Supplement to “ Demand heterogeneity in insurance markets : Implications for equity and efficiency ”

Content Provider	Semantic Scholar
Author	Ichael Eruso
Copyright Year	2017
Abstract	Consider an insurance market in which consumers are associated with a type z that represents a signal of insurance valuation, conditional on marginal cost. Assume that within potential submarkets defined by types z, both the demand and marginal cost curves are strictly decreasing (monotonicity), that demand is more steeply sloped than marginal costs, and that demand and marginal costs cross exactly once (single crossing). Let the rank order of consumer valuations across types z hold conditional on any level of costs. Heterogeneity of this form implies there is correlation between v and z conditional on c. Under these conditions, if the efficient take-up of insurance is strictly between 0 and 1 within each of the submarkets and if there exists some common support across the z submarkets in the continuous distributions of marginal cost, then optimal prices differ across types z. That is, there is welfare-improving price discrimination along the characteristic z, relative to the best uniform price. To prove welfare-improving price discrimination, define va(c) and vb(c) as willingness-to-pay conditional on costs for a fixed contract among consumers in groups a and b, respectively. By the assumptions above, these functions are one-to-one mappings of costs to valuations. Define the group z = a as the group for which willingnessto-pay conditional on costs is higher and define z = b as the remainder of the market, so that va(c) > vb(c) ∀c. Except for the degenerate cases where va(c) > vb(c) > c ∀c (all enrollees in the market efficiently insured) or where c > va(c) > vb(c) ∀c (all enrollees in the market efficiently uninsured), there exists some level of costs, c, for which va(c) > c > vb(c). That is, there exists some level of costs at which it is efficient to insure the a types but not the b types. A simple version of this case that assumes linear v(c) functions is displayed in Figure 2.
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Language	English
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Content Type	Text
Resource Type	Article