A lawyer has two clients. She charges a yearly retainer plus a separate fee for each consultation. The retainer is a fee each client pays just to secure the services of the lawyer for the followingyear, and the consultation fee is the price the lawyer charges to do one legal job for the client. Theclients' annual demand curves for legal jobs are

Client1: Q1=20P

Client2: Q2=182P

where P is the consultation fee in thousands of dollars for one legal job and Qi is the number of legal jobs done for client i.

Thelawyer's marginal cost for completing one legal job is 2.7 (also in thousands ofdollars).

The lawyer wants to determine the fee schedule(retainer and consultationfee) that will maximize her profit. She feels she cannot use a different fee schedule for eachclient, so she must set one retainer and one consultation fee that apply to both clients.

She should charge a consultation fee of $

nothing

thousand per legal job.