Macroeconomics
10th Edition
ISBN: 9780134896441
Author: ABEL, Andrew B., BERNANKE, Ben, CROUSHORE, Dean Darrell
Publisher: PEARSON
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Chapter A, Problem 2P
To determine
To plot:The function and slope of the function.
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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…
Quadratic Functions #2
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Chapter A Solutions
Macroeconomics
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- The line in the graph shows a relationship between two variables, x and y. What is the slope of the curve? ... The slope of the curve is >>> If the slope is negative, use a minus sign. If the slope is positive, do not use a plus sign. 8 7 5- 4- 3- 2- 1- 0- y 0 1 2 3 4arrow_forwardFind an equation in point-slope y -y, = m(x-x,) for the line through the given points. (- 3, – 3) and (2,7) What is the equation of the line in point-slope form? (Use integers or simplified fractions for any numbers in the equation.)arrow_forwardGraph the function C=50+0.8Y and give economic interpretations of the elements of the equation.arrow_forward
- Consider the function Y = *square root*pXZ where X > 0 and Z > 0. Draw the contour lines (in the positive quadrant) for this function for Y = 4, Y = 5, and Y = 10. What do we call the shape of these contour lines? Where does the line 20X + 10Z = 200 intersect with the contour lineY = 50?arrow_forwardConvexity & Concavity Consider the function defined by the formula This function is 200 if 0 < x < 20 x y = f(x) = 30- x if 20 ≤x≤40 200 if 40 < x < 60 x a. Concave but not strictly concave b. Strictly convex c. Strictly concave d. Convex but not strictly convex e. I cannot tell because the second derivative of f(x) cannot be calculatedarrow_forwardYou are given the function y=11−1.5x. The slope of the equation is enter your response here. (Round your answer to one decimal place.)arrow_forward
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