Thank you so much economyst but i do'nt understand the ans for part (b)
The demand function for a well known economics textbook is:
P = 100 - .005Q
The publisher must pay $20 per book in printing and distribution costs and, in
addition, it must pay the author a $20 royalty for each book sold.
(b) A consultant says that the publisher and the author have the wrong type of
agreement. He says that the author and the publisher should tear up their
original agreement, in which the author gets $20 per book sold, and enter
into a profit-sharing agreement. He recommends that the author gets 40%
of the profit and the publisher 60%. What price should the publisher set
with this profit-sharing agreement?
MC=20+0.4*profit
why is profit (P-20)
In order to understand why the profit in the equation is represented as (P-20), let's break down the cost structure and profit calculation for the publisher.
The publisher's cost consists of two parts: the printing and distribution cost ($20 per book) and the royalty paid to the author ($20 per book). Therefore, for each book sold, the publisher incurs a cost of $20 + $20 = $40.
Now, let's consider the profit-sharing agreement. The consultant suggests that the author receives 40% of the profit, and the publisher receives 60% of the profit. To calculate the profit, we subtract the cost from the revenue generated by selling each book.
The revenue is represented by the demand function: P = 100 - 0.005Q, where P is the price and Q is the quantity sold. The revenue generated by selling Q units is P * Q.
To calculate the profit, we subtract the cost per unit (which is $40) from the revenue per unit. So, the profit per unit can be represented as P - 40.
However, the demand function gives us the price as a function of quantity, and we need to express the profit as a function of the price. To do this, we can rearrange the demand function to solve for Q. The demand function becomes: Q = (100 - P) / 0.005.
Substituting this expression for Q into the profit equation, we have: Profit = P - 40.
Therefore, the profit is represented as (P - 40) rather than (P - 20) because the publisher incurs a cost of $40 ($20 for printing and distribution + $20 royalty paid to the author) per book sold.