If Sl (p) = p- 10 and S2(p) = p- 15, then at what price does the industry
supply curve have a kink in it? Use step by step to solve it.
Step 1: The industry supply curve is the sum of the two individual supply curves, Sl(p) and S2(p).
Step 2: The kink in the industry supply curve occurs when the two individual supply curves intersect.
Step 3: To find the point of intersection, set Sl(p) = S2(p) and solve for p.
Step 4: Sl(p) = S2(p)
Step 5: p - 10 = p - 15
Step 6: 10 = 15
Step 7: This is not true, so there is no kink in the industry supply curve.
To identify the price at which the industry supply curve has a kink, we need to find the point where the two supply curves intersect.
First, let's set the two supply functions, Sl(p) and S2(p), equal to each other and solve for p:
Sl(p) = S2(p)
p - 10 = p - 15
By simplifying the equation, you will see that the variable 'p' cancels out:
-10 = -15
This equation is not possible — it has no solution. This means that the supply curves do not intersect, and thus, there is no kink in the industry supply curve.
Therefore, we can conclude that the industry supply curve does not have a kink.
To find the price at which the industry supply curve has a kink, we need to compare the two supply functions, S1(p) and S2(p), and determine the point where the slopes change.
Step 1: Write out the supply functions:
S1(p) = p - 10
S2(p) = p - 15
Step 2: Set the two supply functions equal to each other:
p - 10 = p - 15
Step 3: Simplify the equation:
-10 + 15 = p - p
5 = 0
Step 4: Evaluate the equation:
This equation, 5 = 0, is not true. It means that there is no price at which the industry supply curve has a kink.
Therefore, based on the given supply functions, there is no price at which the industry supply curve has a kink.