生产与成本分析.docx

·  生產與成本分析
(一)互為表裡的生產與成本函數
                生產函數 Q=f(K,L,…)
                成本函數 C=C(w,r) | Q=Q°
               1.何謂短期與長期生產函數
                   Q=f(α,βi)
                   Q=f(αi)
                   Q=g(αi)
              2.短期的生產函數
                  (1)生產函數-- Q=f(K，L)
                       生產函數是指存在新生產過程中投入與產出間的技術關係。
                       生產力--某生產要素的生產力是指在其他生產要素維持不變時
                      ，該要素的產出量。
                 (2)報酬遞減法則--在短期中的固定要素不定時，變動要素增加，
                      致總產出增加，及隨後減少的現象。
                 (3)TP、MP & AP --總產出、邊際產出與平均產出。
              3.短期與長期成本曲線
                 (1)固定總成本 (Total fixed cost ,TFC ) 。 即短期分析中固定
                      成本支出總額。在短期中為一固定數值。
                 (2)可變總成本 (Total variable cost ,TVC) 。 即短期分析中為
                      生產一定產量可變成本總額 ，此數值隨產量的變化而變化。
                 (3)總成本 (Total cost ,TC) 。 即短其分析中生產一定產量固定
                      總成本與可變總成本之和 ，即
                                 TC=TFC+TVC
                 (4)平均固定成本 (Average fixed cost ,AFC ) 。 即短期中平均
                      每一產品單位所分攤的固定成本數額 ，亦即固定總成本與生
                      產量之商數，即
                                AFC=TFC/Q
                (5)平均可變成本 (Average variable cost ,AVC ) 。 即短期中平
                     均每一產品單位所分攤的可變成本數額 ， 亦即可變總成本與
                     生產量之商數，即
                              AVC=TVC/Q
               (6)平均單位成本或平均總成本 (Average Unit Cost, or
                    Average Total cost ,AC ) 。 即短期中平均每一產品單位所
                   分攤的固定成本與可變成本之總和 ，亦即平均固定成本與平
                   均可變成本之和 ，即
                               AC=TC/Q 或 AC=AFC+AVC
              (7)邊際成本 (Marginal cost ,MC ) 。及短期中生產量每增加一
                   單位時，總成本所增加的數量 ，即
                               MCn=TCn- TCn-l或MC=d(TC)/dQ
　               TC AC=TC/Q MC=ΔTC/ΔQ=ΔTVC/ΔQ
                  TFC AFC=TFC/Q
                  TVC AVC=TVC/Q
                  TP AP=TP/Q MP=ΔTP/ΔQ
                  TP(=Q) = f(K,L)
                  TC(=C) = C(w,r) | Q=Q°
                  TC=TFC+TVC
                  AC=AFC+AVC
         (二 )產能決策
                1. 短期供給決策
                     (1)穩定單位成本的方法
                          a.存貨(Inventories)
The firm would maintain its output rate at a constant rate per period and run down its inventories when there is an unexpected increase in demand, rather than be forced to produce at higher levels of marginal cost. Later reductions in demand will give the firm the opportunity to rebuild its inventories to the desired levels. Thus, when demand is uncertain, a firm may choose to produce the e>q~ected value of quantity demanded in each period, adding to inventories when demand falls short of expectations and selling from inventories when demand exceeds expectations.
