In Paul Krugman's articile on the trade model with a monopolistically competitive market (https://www.sciencedirect.com/science/article/pii/0022199679900175
Links to an external site.
), a CES (Constant Elasticity of Substitution) utility function is used. A typical expression of the CES preferences is

The Greek letter sigma () indicates the elasticity of substitution. A higher value of sigma means that the variety of the product is ...

Question

In Paul Krugman's articile on the trade model with a monopolistically competitive market (https://www.sciencedirect.com/science/article/pii/0022199679900175
Links to an external site.
), a CES (Constant Elasticity of Substitution) utility function is used. A typical expression of the CES preferences is

The Greek letter sigma () indicates the elasticity of substitution. A higher value of sigma means that the variety of the product is ...

BlackTom AI · Accepted Answer

In CES preferences the elasticity of substitution σ measures how easily consumers switch between varieties: a larger σ means varieties are closer substitutes and therefore more homogeneous.

1) Relevant knowledge points
- CES aggregator: U = {Σ_i x_i^{(σ-1)/σ}}^{σ/(σ-1)}. The parameter σ is the constant elasticity of substitution between varieties.
- Under CES utility the own-price elasticity of demand for a variety equals σ.
- In Krugman-style monopolistic competition, markups = σ/(σ−1), so higher σ reduces markups toward marginal cost (σ→∞ → perfect substitutes).

2) Step-by-step reasoning
- From CES preferences one derives the individual demand for variety i (price p_i) in aggregate terms, which takes the form x_i ∝ p_i^{−σ}. More precisely, x_i = E · p_i^{−σ} / Σ_j p_j^{1−σ}, where E is expenditure and the denominator is the price index normalization.
- Compute own-price elasticity: (∂x_i/∂p_i) · (p_i/x_i) = −σ. Thus the percentage change in quantity demanded when p_i changes is −σ times the percentage price change.

3) Intermediate calculation shown
- Starting from x_i ∝ p_i^{−σ}:
  ∂x_i/∂p_i = −σ · p_i^{−σ−1} · (constant)
  => (∂x_i/∂p_i)·(p_i/x_i) = −σ.

4) Why the correct answer is correct
- A larger σ means a larger (in absolute value) response of demand to price differences, i.e., consumers readily switch across varieties. That is exactly the economic definition of being more substitutable or more homogeneous. In the limit σ→∞ varieties become perfect substitutes (fully homogeneous).

5) Why other options are incorrect
- “More differentiated” is the opposite of higher substitutability. Higher σ reduces differentiation.
- “More expensive” is not implied by higher σ (in fact higher σ tends to lower markups, reducing price).
- “Less expensive” mixes up price and substitutability; the question asks about variety characteristics, not price.

6) Conclusion
Therefore a higher value of σ means the variety of the product is more homogeneous, which matches the provided answer.

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