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.

Certainly! I apologize for the confusion earlier. Let me help you with the answers to the question.

a) To maximize the publisher's profit, we need to find the quantity (Q) at which marginal revenue (MR) equals marginal cost (MC). The demand function is given as P = 100 - 0.005Q. From this, we can derive the revenue function as TR = P * Q = (100 - 0.005Q) * Q = 100Q - 0.005Q^2. The marginal revenue is the derivative of the revenue function with respect to quantity, so MR = 100 - 0.01Q.

The marginal cost (MC) is the sum of printing and distribution costs ($20 per book) and the royalty payment per book ($20). Therefore, MC = 20 + 20 = 40.

To find the profit-maximizing quantity, set MR = MC and solve for Q:
100 - 0.01Q = 40
0.01Q = 60
Q = 6000

Substitute this value of Q back into the demand function to find the price (P):
P = 100 - 0.005Q
P = 100 - 0.005 * 6000
P = 100 - 30
P = 70

The price that maximizes the publisher's profit is $70. To calculate the profit, subtract the total cost from the total revenue:
Profit = TR - TC
Profit = (70 * 6000) - (40 * 6000)
Profit = 420,000 - 240,000
Profit = $180,000

The publisher will earn a profit of $180,000.

The total royalty payment earned by the author is the royalty per book multiplied by the quantity (Q):
Total Royalty Payment = Royalty per book * Q
Total Royalty Payment = $20 * 6000
Total Royalty Payment = $120,000

b) With the profit-sharing agreement, the author will receive 40% of the total profit, and the publisher will receive 60%. Let's calculate the new price (P) using this agreement.

The gross profit per book is P - 20. Therefore, the total profit per book is 0.6 * (P - 20). The total cost function remains the same as in part a, which is 20Q + 40.

Set the new marginal cost (MC) equal to the new marginal revenue (MR) to find the price (P):
MC = 20 + 40 = 60
MR = 100 - 0.01Q
60 = 100 - 0.01Q
0.01Q = 40
Q = 4000

Substitute this value of Q into the demand function to find the new price (P):
P = 100 - 0.005Q
P = 100 - 0.005 * 4000
P = 100 - 20
P = $80

The price that the publisher should set with this profit-sharing agreement is $80.

c) The author and the publisher prefer the profit-sharing agreement to their original agreement if they earn more profit with it.

In the profit-sharing agreement, the author's payment depends on the total profit, while in the original agreement, the author receives a fixed royalty per book. If the profit increases with the profit-sharing agreement compared to the original agreement, then both the author and the publisher will prefer it.

To determine which agreement the students who buy the textbook prefer, we need to analyze the impact of the price on their willingness to buy.

d) To prove that there is an inherent conflict between the author and the publisher, we need to analyze their interests concerning the book's price.

Suppose the royalty payment is such that the author receives a payment equal to 15% of sales revenue. This means the royalty payment is 0.15 times the price (P). The MC for the publisher remains the same as in part a: MC = 20 + 20 = 40.

To find the price that maximizes the publisher's profit, set MR equal to MC:
100 - 0.01Q = 40
0.01Q = 60
Q = 6000

Substitute this value of Q into the demand function to find the price (P):
P = 100 - 0.005Q
P = 100 - 0.005 * 6000
P = 70

Therefore, the price that maximizes the publisher's profit is $70.

Now, let's calculate the author's payment based on the royalty percentage:
Author's payment = Royalty percentage * Sales revenue
Author's payment = 0.15 * (P * Q)
Author's payment = 0.15 * (70 * 6000)
Author's payment = $63,000

This means the author's payment is $63,000 when the price is $70.

If the price were to increase above $70, the publisher's profit would decrease. However, the author's payment is 15% of sales revenue, so the higher the price, the higher the author's payment. This creates a conflict of interest where the author wants the price to be higher, while the publisher wants to maximize profit by keeping the price lower.

I hope this helps! Let me know if you have any more questions.