Similarly, other more sophisticated versions are available for surface-water groundwater interactions such as partially penetrating wells or streambed clogging (e.g. Hunt, 1999, Hunt, 2012). The Lagrange multiplier A may then be interpreted as the effective (present value) entitlement price. If the marginal damage of the externality is equivalent for all firms, this outcome can be induced with marketable entitlements that are traded on a one-to-one basis, where marginal abatement costs of all firms will equal marginal damage multiplied by A (Kuwayama and Brozovid, 2013, Palazzo and Brozovic, 2014).