                          b.委外(外包)(Contracting Out)
If producing the output would cause the firm's MC values to rise steeply, the firm may be able to purchase the items at low cost from another firm that has excess capacity and can produce the same product at a similar quality level. Initial setup costs may be involved, if the subcontractor has imprint the firm's logo or follow the firm's special design.
                         c.排隊(Backlists)
This approach may only be feasible if the firm's products are unique or customized, or if the delay cause the customer minimal problems, or if all rival suppliers are similarly operating with a backlist or waiting line. It may pay the firm to offer a discount for delayed delivery rather than incur the additional cost of producing the item on demand. This discount would encourage advance orders, which would help the firm in its production planning.
                  (2).訂價決策、利用規劃與供給決策
              when SAC>P>AVC – 繼續生產
              繼續生產
                                  TR(=P,Q) > TVC(=AVC.Q)
              關廠             TR(=P,Q) < TVC(=AVC.Q)
            2.長期供給曲線
                SAC → LAC
                                 包絡曲線
                SMC → LMC
                (1)市場需求的不確定性與產能規模選擇
             MC=SAC Full Capacity
             MC>SAC Excess Capacity
          偏好Excess Capacity的原因
                      a.擴張市場與維持或增加市場佔有率
                     b.市場需求不確定的抉擇
                     c.存貨、罷工、停工的考慮
                     d.競爭優勢問題
                 (2)工廠規模與廠商規模報酬
                     a.多廠營運—管理、電`腦、廣告的效果
                     b.學習曲線
                     c.要素價格
             3.等量線與等成本線分析
                (1)技術效率與經濟效率
           MRTS=ΔK/ΔL=-MPL/MPK ……. Isoguant slope
           E=K、PK+L、PL
           K=E/PK-PL/PK、L ……Isocost slope
           MPL/PL=MPK/PK
                 (2)擴張線(Expansion Path)
                  --TP & EP
                 (3)要素價格變動與要素代替
          (三)技術抉擇與成本優勢的形成
                 1.技術抉擇的利弊分析
                 2.成本優勢的形成的決策
         (四)案例—不同產業的成本估計
案例1. Peachy Cosmetics公司設立了面霜產品，在各種不同投入與產出水準的下例關係，每單位產品包含一個人，一週工作４０小時，必須用品，及各種比例的多種投入，包括裝面霜的小玻璃瓶，包裝紙，包裝紙箱；這些投入每單位成本案$600,固定成本每週為$60,000試問:
a. 利用這些資料,在已知的產出水準之下,導出該公司的AVC與SAC
b. 以圖表示出AVC曲線和SAC曲線,並繪出估計的邊際成本曲線
c. 在何產出水準時,報酬開始遞減?用圖參考配合投入產出資料,說明其一致性結果
d. 什麼是全能產出水準?在該產出水準平均成本是多少?在什麼情況下,Peachy是在它的成本曲線上的超額產能範圍生產?
分析a.
Output Level unit
AVC
SAC
6500
$9.23
$18.46
14300
$8.39
$12.59
20200
$8.91
$11.88
24400
$9.84
$12.30
27800
$10.79
$12.95
30220
$12
$14.00

