What is the equation for the social demand curve to the for values of Q that are less than the value where the kink occurs?

Question

BlackTom AI · Accepted Answer

To tackle the question, we first restate the setup and the options to keep the context clear.
Option A: P=200-Q. This form represents a linear relationship with slope -1 and intercept 200. If the kink occurs at a Q value that changes the slope, this option would only be correct if the social demand curve had a slope of -1 in the region below the kink, which would place the intercept accordingly. Without that intercept being 300, this option seems to describe a different segment than the one specified for Q below the kink.
Option B: P=100-Q. Here the intercept is 100 with a slope of -1. This would imply an even lower starting price than A for small Q, but again does not align with an intercept of 300 that would typically be associated with the higher baseline before the kink, unless the kink itself is at a different Q value and the intercept shifts accordingly. The slope matches a typical linear demand form, but the intercept seems inconsistent with the given kink scenario.
Option C: P=300-Q. This has intercept 300 and slope -1. If the kink region below the kink uses a steeper or different slope, this could be plausible for the segment above the kink, but for Q below the kink, the standard social demand relationship would usually differ from the lower-Q segment if the kink represents a change in slope. Thus, this option is a candidate for the post-kink segment rather than the pre-kink one.
Option D: P=300-2Q. This form has intercept 300 and a steeper slope of -2, indicating a faster price decline as quantity rises. In many kinked demand scenarios, the pre-kink segment (the region with Q less than the kink) indeed exhibits a steeper slope, reflecting a stronger price response to quantity changes before the kink occurs. The intercept of 300 matches a high starting price before the kink, which is consistent with the given context where the kink sits at a higher intercept.
Reasoning across options shows that the intercepts and slopes must align with the described region (Q below the kink) and the typical interpretation of a kinked demand curve. The option with intercept 300 and a steeper slope (-2) is the one that best matches a pre-kink social demand relationship in many standard kinked-demand models, whereas the other options either have a lower intercept or a gentler slope that would suit other regions or misalign with the kink structure.
In summary, while each option presents a plausible linear form, the combination of a high intercept (300) with a steeper slope (-2) uniquely corresponds to the pre-kink region in the common kinked-demand framework, whereas the other options either misplace the intercept or do not capture the expected slope change at the kink.

ECON_104B_001_25S Lecture Quiz #4

What is the equation for the social demand curve to the for values of Q that are less than the value where the kink occurs?

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