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2022 PEA Q11

Let ei(p0)e_i(p_0) be the price elasticity of demand for good XX of consumer ii at p0p_0, with heterogeneous quantities. What is the elasticity of the aggregate demand at p0p_0?

Reveal answer and solution

Answer

B

Solution

  1. 1

    Let Q(p)=∑iqi(p)Q(p) = \sum_i q_i(p). Then

  2. 2
    eagg(p0)=p0Q(p0)∑iqi′(p0)=∑iqi(p0)Q(p0)⋅p0 qi′(p0)qi(p0)=∑iqi(p0)∑jqj(p0) ei(p0). e_{\text{agg}}(p_0) = \frac{p_0}{Q(p_0)} \sum_i q_i'(p_0) = \sum_i \frac{q_i(p_0)}{Q(p_0)} \cdot \frac{p_0\, q_i'(p_0)}{q_i(p_0)} = \sum_i \frac{q_i(p_0)}{\sum_j q_j(p_0)}\, e_i(p_0).
  3. 3

    The aggregate elasticity is the consumption-share-weighted average of individual elasticities.

Answer structure / marking notes

Equal weights 1/N1/N are valid only when all consumers buy equal quantities.

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.