1. Chapter 8: Cost Curves A firm aims to MAXIMIZE PROFITS
In order to do this, one must understand how to MINIMIZE COSTS
Therefore understanding of cost curves is essential to maximizing profits 6

2. Chapter 8: Costs Curves In this chapter we will cover:
8.1 Long Run Cost Curves
8.1.1 Total Cost
8.1.2 Marginal Cost and Average Cost
8.2 Economies of Scale
8.3 Short Run Cost Curves
8.3.1 Total Cost, Variable Cost, Fixed Cost
8.3.2 Marginal Cost and Average Cost
8.4 Economies of Scope
8.5 Economies of Experience 6

3. 8.1 Long Run Cost Curves
In the long run, a firm’s costs equal zero when zero production is undertaken
As production (Q) increases, the firm must use more inputs, thus increasing its cost
By minimizing costs, a firm’s typical long run cost curve is as follows: 6

4. • • K L (labor services per year) TC ($/yr) LR Total Cost CurveQ1 Q0 •
TC = TC0 K1 • K0
TC = TC1 L0
L (labor services per year) L1
TC ($/yr)
LR Total Cost Curve
TC1=wL1+rK1
TC0 =wL0+rK0
Q (units per year) Q0 Q1

5. Input Prices and LR Cost Curves
An increase in the price of only 1 input will cause a firm to change its optimal choice of inputs
However, the increase in input costs will always cause a firm’s costs to increase:
-(Unless inputs are perfect substitutes)

6. • • C1: Original isocost curve (TC = $200) C2: Isocost curve afterK
C1: Original isocost curve
(TC = $200)
C2: Isocost curve after
Price change (TC = $200)
C3: Isocost curve after
Price change (TC = $300)
Slope=w1/r
TC1/r • A
TC0/r • B
Slope=w2/r Q0 C2 C3 C1 L

7. Change in Input Prices -> A Shift in the Total Cost Curve
TC ($/yr)
Change in Input Prices -> A Shift in the Total Cost Curve
TC(Q) new
TC(Q) old
300
200
Q (units/yr) Q0

8. Example Let Q=2(LK)1/2 MRTS=K/L, W=5, R=20, Q=40
What occurs to costs when rent falls to 5?
Initially:
MRTS=W/R
K/L=5/20
4K=L
Q=2(LK)1/2
40=2(4KK)1/2
40=4K
10=K
40=L

9. Example Let Q=2(LK)1/2 MRTS=K/L, W=5, R=20, Q=40
What occurs to costs when rent falls to 5?
After Price Change:
MRTS=W/R
K/L=5/5
L=K
Q=2(LK)1/2
40=2(LL)1/2
40=2L
20=L
20=K

10. What occurs when rent falls to 5?
Initial: L=40, K=10 Final: W=5, R=20
Initial: TC=wL+rK
TC=5(40)+20(10)
TC=400
Final: TC=5(20)+5(20)
TC=200
Due to the fall in rent, total cost falls by $200.

11. Change in Rent TC ($/yr) TC(Q) initial TC(Q) final 400 200
Q (units/yr) 40

12. 8.1.1 Total Cost
To calculate total cost, simply substitute labour and capital demand into your cost expression:
Q= 50L1/2K1/2 (From Chapter 7:)
L*= (Q0/50)(r/w)1/2
K* = (Q0/50)(w/r)1/2
TC = wL +rK
TC= w [(Q0/50)(r/w)1/2 ] +r[(Q0/50)(w/r)1/2 ]
TC= [(Q0/50)(wr)1/2 ] +[(Q0/50)(wr)1/2 ]
TC = 2Q0(wr)1/2 /50

13. Total Cost Example 2
Let Q= L1/2K1/2, MPL/MPK=K/L, w=10, r=40. Calculate total cost.
MRTS=w/r
K/L=10/40
K=4L
Q=L1/2K1/2 =L1/2(4L)1/2
Q=2L
L=Q/2

14. Let Q= L1/2K1/2, MRTS=K/L, w=10, r=40.
Total Cost Example 2
Let Q= L1/2K1/2, MRTS=K/L, w=10, r=40.
Calculate total cost.
Q=L1/2K1/2 Q=(K/4)1/2K1/2
Q=1/2K
K=2Q
TC = wL +rK
TC = 10(Q/2) +40(2Q)
TC=85Q
K=4L
L=K/4
L=Q/2

15. Input Prices and LR Cost Curves
When the prices of all inputs change by the same (percentage) amount, the optimal input combination does not change
The same combination of inputs are purchased at higher prices

16. K (capital services/yr)
C1=Isocost curve before ($200) and after ($220) a 10% increase in input prices • A Q0 C1
L (labor
services/yr)

17. Example: A Shift in the Total Cost Curve When Input Prices Rise 10%
TC ($/yr)
Example: A Shift in the Total Cost Curve When Input Prices Rise 10%
TC(Q) new
TC(Q) old
220
200
Q (units/yr) Q0

18. 8.1.2 Average and Marginal Cost Functions
Definition: The long run average cost function is the long run total cost function divided by output, Q.
That is, the LRAC function tells us the firm’s cost per unit of output…

19. Long Run Average and Marginal Cost Functions
Definition: The long run marginal cost function is rate at which long run total cost changes with a change in output
The (LR)MC curve is equal to the slope of the (LR)TC curve

20. Average vrs. Marginal Costs
TC ($/yr)
Average vrs. Marginal Costs
TC(Q) post
Slope=LRMC
TC0
Slope=LRAC
Q (units/yr) Q0

21. Relationship Between Average
and Marginal Costs
When marginal cost is less than average cost, average cost is decreasing in quantity. That is, if MC(Q) < AC(Q), AC(Q) decreases in Q.
When marginal cost is greater than average cost, average cost is increasing in quantity. That is, if MC(Q) > AC(Q), AC(Q) increases in Q.
When marginal cost equals average cost, average cost is at its minimum. That is, if MC(Q) = AC(Q), AC(Q) is at its minimum.

