To calculate the point price elasticity of demand, we use the formula:

$E_p = \frac{dQ}{dP} \cdot \frac{P}{Q}$

Here are the steps to solve:

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1. Rearrange the demand function to express $Q$ in terms of $P$:

The given demand function is: $P = 16 - 5Q$

Rewriting this: $Q = \frac{16 - P}{5}$

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2. Differentiate $Q$ with respect to $P$:

$\frac{dQ}{dP} = -\frac{1}{5}$

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3. Determine $Q$ when $P = 2.5$:

Substitute $P = 2.5$ into $Q = \frac{16 - P}{5}$: $Q = \frac{16 - 2.5}{5} = \frac{13.5}{5} = 2.7$

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4. Substitute into the elasticity formula:

Now substitute the values: $E_p = \frac{-1}{5} \cdot \frac{2.5}{2.7}$

Simplify: $E_p = -\frac{2.5}{13.5} \approx -0.185$

The absolute value of elasticity is: $|E_p| \approx 0.185$

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5. Compare to choices:

None of the listed answers match exactly. Let me double-check for accuracy. Given demand function and values P = 2.5 # Price dQ_dP = -1 / 5 # Derivative of Q with respect to P

Calculate Q when P = 2.5

Q = (16 - P) / 5

Point price elasticity formula

E_p = dQ_dP * (P / Q)

Absolute value of elasticity

abs_E_p = abs(E_p) E_p, abs_E_pThe calculated point price elasticity of demand is approximately $-0.185$, with an absolute value of $0.185$. None of the provided options match this value exactly, so there may be a discrepancy in the question or its choices.

Would you like to clarify or check for other aspects?

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Related Questions:

1. How is the price elasticity of demand different at other price points for this function?
2. Can we interpret the meaning of inelastic demand from this calculation?
3. How does the demand curve's slope affect elasticity?
4. What happens to $E_p$ as $P$ approaches $0$?
5. Can this concept be applied to real-world markets with nonlinear demand curves?

Tip: Always confirm that the demand equation is correctly provided and consistent with the answer options!