Question

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 following​ year, and the consultation fee is the price the lawyer charges to do one legal job for the client. The​ clients' annual demand curves for legal jobs are

Client​ 1:

Upper Q 1 equals 24 minus Upper PQ1=24−P

Client​ 2: Upper Q 2 equals 20 minus 2 Upper PQ2=20−2P

where P is the consultation fee in thousands of dollars for one legal job and

Upper Q Subscript iQi

is the number of legal jobs done for client

i.

The​ lawyer's marginal cost for completing one legal job is

2.3

​(also in thousands of​ dollars).

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

She should charge a consultation fee of ____ thousand per legal job. ​(Enter your response rounded to two decimal​ places.)

Answer 1

if you want to have both kind of clients, you would sot a retainer fee I which is equal to the consumen surple of lower demend group dient 2. Then price per legal job will be i. Find the price that I will be charged per wit by finding the maximized prift functum. Profit funchen - 2.5+ (-me) ( +62) Note: I = Consumer Surplus of client 2 at - pruht maximized price p. Pnce 02 20 Censumer Censumer Consumer Surplus = Area of AABC Surplus = 0.5 (10-p) (2) Surplus = 0.5 (10-1) (20-22) > F:0.5 (10-2) (20-28)

Bolt 25+(P-NC) (6,700.) 1-2 (0.5) (lo-p) (20-2p) + (P-213) (44-3p) 1. (10-P) (20-2p) + (P–23) (44-38) T = (200 - 2up - 2up + 274) + (448-312 - 101.276.90 T = (20 - 40p +2p2) + (50.qp-3p²-10112) q - 2W-4up + 2p2 + Su.ap-3p2- 1012 7 - 98.8 +10.9 p-pa da, 10.9 - 2p. 30. - ap- 10.9 p= (10.9 /2) 1p = 8.45 [Consultant fee) and I = 0.5 (u-p) (20-27) F: 05 (1U-5:45) (20 – (2)(5:45) F 20.5 (4.55) (9.1) = 20.7025 (Retainer fee) She shoul charge a consultation fee of $ 5.45 thousand per legal jub She should charge a retainer fee of $20.70 thowand
Q1 + Q2 = 24-P + 20-2P

Q1+Q2= 44-3P