This paper investigates equilibrium in an insurance market where risk classification is restricted. Insurance demand is characterised by an iso-elastic function with a single elasticity
parameter. We characterise the equilibrium by three quantities: equilibrium premium; level of adverse selection; and “loss coverage”, defined as the expected population losses compensated
by insurance. We find that equilibrium premium and adverse selection increase monotonically with demand elasticity, but loss coverage first increases and then decreases. We argue that
loss coverage represents the efficacy of insurance for the whole population; and therefore, if demand elasticity is sufficiently low, adverse selection is not always a bad thing
