Bavarian Crystal Works Marginal Production Analysis Paper

Mathematics

Bavarian Crystal Works designs and produces lead crystal wine decanters for export to international markets. The production manager of Bavarian Crystal Works estimates

total and marginal production costs to be
TC = 10,000 + 40Q + 0.0025Q2

and

MC = 40 + 0.005Q

where costs are measured in U.S. dollars and Q is the number of wine decanters pro- duced annually. Because Bavarian Crystal Works is only one of many crystal producers in the world market, it can sell as many of the decanters as it wishes for $70 apiece. Total and marginal revenue are

TR = 70Q and MR = 70
where revenues are measured in U.S. dollars and Q is annual decanter production.

  1. What is the optimal level of production of wine decanters? What is the marginal revenue from the last wine decanter sold?
  2. What are the total revenue, total cost, and net benefit (profit) from selling the opti- mal number of wine decanters?
  3. At the optimal level of production of decanters, an extra decanter can be sold for $70, thereby increasing total revenue by $70. Why does the manager of this firm notproduce and sell one more unit?
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