Question

For the next year, Dunder-Mifflin is planning to expand its paper business beyond the East Coast to the Midwest. Ryan used all the tools that he learned at business school to estimate Dunder-Mifflin's demand for paper in the Midwest. He estimates that the amount of sales (in thousands of tons) that Dunder Mifflin would make if their price was p (per ton) is equal to D(p) = 10 - p/40. The cost of producing one ton of paper is equal to $40. Note that the demand function and the marginal cost stay the same throughout the problem. In order to scale up their production to that extent, they have three options: Option 1: Lease for $500,000, a state-of-the-art factory that would allow them to produce 7,000 tons of paper in a year. a) What is the optimal price and the optimal profit if Dunder Mifflin goes with this option? Optimal price is $220 and net profit is $310,000. Option 2: Spend $600,000 on startup that will not only take care of production and ensure that capacity is unlimited, but also would help them identify all the firms that are willing to pay a price of $300 per ton as well as all the firms who are only willing to pay $150 per ton (but not $300 per ton). b) What is the profit if Dunder Mifflin goes with this option? (Remember, the cost of producing one ton of paper is equal to $40) $462,500. Option 3: Trust Dwight and Mose to run the production plant in their beet farm. Unfortunately, this is a risky option. With a probability of 70%, they can produce unlimited amounts of paper, but with a probability of 30%, there are breakdowns in which case they can only produce 4,000 tons of paper in a year. This option would cost $450,000 for the year. c) What is the optimal price and the optimal revenue if the production capacity is 4,000 tons? $960,000. d) What is their (expected) profit if they go with this option? $357,000.

For the next year, Dunder-Mifflin is planning to expand its paper business beyond the East Coast to the Midwest. Ryan used all the tools that he learned at business school to estimate Dunder-Mifflin's demand for paper in the Midwest. He estimates that the amount of sales (in thousands of tons) that Dunder Mifflin would make if their price was p (per ton) is equal to D(p) = 10 - p/40. The cost of producing one ton of paper is equal to $40.

Note that the demand function and the marginal cost stay the same throughout the problem.

In order to scale up their production to that extent, they have three options:

Option 1: Lease for $500,000, a state-of-the-art factory that would allow them to produce 7,000 tons of paper in a year.

a) What is the optimal price and the optimal profit if Dunder Mifflin goes with this option? Optimal price is $220 and net profit is $310,000.

Option 2: Spend $600,000 on startup that will not only take care of production and ensure that capacity is unlimited, but also would help them identify all the firms that are willing to pay a price of $300 per ton as well as all the firms who are only willing to pay $150 per ton (but not $300 per ton).

b) What is the profit if Dunder Mifflin goes with this option? (Remember, the cost of producing one ton of paper is equal to $40) $462,500.

Option 3: Trust Dwight and Mose to run the production plant in their beet farm. Unfortunately, this is a risky option. With a probability of 70%, they can produce unlimited amounts of paper, but with a probability of 30%, there are breakdowns in which case they can only produce 4,000 tons of paper in a year. This option would cost $450,000 for the year.

c) What is the optimal price and the optimal revenue if the production capacity is 4,000 tons? $960,000.

d) What is their (expected) profit if they go with this option? $357,000.