分析b.
Input
(unit)
Output
(unit)
ΔQ
(unit)
ΔTC
(&)
MC
(ΔTC/ΔQ)
SAC
AVC
100
6,500
6,500
60,000
9.23
18.46
9.23
200
14,300
7,800
60,000
7.69
12.59
8.39
300
20,200
5,900
60,000
10.17
11.88
8.91
400
24,400
4,200
60,000
14.28
12.30
9.84
500
27,800
3,400
60,000
17.64
12.95
10.79
600
30,000
2,200
60,000
27.27
14.00
12
大約在投入150單位或產出10,000單位之水準時,報酬開始遞減,因為在該水準時,邊際成本開始遞增
分析d
MC=時為全能產出水準,大約在產出為20,000單位時,此時平均成本大約是$11.87元,當MC>SAC時,是Peachy的超額產能範圍

案例2:某甲電腦公司正處於全能生產階段，而該公司的固定投入是完全可以分清濋的，例如其平均變動成本在全生產狀態下為一定值，市場上對公司的需求量不繼的增加，使得該公司累積了1500台的訂單，由於該公司並無存貨，故如果在下個月底前不能準時交貨，則將喪失20%的buyer該公司為解決這個問題，提出了二個方案，方案Ａ是採用“超能”生產，該公司現在每個月的產能是500台而邊際成本每台$1500元，如果”超能”生產,則其邊際成本每增加100台將增加$300，而方案Ｂ也就是全數外包給不同的組件廠最後再由另一個工廠裝配成品而估計外包的全部費用為每台＄2200不管其數量多寡，電腦每台的售價為＄2995且不管選擇那一個方案,該公司每個月攤提的固定成本為$250,000
問：(a)試計算該公司利潤為何?假如採用方案A且產量從500至1500台(以每增加100台計算)每個月以生產多少台最佳?
(b)如選擇方案B則利潤為何?對於這兩種方案何者較佳A或B?為什麼?
c)如果合A,B兩方案,試對管理當局提出你的建議
分析：(a)方案A不同產量下之利潤
產量
銷售金額
固定成本
變動成本
利潤
500台
500x2995=1497500
250000
1500x500=750,000
497500
600台
1797000
250000
750000+1800x100=930,000
617000
700台
2096500
250000
930000+2100x100=1140000
706500
800台
2396000
250000
1140000+2400x100=1380000
766000
900台
2695500
250000
1380000+2700x100=1650000
795500
1000台
2995000
250000
1650000+3000x100=1950000
795000
1100台
3294500
250000
1950000+3300x100=2280000
764500
1200台
3594000
250000
2280000+3600x100=2640000
704000
1300台
3893500
250000
2640000+3900x100=3030000
613500
1400台
4193000
250000
3030000+4200x100=3450000
493000
1500台
4492800
250000
3450000+4500x100=3900000
342800
(b)方案B不同產量下之利潤
產量
銷售金額
固定成本
變動成本
利潤
500台
500x2995=1497500
0
500x2200=1100,000
397500
600台
1797000
0
1320,000
477000
700台
2096500
0
1540,000
556500
800台
2396000
0
1760,000
636000
900台
2695500
0
1980,000
715500
1000台
2995000
0
2200,000
795000
1100台
3294500
0
2420,000
874500
1200台
3594000
0
2640,000
954000
1300台
3893500
0
2860,000
1033500
1400台
4193000
0
3080,000
1113000
1500台
4492800
0
3300,000
1192800
每月產量低於1000台時以選擇A方案為佳,如高於1000台則以B方案為佳
(c)由於整個訂單是1500台,也就是planA 跟planB合起來要1500台
Plan A
Plan B
利潤總合
500
1000
497500+795000=1292500
600
900
617000+715500=1332500
700
800
706500+636000=1342500
800
700
766000+556500=1322500
900
600
795500+477000=1272500
1000
500
795000+397500=1192500
由利潤之最大值知採用planA生產700台並採用planB(外包)800台時有最大之利潤
TABLE 1-1 . Motor Vehicle Assembly Production Function
                                          Labor Units (L) (hundreds of person hours)
Capital

1
2
3
4
5
6
7
8
Units (K) 
(000s of  
machine 
hours)    
1
1
3
7
10
12
13
13.5
13
2
3
8
14
19
23
26
28
29
3
8
18
29
41
52
62
71
79
4
11
23
36
50
65
78
90
101
5
12
26
42
60
80
98
112
124
                 TABLE 6-2. The Law of Variable Proportions Exhibited by the Marginal Product of the Variable Factors
Units of the Variable Factor (L)
Units of Output (for K = 3) (total product)
Increment to Output over Preceding Row (marginal product)
Returns to the  Variable Factor  (for K = 3)
0
0
--
--
1
8
8
Increasing
2
18
10
Increasing
3
29
11
Increasing
4
41
12
Increasing
5
2
11
Diminishing
6
62
10
Diminishing
7
71
9
Diminishing
8
79
8
Diminishing

