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?

Option 2: Spend $600,000 on a 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)?

Option 3: Trust Dwight and Mose to run a production plant in their beet farm. Unfortunately, this is a risky option. With probability 70% they can produce unlimited amounts of paper, but with probability 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 ?

d) What is their (expected) profit if they go with this option?

Answer 1

Option-1:-

Pr(p)=1,000 * ((10-p/40)(p-40). Pr’(p)=1,000*(10- 2p/40+1) =0 therefore optimal price is $220per ton.

At this price, DM sells 4,500 tons which would bring 4500*(220-40)=$810,000 dollars. Thecorresponding net profit would be $310,000.

Grading:

• 2 points if revenue maximization forgetting about the cost.
• 3 points for getting optimal price.
• 2 points for getting optimal profit. -1 point If the 500,000 cost was not used in the net profit

Option-2:-

Solution with no marginal cost:

The high willingness to pay demand is equal to 2,500 tons. The low willingness demand is 3,750 tons. Net profit from selling is equal to (2,500*300+3,750*150)-600,000 = $712,500.

Solution with marginal cost:

The high willingness to pay demand is equal to 2,500 tons. The low willingness demand is 3,750 tons. Net profit from selling is equal to (2,500*260+3,750*110)- 600,000 = $462,500