Consider two markets with goods that are perfect substitutes. The consumer has a demand function for the first good given by D(P)=8−4P, where P is the price of the first good. If the price of the other good decreases, the new demand function for the first good is most likely:

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When two goods are perfect substitutes, a fall in the price of one good typically causes the consumer to substitute toward that cheaper good. This means the demand for the first good decreases at every possible price P, which is a leftward shift of its demand function.

Option a: D(P)=8−2P. Here the slope is less steep (slope −2 instead of −4) and the intercept remains 8. A substitution to a cheaper substitute would not make the demand curve flatter at the same intercept; moreover, the intercept would not stay the same if the other good’s price fell. This option therefore misrepresents both the intercept and the slope change expected from a substitution to a cheaper substitute.

Option b: D(P)=10−4P. This keeps the same slope but increases the intercept to 10. An increased intercept means higher quantity demanded for all prices, which contradicts the idea that demand for the first good decreases when the other good becomes cheaper. So this cannot be correct.

Option c: D(P)=4−4P. This option preserves the slope −4 and lowers the intercept from 8 to 4, reflecting a uniform decrease in quantity demanded across all prices due to the shift to the cheaper substitute. This matches the intuition of a leftward shift in a perfect substitute scenario where the other good becomes relatively cheaper.

Option d: D(P)=8−4P. This is identical in slope to the original but with no intercept change, implying no shift in demand. If the other good’s price has fallen, we would typically expect a shift, not a mere rotation along the same curve. Therefore this option fails to capture the substitution effect.

In summary, the substitution effect toward the cheaper substitute reduces quantity demanded of the first good at every price, which is captured by a lower intercept while keeping the same slope. Among the provided forms, only D(P)=4−4P satisfies that leftward shift with the same slope.

SESS0007_24-25 LSA Test

Consider two markets with goods that are perfect substitutes. The consumer has a demand function for the first good given by D(P)=8−4P, where P is the price of the first good. If the price of the other good decreases, the new demand function for the first good is most likely:

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