Contracting Situations of Imperfect Information

Contracting with Imperfect Information

The manufacturing firm marginal benefit, MB, for hours of legal service is

MB=$400-2L, where L=hours per week of legal services.

Marginal benefit represents the maximum price that a rational buyer would pay for an additional unit of anything. This means that the marginal benefit curve can be considered to be the demand curve. This curve can be represented on a graph by figuring out the end point and then drawing a straight line between these points.

For this case, we will take the formula MB=$400-2L, where L represents hours of legal services. The first step is to find out the value of MB when L=0 (this will give the value $400-0, therefore the vertical intersection point is $400) and when the value of MB=0, the value of L will be (0=400-2L L=200). For this question there are no fixed costs and the marginal costs (MC) is constant and equal to $200 per hour of legal services (L). For this case, the most efficient outcome would be to have the law firm supply legal services up to the point where the marginal cost is equal to the marginal benefit. This means that the law firm will supply a total of 100 hours of legal services.

Therefore, the total cost to the law firm would be $20,000 and surplus from providing this services would be $10,000. This is shown in the diagram below.

If we assume that the law firm ends up supplying 100 hours. If the law firm has all the market power and is able to dictate terms to the manufacturing firm, then the law firm might simply bill the tire company a total of $30,000 for 100 hours of legal services. In this case, the law firm would keep all the surplus of $10,000. The law firm would essentially be acting as a perfectly discriminating monopolist. The outcome is the same as what you would get by having the law firm charge a different price for each hour of service. If the law firm has all the power along with full knowledge of the benefits of its services to the manufacturing firm, then the law firm will tailor it’s pricing to extract all of the surplus.

If the tire company has all the market power and is able to dictate terms to the law firm, then the law firm would simply get $200 for each of the 100 hours of legal services that it provides for a total bill of $20,000 and thus the tire company would keep all the surplus of $10,000. This might happen if there is a large number of law firms competing to offer services to the manufacturing firm. This would leave the law firm with little market power and force it to charge a price equal to its marginal cost of $200 per hour of legal services. In other words, this would make the law firm a price taker rather than a price maker.

Another possibility is that the two parties might agree to split the surplus evenly. In that case, each of them would get, $5,000. The law firm would then add half of the surplus to its total cost of $20,000 and bill a total of $25,000 ($5,000+$20,000) for a total of 100 hours of legal services.

The key thing here would of course be that whenever a monopolist faces a linear downward sloping demand curve, the corresponding marginal revenue curve starts out where the demand curve intersects the vertical axis (or in this case at $400), but it has twice the slope of the demand curve. So if the formula for the demand curve can be written as P=400-2L (with a slope of -2) then the corresponding marginal revenue curve can be written MR=400-4L (with a slope of -4). By setting MC=MR and solving for the amount of legal services, we get 200=400-4L, so L = (400-200)/4=50. The price per unit on the demand curve that corresponds to L=50 is $300. This result is outlined in the diagram below:

Note that in this case, the profits for the law firm would equal $2,500, but the remaining surplus, SR, for the manufacturing firm client will have shrunk to SR = ((400-300) ×50)/2 = 2,500 and the lost surplus, SL, due to the fact that the law firm will now only be supplying 50 hours will be SL = ((400-300) ×(100-50)/2 = 2,500.

There is a situation where the manufacturing company seeking legal help may not be fully assured that the law firm will indeed provide what is promised or needed or that the law firm is overcharging for hours provided.