = 100
ECONOMICS 207 PROBLEM SET 8 KEY
Problem 1. Consider the following matrices. ] ] [ [ 3 -2 5 3 2 C B = A = -4 3 1 4 3 7 19 1 2 3 G = -3 -8 F = -3 -7 -2 0 -1 3 7 1 [ ] 1 1 2 -2 1 c = a = b = 3 1 2 Compute the following a. A + C [ A+C = 3 4 2 3 ] [
[
=
17 -7