Question

A publisher has an opportunity to buy the book rights from an author and expects that with the book rights they will be able to make $5 million. To buy the rights the publisher must make an offer to the author. The publisher believes that a competing publishing company willalso offer the author a contract and that the offer is uniformly distributed between $1 million and $2 million.  

How much should the publisher off the author to maximize its expected profit? NOTE the value is in the millions so make you answer in millions of dollars. For example, if the amount is $1,150,000 then enter 1.15. HINT: your answer should be less than 5.

Answer 1

Solutions:-

Total profit = $ 5 million

Offer rom cometing publishing company is let say y  

f(y) = 1/(2- 1) =1; 1< y < 2

let say the publisher offer x amount to publisher but that x amount shall be greater than y

Profit = 5 - x ; when x > y

= 0 ; when x < y

so here profit in terms of probability

Profit = (5-y) * F(y)

here F(y) = (y - 1)/1

so profit = (5- y) * (y-1)/1= [y-y^2+5y-5]

now differentiating it with respect to y

dP/dy= (5-2y+1)

= (4-2y)

that must be equal to 0.

so,

2y= 4

y = 4/2

so here the amount is $ 2 million for which publisher should give to book writer.

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