6) Bavarian Crystal Works designs and produces lead crystal wine decanters for e

Question

6) 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 $50 apiece. Total and marginal revenue are TR = 50Q and MR = 50 where revenues are measured in U. S. dollars and Q is annual decanter production. 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. Is the optimal profit in answer b good enough to keep Bavarian Crystal Works in the market? Please comment on it.

Explanation / Answer

(a)

TR = 50Q

Since TR = P x Q, P = TR / Q = 50Q / Q = 50

MC = 40 + 0.005Q

The firm operates in a competitive market and therefore, is a price taker. It will equate price with MC:

50 = 40 + 0.005Q

Q = 10 / 0.005 = 2,000

Marginal Revenue = 50

(b) When Q = 2,000

TR = 50Q = 50 x 2,000 = 100,000

TC = 10,000 + 40Q + 0.0025Q2

= 10,000 + (40 x 2,000) + (0.0025 x 4,000,000) = 100,000

Profit = TR - TC = 0

(c)

In perfect competition, firms cannot earn supernormal profit. All firms earn zero economic profit in long run. If the firm cannot cover its costs by revenue in the long run, or if a zero-economic-profit earning firm targets a supernormal economic profit, then it exists the market. Hence, stay or exit decision will depend on the firm's vision and business strategy.

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