· 第二章 決策成本觀念
       (一)經濟與會計觀念下的成本與利潤
                1.直接成本與間接成本←→變動成本與固定成本
                2.外顯成本與內涵成本--是否有現金流出?如折舊
                3.機會成本與歷史成本—時間因素(折舊、技術、價格)
                4.正常利潤與風險考慮—以風險貼水納入考慮
         (二)增殖成本分析—指因決策致產生的成本,包括變動成本與固定成本,甚至包括是否採用新技術皆屬之。與邊際成本不同,不過,MC的觀念仍相當具參酌價值。
                1.相關成本與不相關成本—如沉沒成本屬不相關成本。
                2.增殖成本分類:
                   (1)即期外顯成本。
                   (2)機會成本—如是否接單?機會成本?
                   (3)未來成本(Future cost)—含外顯成本與內涵成本。
    例如:1.非法拷貝致可能產生的法律訴訟與賠償費用。
                                 2.勞工問題(如暫時解僱)
                       3.生意機會
                                 4.協力廠商的關係
                                 5.現金流量致借貸成本提高
       (三)貢獻分析(Contribution Analysis)
             1.增殖收益(Incremental revenue):
                (1)即期外顯收益—265000的合約
                (2)機會收益—100000的遣散費用
                (3)未來收期—50000x0.8696x50%=21740
                (4)EPVC=IR(386740=265000+100000_21740)-IC
            2.應用案例—A案或B案
                     —自製或外購
                    —接單或不接
           3.多期的貢獻分析—決策樹的應用
       (四)結語—廣義與狹義的成本
            --理念與決策的經濟概念VS.管制與稅法的會計作為
            --時間(Time)與技術(Fechnology)
 TABLE 2-l The Interpretation of Accounting Reports in Economic Terms
Costs of Production
Total Costs
Average Cost
Direct labor
$ 77,700
$ 52.50
Direct materials
36,260
24.50
Variable overhead
4.930
3.33

TVC = $118,890
AVC = $80.33
Fixed overhead
TFC = $ 36,800
AFC = $ 24.86
Total costs
TC = $155,690
AC = $105.19
 TABLE 2-2. Accounting Income Statement for the Small-Store Owner
Sales

$160,000
Cost of goods sold
$120,000

Salaries
20,000

Depreciation expense
5,000
145,000
Accounting profit

$ 15,000

TABLE 2-3. Economic Statement of Proftt to Small~Store Owner
Sales

$160,000
Cost of goods sold
$120,000

Salaries
20,000

Depreciation expense
5,000

Imputed salary to owner-manager
15,000

Imputed interest cost on equity
4,000
164,000
Economic profit

$-4,000
 TABLE 2-4. Expected Present Value of Future Incremental Costs
Costs Expected ($)
Present Value
Probability
Expected Value  ($)
0
0
0.10
0
50,000
32,875
0.20
6,575.00
100,000
65,750
0.30
19,725.00
150,000
98,625
0.25
24,656.25
200,000
131,500
0.10
  13,150.00
250,000
164,375
0.05
8,218.75
Expected present value
$72,325.00

TABLE 2-5. Summary of Cost Concepts for Decision Making
RFLEVANT COSTS
RRELEVANT COSTS
Incremental Costsa
Committed Costsa
Sunk Costsb
Present-period explicit costs:
Variable :
         Direct labor
         Direct materials
         Variable overheads
Fixed:
     New equipment
     New personnel
Opportunity costs:
    Contribution foregone on the
    best alternative use of the
    resources involved
Future-period incremental costs:
    EPV of probable costs to
    follow in the future as a
    consequence of the decision
Managers' salaries
Payments on debt
Rental and lease costs

Wage contracts or wages
of ongoing workers

All other payments that
must be made regardless of
the decision at hand

Previously paid-for
purchases of assets,
including land, buildings,
plant and equipment, and
depreciation expenses
based on these assets

Prepaid and nonrecoverable
expenses

aFuture costs
bPast costs
 TABLE 2-6. Income Statements for Projects A and B
Project A
Project B
Revenues (10,000 @ $2)
$20,000
Revenues (6,000 @ $3)
  $18,000
Costs
Costs
Materials
$2000

