Consider the market for attorneys of Section 11.3. Suppose that each attorney can handle only one case (either as a prosecutor or as a defense attorney). In view of (11.18), assume that the demand for attorneys as a function of the supply of attorneys is now given by Q =  η + ηL as long as ηL < η 2η for ηL > η. which means that for every attorney filing a law suit on behalf of a plaintiff, there is a demand for one additional attorney to serve as a defense attorney. That is, unlike the previous analysis where each law suits generated a demand for two attorneys in additional to the prosecutor who is filing the suit on behalf of the plaintiff, here we assume that there is a demand only for one additional attorney to serve on a defense, and that the legal system (judges, clerks, etc.) does not demand attorneys. Answer the following questions.

(a) Write down and plot the excess demand for attorneys as a function of the supply of attorneys. Indicate the levels of ηL at which excess demand is maximized, and the level at which demand for lawyers equals the supply of lawyers.

(b) Suppose that the probability that plaintiffs win a law suit is / = 1/2, and that upon winning the plaintiff is awarded $120 to be paid by the losing defendant. Using the utility functions (11.16) and (11.17), calculate the maximum fee, fmax, which plaintiffs and defendants are willing to pay to an attorney for handling their case. Show your calculations.

(c) Suppose that the market attorney’s fee level is determined by f def =    120 if ED > η 60 + 60 η ED if − η ≤ ED ≤ η 0 if ED < −η, where ED is the excess demand for attorneys you calculated in part (a). Calculate the market-determined attorneys’ fee level assuming that the population size of this economy is η = 100, 000 and that the supply of attorneys is ηL = 5000.

(d) Answer the previous question assuming that ηL = 120, 000.