# microeconomics- demand function

posted by
**michael** on
.

hey thanx for "economyst" for his input, he/she was a HUGE help :)

just stuck on a dmeand function question

p.s. i don't mean to be a nuisence but if you can please, explain each answer, if not tell me wat i should write about

Q: a demand function for a economics book is P = 100 - 0.005Q

the publisher must pay $20 per book in prinitng and distribution costs and in addition it must pay the author $20 royalty for each book sold

a) your job is to provide advice to the publisher. what price will maximise the publishers profit ? how mush profit will the publisher earn ? what will be the total royalty payment earned by the author ?

b) a consultant says that the publisher and the author have the wrong type of agreement. he says the author and the publisher should tear up hteir original agreement, in which the author gets $20 per book sold, and enter into profit-sharing agreement. he recommends that the author gets 40% of the profit and the publisher gets 60%. what price should the publisher set with this profit-sharing agreement ?

c) will both the author and the publisher prefer the profit-sharing agreement to their original agreement ? which agreement will the students who buy the textbook prefer ?

d) given the demand and cost conditions indicated above suppose thath the royalty payment was such that the author received a payment which was 15% of sales revenue. prpve that there is an inherent conflict between the author and publisher in that the auhtor has an interest in the book's price being lower than the price which maximises the publisher's profit.

thanx !!

The key here is to recognize that the publisher is a monopolist with respect to the books he publishes. So the publisher will opperate where marginal cost=marginal revenue. Total revenue is P*Q=100Q-0.005Q^2. So MR=100-.01Q

In a) MC=20+20=40. Solve for Q. Total profit will be P*Q-40*Q.

b) is a bit tougher, but still straight algebra. Gross profit per book (profit before royalty) is simply P-20. So, the Total Costs = 20*Q + .4*(P-20)*Q. MC becomes 20 + .4*(P-20).

Substitute the demand equation for P. Thus MC=20 + .4*(100-.005Q). Solve for Q.

c) I get that price goes up and the publisher is worse off.

d) Repeat b cept put in .15 instead of .4 It should be easy to show that, at the optimal point for the publisher, the author would make more money if the price of the book was lowered (and sales increased). The confict arises because the MC to the author is zero, while the publisher has, at a minimum, production costs.

sorry, I did not proof-read carefully. in b) MC becomes 20 + .4*(P-20) = 12 + .4P Now substitute the demand equation for P. MC = 12 + .4*(100-.05Q)

Sorry #2. When re-reading d) I see that the MC for d) should be MC=20+.15P. Still follow the same methodology as b.

um sorry, these answers are wrong i will get back to you on monday as i am busy on the weekend. Sorry, keep working on this and on monday i should be able to get the right answers.

Hi economyst, Ill be interested to know if you have worked out the correct answer =) I just find this mind boggling!

I have chosen not to answer these questions upon knowledge that these are part of a university assesment. I would be glad to help you after the due date!

econonmyst please don't help these students as this is an assignment and it should be there own work,.

screw yourself ALLan.!!!!

Can you please post the answers to the above question.