its been three weeks since you started working

Question

It's been three weeks since you started working for BioMed and there's still no trace of Selwyn.

That means you're still BioMed's resident economic expert. Harry the CEO was pleased with your earlier work estimating and interpreting the demand function for QuickKits^TM, so he is asking you to complete another time-sensitive project that Selwyn was working on before he disappeared.
Harry explains that BioMed has a manufacturing plant that produces a prescription topical cream called DermaPlus^TM, which is used for treating certain skin conditions. Hospitals and pharmacies are the main buyers of DermaPlus^TM.
A number of other firms produce creams that are almost identical to DermaPlus^TM and the market for these creams is extremely competitive. In fact, BioMed's current share of the market for this type of topical cream is small, so it has no ability to influence the market price. On the other hand, because Biomed is relatively small compared to the size of the market, it can sell as much of the cream as it likes at the prevailing market price.
The plant producing DermaPlus^TM has been operating for a little over three years with the same manufacturing equipment. Currently there are no plans for upgrading or adding to this equipment. Over the last three years, the price of DermaPlus^TM and related creams has been quite volatile and BioMed has tried to react to the changing price by varying its output level to constantly maximize its monthly profit. To date, BioMed has been able to vary monthly production quite easily by taking advantage of a flexible, non-union workforce with a large number of part-time workers. However, the workforce at the DermaPlus^TM plant is just about to be unionized. Once that happens, it will become much more difficult to vary the amount of labour used in the short run and therefore much more difficult to vary the monthly production of DermaPlus^TM.
Before he disappeared, Selwyn had been asked to estimate the short-run cost functions for the DermaPlus^TM manufacturing plant. The goal was to use this information to determine the profit maximizing output level and use that information to estimate the optimal size for the new unionized workforce.
Harry tells you that DermaPlus^TM and related products are just about to come under the umbrella of a new reference-based pricing scheme. Under the new scheme, the government will set the price of DermaPlus^TM and competing creams, and review that price every two years.
Once the price has been set, BioMed and other manufacturers simply have to decide how much of the cream, if any, they want to produce and sell.
Unfortunately, although the workforce will be unionized in just over a week, the referencedbased price for DermaPlus^TM will not be announced for another two months. Consequently, BioMed has to choose the size of its workforce (and therefore its production capacity) before it knows the price it will get for its product. To reduce the uncertainty about this decision, Harry recently hired a consultant with expertise in the pharmaceutical industry and reference-based pricing to estimate the price that will be announced for DermaPlus^TM. The consultant estimates that there is a 5% chance that the price will be $50 per unit, a 20% chance that the price will be $100 per unit, and a 75% chance that the price will be $150 per unit. This is the best estimate the consultant can provide given the lack of information coming from the government about the issue.
After giving you this background information, Harry asks you to complete the following tasks:
1. Determine the profit-maximizing average daily production capacity for DermaPlus^TM for each of the possible reference-based prices identified by the consultant. Estimate the expected daily profit in each case.
2. Recommend an average daily production capacity for the next 12 months given the uncertainty about the price of DermaPlus^TM. Your recommendation will be used to set the size of the manufacturing plant's unionized workforce. (Note: You simply have to determine the best daily production capacity for the next 12 months, not the number of workers required.)
3. Write a short report summarizing the results of your analysis and any recommendations.
Once again you only have a week to complete the analysis, interpret the results, and summarize your findings and recommendations in a brief report. Harry tells you that the structure and format of the report should adhere to the recommendations he gave you last time when he asked you to estimate the empirical demand function for QuickKits. He suggests that you review Assignment 1 to refresh your memory.
Finally, Harry gives you a copy of another of Selwyn's spreadsheets. This one contains data that Selwyn collected on the variables he thought would be needed to estimate the short-run cost functions for DermaPlus^TM and the firm's profit-maximizing output level.
Harry reminds you that he has complete confidence in Selwyn's technical abilities and professional judgment and again tells you to take the information in Selwyn's spreadsheet at face value and to use it as a starting point for your analysis.