Answer:
D2 is relevant when rivals match the firm’s price changes
D1 is relevant when rivals do not match the firm’s price changes
Explanation:
Given
See attachment for graph
Solving (a): Which is relevant to price changes
Calculate the slope of D1 and D2 using:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
For D1
[tex](x_1,y_1) = (0,70)\\ (x_2,y_2) = (21,50)[/tex]
So:
[tex]m = \frac{50- 70}{21- 0}[/tex]
[tex]m = \frac{- 20}{21}[/tex]
[tex]m_{D_1} = -0.9524[/tex]
For D2
[tex](x_1,y_1) = (0,100)\\ (x_2,y_2) = (20,20)[/tex]
So:
[tex]m = \frac{20 - 100}{20 - 0}[/tex]
[tex]m = \frac{-80}{20}[/tex]
[tex]m_{D_2} = -4[/tex]
By comparison:
[tex]|m_{D_2}| > |m_{D_1}|[/tex]
i.e.
[tex]|-4| > |-0.9524|[/tex]
[tex]4 > 0.9524[/tex]
This means that D2 is steeper than D1. Hence, D2 is relevant to price changes
Solving (b): Which is not relevant to price changes
In (a), we concluded that D2 is relevant to price change.
Hence, D1 is relevant when price does not change.
