Question: Sketch the graphs of the linear functions 1 to 8 below, identifying the relevant intercepts on the axes. Assume that variables represented by letters that suggest they are economic variables (i.e. all variables except x and y) are restricted to non-negative values.
1. y = 6 + 0.5x
2. y = 12x - 40
3. P = 60 - 0.2Q
4. Q = 750 - 5P
5. 1,200 = 50K + 30L
(Note that this budget constraint for a firm is an accounting identity rather than a function although a given value of K will still determine a unique value of L, and vice versa.)
6. TR = 8Q
7. TC = 200 + 5Q
8. TFC = 75
9. Make up your own example of a linear function and then sketch its graph.
10. Which of the following functions do you think realistically represents the supply schedule of a competitive industry? Why?
(a) P = 0.6Q + 2
(b) P = 0.5Q - 10
(c) P = 4Q
(d) Q = -24 + 0.2P
Assume P ≥ 0, Q ≥ 0 in all cases.