Let’s consider the supply curve S(P)=8+2P, where P is the price of the good. As the price of the good decreases, the absolute value of the price elasticity of supply:

Question

BlackTom AI · Accepted Answer

Let's walk through how the price elasticity of supply is defined for the given supply function.
The supply curve is Q(P) = 8 + 2P, so dQ/dP = 2.
The price elasticity of supply is e_s = (dQ/dP) * (P/Q) = 2 * P / (8 + 2P).
This can be simplified to e_s = P / (4 + P).
Now consider how e_s changes as P changes. If P increases, the numerator grows and the denominator grows as well, but the derivative with respect to P is positive, which means e_s increases with P; equivalently, as P decreases, e_s decreases. In other words, the absolute value of the price elasticity of supply falls when the price falls.
Option a: 'increases' would imply e_s rises as price falls, which contradicts the derived monotone relationship. This is incorrect.
Option b: 'stays constant' would mean e_s does not depend on P, but e_s = P/(4+P) clearly depends on P, so this is incorrect.
Option c: 'decreases' matches the finding that e_s is an increasing function of P, hence decreases as P decreases. This is correct.
Option d: 'equals to the slope of the supply curve' suggests e_s = dQ/dP = 2, which is not true in general; elasticity is a ratio that depends on P and Q, not simply the slope. This is incorrect.
Therefore, the only accurate statement is that the absolute value of the price elasticity of supply decreases as the price decreases due to the functional form e_s = P/(4+P).

Let’s consider the supply curve S(P)=8+2P, where P is the price of the good. As the price of the good decreases, the absolute value of the price elasticity of supply:多项选择题

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