Materials
$5000

Direct labor
6000

Direct labor
3000

Variable overhead
4000

Variable overhead
3000

Fixed overhead
6000
18000
Fixed overhead
3000
14000
Profit
$2000
Profit
$4000

TABLE 2-7. Contribution Analysis for Projects A and B
Project A
Project B
Incremental Revenues
$20,000
Incremental Revenues
$18,000
Incremental Costs
Incremental Costs
Materials
$2000

Materials
$5000

Direct labor
6000

Direct labor
3000

Variable overhead
4000
12000
Variable overhead
3000
11000
Contribution
$8000
Contribution
$7000
 TABLE 2-8. Wilson Tool Company: Bearing Department Costs

Total
Per Unit
Direct materials
$ 38,640
$ 0.56
Direct labor
126,390
1.81
Allocated overhead
252,780
3.63

$417,810
$ 6.00
Total bearing units produced:

69,635

TABLE 2-9. Incremental Costs of Making the Bearing Units

Total
Per Unit
Direct materials
$4,637
$0.62
Direct labor
18,959
2.53
Allocated overhead
(?)
(?)

$23,596
$3.15

TABLE 2-10. Idaho Instruments Company: Per-Unit Data on Calculators

Model X1
Model X2
Materials
$ 1.65
  $ 1.87
Direct labor
2.32
3.02
Variable overhead
1.03
1.11
Fixed overhead allocation
5.00
6.00
Profits
2.00
2.40
Price to distributor
$12.00
$14.40

TABLE 7-11. Contribution Analysis of Calculator Decision Problem
Incremental revenues
          20,000 units of X1 @ $8.00
$160,000
Incremental costs
     Variable costs
20,000 units of X1 @ $5.00
$100,000

Opportunity costs (contribution foregone)
    5,000 units of X2 @ $8.40
42,000
142,000
       Contribution
$18,000

案例:接受訂單與否?
8,000 units的生產成本表

Total costs
Per Unit
Raw materials
9600
1.2
Direct labor
17600
2.2
Variable overhead
9200
1.5
Fixed overhead
14500
1.8125
因為目前最大產能為10000 units,如果要接單,則還要生產400O units ，則
須加班，加班之直接勞動單位成本(Direct labor)為平常之l.15倍、 變動單
成本為平常之1.1倍 ，其成本如下表

1~2000 units
2000~4000 units
Total Cost
Raw materials
1.2
1.2
4800
Direct labor
2.2
2.53(=2.2x1.15)
9460
Variable  overhead
1.15
1.265(=1.15x1.1)
4830
若每單位賣6元，其總收入TR=6*4000=24000
又總成本TC=為4800+9460+4830=19090
淨收入=TR-TC=2400O-19090=49l0
故可接受此訂單

案例:自製或外購
     1.外購
    成本 2.25x160,000=360,000
    利潤 160,000x2.5-360,000=40,000
     2.自製

每單位物料成本
每單位勞動成本
A產品
0.46
0.63
B產品
0.48
1.26
自製時為生產160,000個A產品,必須減產B產品160,000/2=80,000個(此為機會成本)
         自製成本   (0.46+0.63)x160,000+(0.48+1.26)x80,000=35,200
         利潤         160,000x2.5 – 80,000x4.25 – 35,200= 24,800
    3.外購
       外購利潤(40,000)>自製利潤(24,800),因此如果自製與外購所得品質一致,則應外購。

案例：接單與否？
XYZ公司生產並以每單位六元的價格直接販賣給客戶，銷售額以每個月10％增加並預期會維持同樣趨勢。平均變動成本在目前情況下預期會維持不變，公司以目前的工廠及設備最大產能為200,000。
下表係一月份生產及成本記錄：

January
＄/unit
Sales