Per unit transaction costs
Per unit transaction costs are added to each unit of production that the parties negotiate over. As Chapter 1 illustrated, these kinds of transaction costs drive a wedge between the marginal rates of substitution or marginal valuations of the parties. In this section we show that the existence of per unit transaction costs means that neither the efficiency version nor the invariance version of the Coase Theorem hold.
A rule of no liability
To illustrate this result, suppose that each party faces (possibly different) specific per unit transaction costs. We continue to assume identical, quadratic quasi-linear preferences, but the result still goes through with other assumptions about preferences. Suppose that the factory has the right to choose the level of Q. In the absence of any bargaining with the factory, they would choose Q = Q. Now suppose that the factory and the residents bargain over the level of production of Q. Let the factory face a transaction cost of tF per unit of production of Q that is negotiated below the initial allocation Q = Q. Similarly, let the residents face a transaction cost of tR per unit of production of Q that is negotiated below the initial allocation. This situation is illustrated in Figure 3.5.1.
The marginal benefit received by the factory per unit of reduction in the level of Q now consists of the money price P, less the transaction costs tF it incurs in bargaining with the residents. Thus the price received by the factory is:
Figure 3.5.1 Per unit transaction costs when the factory has the right to pollute
On the other hand, the price paid by the residents per unit of reduction in the level of Q now consists of the money price P which is paid to the factory, plus the transaction costs tR it incurs in bargaining with the factory. Thus the price paid by the residents is:
Note that the gains from trade are still completely exhausted, but in the presence of transaction costs, the gains from trade are now exhausted at the point Q = Q: > Q*.
The common money price P is determined by the commonality of marginal rates of substitution inclusive of transaction costs:
The total transaction costs incurred are
The aggregate gains from trade to each party are lower than they were in the absence of transaction costs, although the gains to each party individually may be higher or lower than they were in the absence of transaction costs, depending on the bargaining power of each party. The presence of transaction costs may alter the distribution of bargaining power between the parties; indeed, one party could deliberately and strategically impose transaction on itself and the other party in order to improve its bargaining position.