Note: The page numbers are the page numbers of the original Wisniewski text.

1. Co-ordinate system. Determine which quadrant the following points are in: a. b. c. d. (x, y) = (-2, 2) (x, y) = (2, -2) (x, y) = ((-1)2, 2) = (1, 2) (x, y) = (2-1, 2) = (1/2, 2)

y

2.5

Coordinates (x, y)

(2-1, 2) ((-1)2, 2)

(-2, 2)

2 1.5 1 0.5

x

-2.5 -2 -1.5 -1 -0.5 -0.5 -1 -1.5 0.5 1 1.5 2 2.5

(2, -2)

-2 -2.5

2. Functions a. Graph y = |x|. (The bar symbols mean take the absolute value of x ie |-3| = 3). If you are not sure what it looks like, plug in a couple values for x and find the corresponding y. ECO2IQA 2010 Tutorial Chapter 2 Solutions Page 1 of 17

10 9 8 7 6 5 4 3 2 1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5

y

x

1 2 3 4 5 6 7 8 9 10

y = |x|

b. Is y a function of x? Explain.

Yes. For each x value there is only one y value.

c. Re-do a) and b) using y2 = x – 1 (where x ≥ 1).

ECO2IQA 2010 Tutorial Chapter 2 Solutions

Page 2 of 17

y

4

y2 = x - 1

3 2 1

x

1 -1 -2 -3 -4 2 3 4 5 6 7 8 9 10

y is not a function of x: one x value (say x = 5) has two y values (y = 2 and y = -2). d. Let f(x) = x2 + 1. Compute f(0), f(-1), f(1/2) and f ( 2) .

f(0) = 02 + 1 = 1. f(-1) = (-1)2 + 1 = 2. f(1/2) = (1/2)2 + 1 = 1.25. f( 2 ) = ( 2 )2 + 1 = 3.

3. Linear functions. Do Exercise 2.2 from the text. (Note: Exercise questions are located at the end of a chapter. Student Activity questions are found within the chapter.)

TC = 100 + 5Q i. ii. Change in TC is 5. Change in TC is 5.

Page 3 of 17

ECO2IQA 2010 Tutorial Chapter 2 Solutions

iii. iv.

Change in Total Cost from a unit change in output is called Marginal Cost (MC). Not realistic to expect constant MC in most industries. With a fixed factor of production (say capital) we would expect (eventually) diminishing marginal productivity of the variable factor (say labour) since more workers are sharing the same amount of capital – eg...

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