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nimum average variable cost? Answer: No change, since AVC doesn’t change. Slide 37 CobbDouglas Production Function and the LongRun Cost Function: Appendix 8A ? Long Run Costs amp。 Production Functions: 1 Input 187。In the long run, total cost is: TC = wL, where w is the wage rate. 187。production function is CobbDouglas: Q = L223。. 187。Solving for L in the CobbDouglas production function, we find: L = Q1/223。. 187。Substituting this into the total cost function, we get: Slide 38 One Input Case ? TC = wQ1/223。. ? This also demonstrates that if the production function were constant returns to scale (223。=1), then TC rises linearly with output and average cost is constant. ? If the production function is increasing returns to scale (223。 1), then TC rises at a decreasing rate in output and average cost is declining. ? If the production function is decreasing returns to scale (223。1), then TC rises at an increasing rate in output and average cost rises. Slide 39 TWO Input Case ? With two inputs, long run cost is: TC = wL + rK, 187。 where w is the wage rate and r is the cost of capital, K. ? CobbDouglas: Q = K?L 223。. ? The manager attempts to minimize cost, subject to an output constraint. This is a Lagrangian Multiplier problem. ? Min L = wL + rK + ?[ K?L 223。 Q ] ? Taking derivatives and solving yields a total cost: ? TC = wL* + rK* = ? TC = wQ(1/(?+223。))( ?w/223。r)(223。/(?+223。)) + rQ(1/(?+223。))( ?w/223。r)(?/(?+223。)) ? If (?+223。1), then 1/(?+223。) less than 1, and total cost rises at a decreasing rate in output. That means that average cost declines. Slide 40 長期收支平衡 ? 是否進入 / 退出 187。價格 ≧ 平均成本 ? 營業(yè)規(guī)模 187。邊際成本=價格 ? 環(huán)境條件和短期決策的十分相似 187。關鍵區(qū)別為所有變量是對長期而言的 ? 長期邊際成本可能和短期的不同 ? 長期價格可能和短期的不同 Slide 41 圖 46 長期產量 0 長期邊際成本 長期平均成本 邊際收益 =價格 收支平衡點 產量(千個 / 週 ) 成本/收益*元 / 個+ Slide 42 案例 44 富士通: 杜翰市與格力斯翰市 ? 已投資英國杜翰市 187?,F(xiàn)有設備僅能生產 4和 16百萬位元 DRAM 187。需投資 10億美元才可生產 64百萬位元 DRAM) 187。長期價格<平均成本(包括重置成本) ? 格力斯翰市 187。平均變動成本<長期價格<平均成本 ? 註釋 187。這只是作者對真實情況的解釋,不包含有關成本的內部訊息 Slide 43 案例 45 石油:該不該生產呢? ? 原油價格上升時,油井平臺的數(shù)量增加 ? 原油價格下降時,油井平臺的數(shù)量減少 Slide 44