1. Behaviours Of Cost Curves
Derivation And Properties of Short Run Total, Average And Marginal Cost Curves

2. How Does Total Cost Change ?
It is actually a phenomenon in real world that as a firm increases its output, its productivity first rises faster and later rises much slower or even decreases.
So, if unit factor costs are kept constant, the total cost first rise relatively slower than the total output, but later rise much faster.

3. Why Does This Happen ?
In CE & AL level, such phenomenon is explained in short run by the Law of Diminishing (Marginal) Returns.
In long run, it is caused by the dominance of economies of scale in early production and diseconomies of scale later on.

4. Law of Diminishing Returns
This law states that when we continuously add variable factors to fixed factors, the total product (output) of a firm will first rise more than proportionally and then less than proportionally, or even decrease.
Alternatively, we say that the marginal product will eventually diminish.

5. An Illustration
Suppose a farmer has a piece of cultivated land and now wants to hire more workers to work on the farm.
Then he discovers that the farm’s output changes as follow:

6. Output Table

7. Output Table Total product rises faster Total product rises slower
Variable factor
Fixed factor

8. Output Table
Marginal product falls when the third worker is added.

9. Plotting Short Run Costs Curves
If factor costs are constant, e.g., the wage of hiring one more worker is no different from those hired before, total variable cost rises proportionally.
But due to the Law of Diminishing (Marginal) Returns, total product rises faster at first and slower later.

10. Cost ($)
Variable cost rises proportionally.
TVC
TP(Q)
TP rises faster at first but slower at the end.

11. Adding Fixed Cost
Fixed cost must occur as the production begins and will not change with total product.
In short run, the total cost of production includes both fixed and variable cost.

12. Cost ($) TC
TC and TVC are parallel because the vertical distance is fixed, that is the same as the fixed cost.
TVC
TVC plus TFC will be TC.
TFC
Total fixed cost is a horizontal line as it will not change with TP.
TP(Q)

13. Cost ($)
TVC
TVC1
TP1
= AVC1
= tan Ø
As tan Ø increases when Ø is larger, AVC is also larger.
TVC1 Ø
TP(Q)
TP1

14. Cost ($)
TVC
Angle Ø decreases first and then rises. So does the AVC. Q3 Q2 Q1
TP(Q)

15. Cost ($)
AVC
AVC also falls at the beginning but rises later on.
TP(Q) Q1 Q2 Q3

16. Cost ($) TC
At same Q, angle Ø for TC is greater than TVC.
TVC
TP(Q) Q1 Q3

17. ATC
Cost ($)
Thus, at same Q, ATC is higher than AVC.
AVC
TP(Q) Q1 Q2 Q3

18. Cost ($)
But for fixed cost, its average tends to fall as the total output increases.
TFC TP
As only TP, not TFC, will increase, the average must be falling.
= AFC
TFC
TP(Q) Q1 Q3

19. Cost ($)
ATC and AVC are closing to each other because AFC is falling all the way.
AFC
ATC
AVC
AVC plus AFC will be ATC
TP(Q) Q1 Q2 Q3

20. Cost ($)
The line from origin forms the lowest angel with TVC if it touches TVC, but not intersecting it.
TVC
This tangency point means at Q’, we have the lowest AVC. Ø Ø’
TP(Q) Q’
Ø > Ø’

21. Cost ($) TC
The line from origin will touch TC at a higher Q than the TVC.
TVC
TP(Q) Q’ Q”

22. Cost ($)
ATC reaches minimum at a larger Q than the minimum AVC.
AVC
ATC
AFC
TP(Q) Q’ Q”

23. ATC
AVC
Cost ($)
At the range Q’ to Q”, AVC is rising but AFC is falling.
AFC
When AVC rises faster, ATC will rise.
When AFC falls faster, ATC still falls
TP(Q) Q’ Q”

24. Cost ($)
Marginal cost =
TVC
Change in Total cost Change in Total Product Ø”
The tangency line will overlap the curve segment if the segment is very small. Q1
This is a tangency line touching TVC.
TP(Q)

25. Cost ($)
TVC Q3
MC = AVC
MC < AVC
MC > AVC Q2 Q1
TP(Q)

26. Cost ($)
AVC MC MC
AVC
MC < AVC
MC > AVC
MC = AVC
TP(Q) Q1 Q2 Q3

27. Cost ($)
MC falls and rises faster than the AVC. MC
AVC
When MC is smaller than AVC, AVC falls.
MC cuts AVC’s minimum.
TP(Q) Q1 Q2 Q3
When MC is larger than AVC, AVC falls.

28. Cost ($) TC
Slopes are equal for the same Q.
TVC Q2 Q1
TP(Q)
So, only one MC for both TC and TVC, since they are parallel.

29. Cost ($) TC
MC also cuts TC’s minimum.
TVC Q” Q’
TP(Q)

30. ATC
Cost ($)
Assembly of all short run cost curves MC
AVC
AFC Q” Q’
MC cuts both ATC and AVC at their minimum.
TP(Q)