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We study the connection between risk aversion, number of consumers anduniqueness of equilibrium. We consider an economy with two goods and $c$impatience types, where each type has additive separable preferences with HARABernoulli utility function,$u_H(x):=\frac{\gamma}{1-\gamma}\left(b+\frac{a}{\gamma}x\right)^{1-\gamma}$.We show that if $\gamma\in \left(1, \frac{c}{c-1}\right]$, the equilibrium isunique. Moreover, the methods used, involving Newton's symmetric polynomialsand Descartes' rule of signs, enable us to offer new sufficient conditions foruniqueness in a closed-form expression highlighting the role played byendowments, patience and specific HARA parameters. Finally, new necessary andsufficient conditions in ensuring uniqueness are derived for the particularcase of CRRA Bernoulli utility functions with $\gamma =3$.

Risk aversion and uniqueness of equilibrium: a polynomial approach