Liability rules versus taxes and quantity regulation

The standard Pigouvian approach to reducing the adverse welfare effects of uncompensated negative external effects is to set a tax equal to the social marginal harm, where the marginal harm is evaluated at the optimal level of production. In some circumstances, this approach may be preferable to a set of liability rules. There are other situations, however, in which liability rules are preferable to taxes. In this section we explore one such situation: where the regulator is uncertain about marginal benefits and marginal costs.

To illustrate the main principles involved, we consider an example based on the classic paper of White and Wittman (1983). Consider an economy with a single firm that produces output of Q. Suppose that regulator knows that the marginal social cost curve is:

where C0 > 1 and C1 > 0. However, the regulator does not know the exact shape of the firm's marginal benefit curve. Suppose that the actual marginal benefit curve is:

where B0 > 0and B1 < 0. The firm's private marginal costs are zero. The regulator knows the values of B0 and B1 but cannot observe v. Suppose that regulator believes that v will take on the following values:

Let Q be the point where expected marginal social benefits equal marginal social costs. Since the expected value of v is zero, this means that at Q, we must have:

So:

Consider the following policy options that are available to the regulator:

  • • Quantity Regulation: Force the firm to always produce at Q = Q.
  • • Tax Regulation: Impose a Pigouvian per unit tax of t on the production of Q , where t is equal to expected marginal social costs evaluated at the point Q = Q.
  • • Strict Liability: Make the firm strictly liable for the 'reasonable' social costs that it creates, where 'reasonable' social costs are interpreted as expected social costs.

Let us examine each of these regulatory mechanisms. Before doing so, however, we establish an important result. Consider Figure 4.6.1 below, which plots marginal social benefits and costs that flow from the production of Q. The efficient level of production is where these marginal benefits and costs are equal, at the point Q*. Other points of production - whether greater or less than Q* - result in welfare losses. As a general rule, the size of these welfare losses can be computed by calculating the area of the shaded triangle, which is the accumulated difference between marginal benefits and costs for all units that are either produced in excess of Q*, or which are less than Q*. To calculate the deadweight loss from not producing Q*, we therefore simply compute the base of the triangle, which is the difference between Q* and the level of actual

Efficient production and the computation of deadweight welfare loss production

Figure 4.6.1 Efficient production and the computation of deadweight welfare loss production, and the height of the triangle, which is the difference between marginal benefits and costs at the actual level of production. So, for example, if production was at Q1 instead of Q* in Figure 4.6.1, the deadweight loss associated with this level of production would be:

Similarly, if production was at Q2 instead of Q*, the deadweight loss would be:

This method of computing deadweight losses will be utilised extensively in the analysis that follows.

 
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