Definition.

TYPE OF COSTS

There are mainly four types of costs:

1. OPPORTUNITY COST:

Opportunity cost refers to the real cost of obtaining something. It involves sacrification. It is not a monetary cost but sacrification

- Opportunity cost refers to the alternative that must be forgone or sacrified when the second alternative is selected

Eg. The consumer decides to hire house instead of a car since his income is not enough to purchase both (Opportunity cost is that alternative forgone (car)

(In detail refers pp and isoquant curve)

IMPORTANCE OF OPPORTUNITY COST

2. SOCIAL COST (COLLECTIVE COSTS)

Social cost refers to cost owned by the society in the whole process of civilizing public goods.

3. PRIVATE COST PUBLIC

Private cost are expenses or expenditure incurred by the individuals (firms, industry) in the process of producing goods and services since the level of production differ from one firm to another.

 TYPES OF PRIVATE COSTS

  i. IMPLICITY COST:

Implicity costs are self-owned are pocket cost or pocket cost. These are self owned costs or self owned resources incurred by the firm or an industry the process of producing output or sometimes called opportunity cost of business operation (sacrification costs) eg salary of the owner and manager who only receive profits.
-         eg estimated rent for his building are implicit costs. These are not estimated or counted.

ii. EXPLICITY COSTS.

TOTAL VARIABLE COST  (TVC)

In short run production function is given by Q= f (L,Te) TVC= PL-L

Where    PL = Price of variable input.
               L = number of variable input.
Example:
A firm employs 10 workers at average of 20,000/- calculate TVC of the firm.
Sol: 
PL = 20,000
L = 10 workers
TVC   = PL.L
         = 20,000*10
TVC   = 200,000
NB.TVC exist in short run and long run period
 * TVC don’t exist if Q=0

THE RELATIONSHIP BETWEEN 
AVERAGE FIXED COST, 
AVERAGE VARIABLE COST, 
AVERAGE COST AND MAGINAL COST IN SHORT RUN PERIOD.

IV) TOTAL FIXED COST AND VARIABLE COST (TFC)

TOTAL FIXED COSTS (TFC)

TFC refers to that costs which don’t vary with the level of output. It means always remain constant at any level of production (OUTPUT).
TFC are also called overhead costs or supplementary costs

These costs exist even if firm produces nothing.
1.      When Q = 0 TFC exists   2.      Exist in only short run

In shorten Production function is given by
Q  =  f(l,k)
TFC = Pk x k
Where 
Pk = Price of fixed factor
k   = Unit of fixed input 

Question
Example: A firm produced a machinery which costs 200,000 Tshs Calculate TFC
Solution 
Given  k = 1
         P = 200,000/Tshs
          TFC = Pk x k
          TFC = 200,000 x 1

AVC = PL.L /Q
AVC = TVC / Q

AVERAGE TOTAL COST OR AVERAGE COST (AC) 

AC refers to TC per Unit of output  
AC refers to the ratio between TC and the level of output

AC = TC /Q

Since   Q   =  f ( l,k )
         TFC =  Pk.k  
         TVC =  PL.L  
         AC = Pk.k + PLxL /Q

  TOTAL COST (TC)

TC refers to the sum of TFC and TVC
TC = TFC + TVC

Where
TC = Total cost
TFC = Total Fixed Cost
TVC = Total Variable Cost

Since in short run period production is given by
Q = f ( L,k )
TFC = Pk x k
TVC = PLx L
TC   = Pk x k + PL* L

TC= TFC + TVC

Note: since the change in the level of output depends on TVC, therefore TC is function of output;
TC = F (Q)
Q  = F(TVC)

When
Q = 0   TVC = 0  and  TC =TFC

The Summary
TC = Pk.k + Pk.L
TC = TFC + TVC
TC = f(Q)

MARGINAL COST (MC)

MC refers to the rate of change of TC with a given one unit.
MC refers to an increment of TC as the result of one more unit change in output.
MC refers to an additional TC with a given one more unit change in output.

MC curve is U-shaped due to the low of variable propotions.
MC curve initially falls reached at a minimum then start to rise as output is  expanded.

The shape of AFC curve is that of rectangular  Hyperbola always is down ward shoping  (negatively sloped ).
A decreases as the level of output increases but will never be eg to zero.
ie. touch the x-axis
- When Q becomes large and larger the values of AFC becomes smaller and  smaller.
- When devide a number which is fixed with a number which is variable the  values of  AFC becomes smaller AFC is always positive .

