Economics

1. Consider the relationship between a shipper and a lorry driver . hires to transport a load from London to Edinburgh. When lands in Edinburgh, will have another load ("back-haul") whose characteristics cannot be contracted in advance. The value of this load is . While driving from London to Edinburgh, can engage in two activities: she can search for an alternative back-haul and she can attend to her lorry. Alternative backhauls have value ₂ with probability and ₁ with probability 1 , where ₂ > > ₁. The probability is a choice variable for the lorry driver, and the cost of effort is ² /2. The value of the lorry, , is also a choice variable for the driver, and the cost of is ² /2. There is symmetric information throughout, but is not verifiable, and contracts on the back-haul cannot be written until the driver reaches Edinburgh. Both parties are risk neutral and there is no discounting.

(i) Solve for the first-best levels of and .

(ii) Assume that the driver owns the lorry. Take this to mean that: (i) in the absence of renegotiation the lorry driver has the right to accept an alternative backhaul, in which case the shipper's payoff is zero (since there are no other drivers to carry her load); (ii) the driver receives the full value of the lorry, (she is the residual claimant). Suppose, however, that renegotiation takes place if the alternative back-haul is inefficient and that this proceeds according to Nash bargaining with a 50-50 split. Solve for the second-best values of and .

(iii) Now assume the shipper owns the lorry. Take this to mean that: (i) in the absence of renegotiation the driver does not have the right to take alternative back-haul, and so receives zero, and the shipper also receives zero (since she needs the driver to carry her load); (ii) the shipper receives the full value (he is the residual claimant). Suppose again that renegotiation takes place as above. Solve for the second-best values of and .

(iv)Provide conditions under which the lorry is optimally owned by the driver and conditions under which it is optimally owned by the shopper. Discuss the trade-off between shipper and driver ownership.