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2022 PEA Q13

C(q)=3q2+800C(q) = 3q^2 + 800; P=280−4qP = 280 - 4q. Find the price elasticity of demand at the profit-maximizing price.

Reveal answer and solution

Answer

C

Solution

  1. 1

    Profit: π(q)=(280−4q)q−3q2−800=280q−7q2−800\pi(q) = (280 - 4q)q - 3q^2 - 800 = 280q - 7q^2 - 800.

  2. 2

    FOC: 280−14q=0⇒q∗=20280 - 14q = 0 \Rightarrow q^* = 20, so P∗=280−80=200P^* = 280 - 80 = 200.

  3. 3

    Elasticity at (P∗,q∗)(P^*, q^*):

  4. 4
    ε=dqdP⋅Pq=−14⋅20020=−2.5. \varepsilon = \frac{dq}{dP} \cdot \frac{P}{q} = -\frac{1}{4} \cdot \frac{200}{20} = -2.5.

Answer structure / marking notes

dq/dP=−1/4dq/dP = -1/4, not −4-4.

Content note

Imported from public/resources/isi/msqe/solutions/pea/2022/ISI_MSQE_PEA_2022_Solutions.tex. Question wording is retained from the available local TeX source; incomplete option blocks or ambiguous source status are flagged for review.