Consider the Case below

A particular rail freight company LogCo needs to set a price/ton (in R$/ton) to transport grains (corn) from the rail terminal of RTE to the seaport of Santos. The company has (for simplicity) 3 customers (farmers) on 3 different locations A, B and C who want to transport the corn to one of Brazil's seaports and from there via a large vessel to its customers worldwide. One customer, located in A needs to transport 400 Ktons, the customer located in B needs to transport 100 Ktons and another customer located in C needs to transport 200 Ktons.

Customer location Ktons

A 400

B 100

C 200

Two of these customers, A and B have 2 viable options:

- Option 1: They can either load the grains onto a number of trucks at the farm, transport them to RTE and unload them onto a number of LogCo's cars which will transport them by rail to the seaport of Santos where they will be unloaded and then uploaded onto a sea vessel. The price per ton to bring the grains to RTE is R$70/t for customer A and R$40/t for customer B (who is located closer to the train terminal).

- Option 2: They can transport the grains by truck from their location all the way to the port of Santos. That costs R$280/t for customer A who is located further from the port of Santos and R$200/t for customer B who is closer to the port of Santos than customer A.

Customer C is located up North in Brazil. This customer has 2 viable options too:

- Option 1: As with customers A and B, the customer can either load the grains onto a number of trucks at its farm who will transport them to RTE and upload them onto a number of train cars which will bring the grains by rail to the port of Santos. The price per ton to bring them to RTE is R$75/t.

- Option 2: As the customer is located more North, it can also take the truck-waterways combination: First transport the grains by truck to the city of Miritituba and load them on a boat that will transport them by waterways to the seaport of Barcarena and from there via a sea vessel to its customers world-wide. You can assume that the cost of transporting grains from both the seaports of Santos or Barcarena to its customers world-wide is the same.

The situation is depicted below:

There are lots of small truck companies in Brazil and their prices are not influenced by the price charged by LogCo. It is determined by the price of diesel and is expected to stay the same next year.

Assume also that there is no difference in quality of service between the truck-rail versus the truck-only or the truck-waterways options with the following exception: There are different percentages of grain losses associated with combined modes of transportation: 0.5% of the grains are lost when unloading from a truck onto a train or vessel; another 0.5% is lost during transportation by train. Hence of the 1 ton of grains loaded onto a truck at the farm only 0.99t reaches Santos when using the truck/train mode; no grains are lost on a vessel. The loss in value of a ton of grains equals R$1000. Also assume that at equal financial benefits from transporting and selling grains to their end customers, customers will take the truck-rail combination over the other alternatives.

The average cost of transportation per ton equals R$15. The LogCo trains run all the time (even empty so to speak) so the marginal cost of transporting extra tonnage of grain is negligible (consider it zero)

SCENARIO 1:

Question 1: What does the demand curve for LogCo look like? Please draw it.

Question 2: Assuming LogCo does not price discriminate (i.e. charges the same price per ton to all customers), what price should LogCo charge per ton to maximize profits.

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