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 produced 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.

NOTE: Do the following before Pt. A: Produce a chart in Excel showing TC & TR with Q on the horizontal axis. Have Q go from 0 to 15,000 units. Produce a second chart showing MC & MR with Q again on the horizontal axis.

A. What is the optimal level of production of wine decanters? What is the marginal revenue from the last wine decanter sold?

B. What are the total revenue, total cost, and net benefit (profit) from selling the optimal number of wine decanters?

C. 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 NOT produce & sell one more unit?

D. At the optimal level of production of decanters, an extra decanter can be sold for $70, thereby increasing total revenue by $70. Why would the manager of this firm NOT produce & sell either one more or one less unit?

The optimal level of production will always be where MR = MC. In this case, you know that MR = 70 and MC = 40 + .005Q. So, subbing the numbers in for MR and MC we get 70 = 40 + .005Q. Then, subtract 40 from both sides and you get 30 = .005Q. Multiply both sides by 200 and you get Q = 6,000. So the optimal level of production is 6,000. The marginal revenue of the last decanter sold is 70, as the problem says that MR = 70.

B.

Total revenue is defined by the problem as TR = 70Q. We found that Q = 6,000 so

TR = 70 x 6,000 = $420,000.

Total cost is is also given in the problem as TC = 10,000 + (40×6000)+ (0.0025×6000×6000)

TC= $340000

Net Benefit = TR-TC

$420000- $340000

Net Benefit= $80,000

C.

Any quantity that goes beyond optimal level leads to decreasing returns.

The manager doesn't produce and sell one more unit because of increasing marginal cost. The extra unit would bring in $70 of revenue, but incurs a cost of 40 + 6,001 x .005= $70.005

D. Selling one more incurs a marginal cost of $70.005, selling one less might result in decrease in net benefit.