AVERAGE VARIABLE COST (AVC)

AVC refers to the variable cost per unit of output.
AVC is  the ratio between TVC and the level or units of output .
AVC =  TVC / Q

IMPORTANCE OF AVC, AC AND MC

A. IMPORTANCE OF AVC

B. AVERAGE COST (AC)

    TC = TFC + TVC
     AC = TRC/Q + TVC /Q
     AC  = AFC + AVC

    C. MARGINAL COST ( MG)

   AC = Pk.k / Q + PL.L / Q
   Ac = AFC +AVC

  AC  =  TC /Q
  AC  =  AFC + AVC

Note: when MC, AVC and AC curves are falling, always MC, AVC and AC curves is below and AVC and AC (MCL, AVC and MC, LAC )       

Why??.
When cast fall, are falling at small rate hence the adition of TC become smaller than AC and AVC

*When MC, AVC and AC curve rise always MC curve is above AVC and AC (MC > AC, MC > AVC)

* When cost rise, they rise at faster rate hence the additional cost become larger than AVC and AC values.

Some points to be noted.
Why AFC curve is down wards sloping.
*When divide fixed costs with output which tend to change with time the values of AFC become smaller and smaller (rectangle hyperbola)

Why: AC curve is above AFC and AVC curves.

  AC > AFC
  AC > AVC        

WHY AVC, AC AND, MC ARE U-SHAPED IN SHORT RUN  

Why AVC is  u-shaped in short run :

METHOD I:
The u-shaped of AVC curve be explained by using the relationship between APL and AVC
TVC =PL.I

Where:
TVC = total variable cost
PL = Price of variable input e.g. wage (w)
L  = No of labour, workers employed by the firm

TVC = PL.L  . .  . (I),
Since PL = W
TVC = W . L  . . . (II)
AVC = TVC / Q .  .  . (III) 
Since TVC = W.L
AVC = W.L / Q .  .  . (IV) 
AVC = W.L / Q .  .  .  (V)
But Q / L = AP   
AVC = W . L / APL

AVC = W . L / APL

AVC is an inverse or mirror reciprocal of APL
When APL at maximum AVC of at minimum when APL falls AVC rises

Therefore the u-shaped of AVC is due to the behavior of APL

 METHOD II:
Method II of variable proportion.

i. APL > AVC ---> IRS
ii. APL ~ AVC  ---> CRS
iii. APL < AVC ---> DRS

Law of Variable Proportions

The u- shaped of AC curve can be explained by the law of variable proportions (return to scale).

WHY MC CURVE IS U-SHAPED IN SHORT RUN
Method I: (Relationship between MC and MPL curve)

TC = TRC +TVC
MC = ATC / 4Q   = A (TFC +TVC)/ 4Q
MC = 4TFC + 4TVC /Q
MC = 4TFC / Q + 4TVC /Q
But  ATFC = O
MC = O / 4Q + 4TVC / 4Q         
MC = O + 4TVC / 4Q
MC = 4TVC / 4Q          But TVC = W.L
MC = 4(W.L) / 4Q
= W.4L / 4Q            Since w is fixed                                  MC  = W. L / MPL         Since   MP = 4Q /4L
MC = W. I / MPL

Therefore MC curve is an inverse or reciprocal of MPL curve

METHOD III :
The Law of Variable Proportions:

LONG RUN THEORY OF COST

In long run the firms are variable. All inputs are variable even those fixed inputs existing in short run .

In long run production function is given by : Q = f(c, k)

In long run in order to produce 6 units of output the firm can employ more units of k and less units of L or more L and less k therefore in long run the firm in curve variable costs.

LONG RUN AVERAGE COST: LRAC
Definition
-       Long run average costs LAC refers to the small summation of Short run average cost curve  
Long run average cost curve is derived from short run average cost curve

Long run AC curve is known as planning curve  or the envelope curve since it envelopes the SAC curve.
- When the two SRAC curve intersects from one firm.-
- SRAC curves touches the longer AC curve (SRAC)curves are tanget to LR Ac curves.
LRAC curve form an “Industry” (Small summation of SRAC curves)

The shape of long run curve is bowed.
*Initially LRAC curve falls reached at a minimum then start to rise.
* The shape of LRAC curve is used to determine Economies and Dis economies of scale.