EBK MACROECONOMICS
10th Edition
ISBN: 9780134896571
Author: CROUSHORE
Publisher: VST
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Question
Chapter A, Problem 2P
To determine
To plot:The function and slope of the function.
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Students have asked these similar questions
Consider the linear spline function
f(x) = 1 + x + h1(x, 2)
where h1(x,2) = x-2 if x>2 and 0 otherwise.
What is the slope of f at the point x=-1?
The following graph contains four lines (A, B, C and D), each of which has a slope that is either positive, negative, zero, or infinite.
For each of the following scenarios, indicate whether the relationship between the two variables is positive or negative, as well as which line on the previous graph has a slope that reflects this type of relationship.
Hint: The X-axis and Y-axis on the graph are not labeled intentionally. You need to substitute the variables from each scenario for the horizontal and vertical axis. For example, in the first scenario, X-axis should be labeled “ The average grade received" and Y-axis should be labeled "The number of hours spent studying".
Scenario: As the number of hours spent studying rises, the average grade received rises.
Relationship: Positive or Negative
Line: A, B, C, or D?
Scenario: As the number of hours spent watching TV rises, the average grade received falls.
Relationship: Positive or Negative
Line: A, B, C, or D?
Scenario: As the…
f(x1,x2)
4
2
0
-2
-4
−1
2
0
1
1
0
2
-1
X1
3-2
x2
Figure 2: Graph of the function f(x1, x2) = 2x1 = x²-x+3
Consider the following function:
f(x1, x2) = 2x1 - x-x+3.
-
For your visual convenience, a portion of the function is depicted in Figure 2.
(a) Compute the gradient vector of f.
(b) Compute the Hessian matrix of f.
(c) Determine all points that yield stationary values of f.
(d) Use the second-order conditions to determine whether each of the stationary val-
ues of f is a maximum, a minimum, or neither.
Chapter A Solutions
EBK MACROECONOMICS
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