El aporte de la legislación

Your client is a book retailer who has been working with a publisher for some years now. In the current model, the retailer buys books from the publisher every month and sells them to customers. Any unsold books are returned to the publisher (the retailer does not have to pay for them).

The client is considering changing this model to a new one. Under this model, he will have to buy a pre- decided number of books and would not be able to return the unsold books. Should he change the model? If yes, how many books should the client purchase from the publisher for it to make economic sense for him?

Preliminary questions:

Why does the client want to shift to the new model? It does not allow him to return the unsold books? Is he being compensated for this?

Good point. The client is going to be able to purchase the books at a lower cost as a result. Hence, there is the incentive to make more profit.

What book is this? If the book is returned to the publisher after every month, the book must be a periodical one - like a magazine. Is that correct?

True. Assume that the unsold books are useless since the book is a periodical one.

Hmm... Can I have details about the earlier model and the proposed one in terms of numerical data? Old model:

Publisher produced 10000 books a month each costing him $5. Purchasing price for the client (retailer) = $10 per book Selling price to end customer = $12 per book

New model:

Publisher produces X (depending on client’s order) books a month each costing him $5. Purchasing price for the client (retailer) = $9 per book

Selling price to end customer = $12 per book

The demand for the books is 7500-10000 with an average of 8000 per month.

The terms of the deal should be such that the publisher on an average makes at least as much as he/she used to in the old model else he will not agree to the new deal. Moreover, this figure should ensure that our client (book retailer) is earning, on an average, more than before.

137 That is correct.

Do we necessarily need to always cater to the demand? Our profits could take a hit as a result of over- purchasing to always satisfy demand. However, if we do not cater to demand, we could stand to lose out on our loyal customers who might start purchasing books from a competitor.

Good point. However, the loss due to over-purchasing is something that the client does not want. He has other loyalty programs to ensure that he retains his customers.

Overall strategy

First, I want to compare the previous and new profits of the book publisher and the retailer (the client). Making sure that the new profits are greater than the earlier ones, I will use the constraints to arrive at a reasonable figure for the number of books to be purchased.

Calculations

Publisher profit comparison:

Publisher’s current monthly profit = Revenue – Expenditure = 8000*10 – 10000*5

= $ 30000

Publisher’s new monthly profit = Revenue – Expenditure = X*9 – X*5

= $ 4X

Hence, for the publisher to have increased profits, 4X >= 30000

I.e., X>= 7500

So, as long as the client orders for more than 7500 books, he is okay. Perfect. Can we look at the client’s profit figures now?

138 Retailer profit comparison:

Client’s current monthly profit = Revenue – Expenditure = 8000*12 – 8000*10 = $ 16000

Let Y be the demand of books in a particular month, Client’s new monthly profit = Revenue – Expenditure Case I: Y>X (supply less than demand)

Monthly profit = X*12 – X*9 = $ (3X)

OR Case II: Y<X (demand less than supply) Monthly profit = Y*12 – X*9

= $ (12Y-9X)

Do we have details about how many books are sold each month in a 12 month cycle? We can optimize the profits by changing the number of books ordered for each month.

We don’t have that information. We only know that the demand for the books is in the range of 7500- 10000 with an average of 8000 per month.

Can you come up with a number for the books to be ordered making necessary assumptions?

Using the previous information that X>=7500, we know that Case I (supply less than demand) is never going to be a concern for our client because a profit of 3X (>=7500*3) is always going to be greater than the previous profit of $16000. Hence, we must look at Case II (demand less than supply) to give us some more insight into X.

So,

New profit = Y*12 – X*9 ...Y<=X

We need to identify an X (books purchased) greater than or equal to 7500 for which the above equation is maximized keeping in mind that it should be greater than $ 16000.

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Now, to arrive at an accurate answer, we will need the distribution of the book demand but to get an approximate figure for X, let’s assume an average scenario where the demand is 8000 books...

For an average month, Y=8000.

Therefore, Client’s new profit = 8000*12 – X*9

Remember that to earn the revenue for 8000 books, the client will have to purchase at least 8000 books.

For maximum profit, X will have to be 8000. Then,

Client profit = $24000

This is greater than 16000 (the earlier profit) and is, therefore, a favorable scenario for the client. This is profitable for the publisher as well (Profit = 4*X = $32000)

Fair enough.

Before we wrap this up, I want to check what the worst case scenario for our client will be assuming he orders 8000 books every month. The worst case scenario is when demand is lowest (Y=7500) i.e. the client has grossly over purchased and some of the books he buys will not get sold.

In this case,

Client’s new profit= 7500*$12 – 8000*$9

= $18000 ...which is greater than $16000, his earlier profit

Hence, even in the worst case scenario for the client (when the demand is at its lowest), purchasing 8000 books from the publisher under the new model is still better than what he typically gets on an average in the old model ($ 16000).

The publisher, as said before, will be more than pleased with this deal since his/her profits will, on an average, have surged to 8000*$4 = $32000 per month.

That is correct.

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