22. • “typical” shape of AC, MC AC, MC ($/yr) MC AC Q (units/yr)
AC at minimum when AC(Q)=MC(Q)
Q (units/yr)

23. 8.2 Economies and Diseconomies of Scale
If average cost decreases as output rises, all else equal, the cost function exhibits economies of scale.
-large scale operations have an advantage
If average cost increases as output rises, all else equal, the cost function exhibits diseconomies of scale.
-small scale operations have an advantage

24. Economies and Diseconomies of Scale
Why Economies of scale?
-Increasing Returns to Scale for Inputs
-Specialization of Labour
-Indivisible Inputs (ie: one factory can produce up to 1000 units, so increasing output up to 1000 decreases average costs for the factory)

25. Economies and Diseconomies of Scale
Why Diseconomies of scale?
-Diminishing Returns from Inputs
-Managerial Diseconomies
-Growing in size requires a large expenditure on managers
-ie: One genius cannot run more than 1 branch

26. Typical Economies of Scale
AC ($/yr)
Typical Economies of Scale
Minimum Efficient Scale – smallest
Quantity where LRAC curve reaches
Its min.
AC(Q)
Economies of scale
Diseconomies of scale
Q (units/yr) Q*

27. Returns to Scale and Economies of Scale
Production functions and cost functions are related:
Production Function
Cost Function
Increasing returns to scale
Economies of Scale
Decreasing returns to scale
Diseconomies of Scale
Constant Returns to Scale
Neither economies nor diseconomies of scale

28. Example: Returns to Scale and Economies of Scale
CRS IRS DRS
Production Function Q = L Q = L2 Q = L1/2
Labor Demand L*=Q L*=Q1/2 L*=Q2
Total Cost Function TC=wQ wQ1/2 wQ2
Average Cost Function AC=w w/Q1/2 wQ
Economies of Scale none EOS DOS

29. Measuring Economies of Scale - Output Elasticity of Total Cost
Economies of Scale are also related to marginal cost and average cost:
If MC < AC, AC must be decreasing in Q. Therefore, we have economies of scale.
If MC > AC, AC must be increasing in Q. Therefore, we have diseconomies of scale. 6

30. Example Let Cost=50+20Q2 MC=40Q
IF Q=1 or Q=2, determine economies of scale
(Let Q be thousands of units)

31. Example TC=50+20Q2 MC=40Q AC=TC/Q=50/Q+20Q Initially: MC=40(1)=40
MC<AC – Economies of Scale
Finally: MC=40(2)=80
AC=50/2+20(2)=65
MC>AC – Diseconomies of Scale

32. 8.3 Short-Run Cost Curves In the short run, at least 1 input is fixed
(ie: (K=K*)
Total fixed costs (TFC) are the costs associated with this fixed input (ie: rk)
Total variable costs (TVC) are the costs associated with variable inputs (ie:wL)
Short-run total costs are fixed costs plus variable costs: STC=TFC+TVC 6

33. Short Run Total Cost, Total Variable Cost and Total Fixed Cost
TC ($/yr)
Short Run Total Cost, Total Variable Cost and Total Fixed Cost
STC(Q, K*)
TVC(Q, K*)
rK*
TFC
rK*
Q (units/yr)

34. Short Run Costs Example:
Minimize the cost to build 80 units if Q=2(KL)1/2 and K=25. If r=10 and w=20, classify costs.
Q=2(KL)1/2
80=2(25L)1/2
80=10(L)1/2
8=(L)1/2
64=L 6

35. Short Run Costs Example:
K*=25, L=16. If r=10 and w=20, classify costs.
TFC=rK*=10(25)=250
TVC=wL=20(64)=1280
STC=TFC+TVC=1530 6

36. Relationship Between Long Run and Short Run Total Cost Functions
The firm can minimize costs better in the long run because it is less constrained.
Hence, the short run total cost curve lies above the long run total cost curve almost everywhere.

37. • • • Only at point A is short run minimized as well as long runK
Only at point A is short run minimized as well as long run
TC2/r Q1
Long Run Expansion path
TC1/r
TC0/r • C Q0 Q0
Short Run
Expansion path • A • B K* L
TC0/w TC1/w TC2/w

38. TC ($/yr)
STC(Q)
LRTC(Q) A •
rK*
Q (units/yr)

39. 8.3.2 Short Run Average and Marginal Cost Functions
Definition: The short run average cost function is the short run total cost function divided by output, Q.
That is, the SAC function tells us the firm’s cost per unit of output…

40. Short Run Average and Marginal Cost Functions
Definition: The short run marginal cost function is rate at which short run total cost changes with a change in input
The SMC curve is equal to the slope of the STC curve

41. Short Run Average and Marginal Cost Functions
In the short run, 2 additional average costs exist: average variable costs (AVC) and average fixed costs (AFC)

42. Short Run Average and Marginal Cost Functions

43. Example
To make an omelet, one must crack a fixed number of eggs (E) and add a variable number of other ingredients (O). Total costs for 10 omelets were $50. Each omelet’s average variable costs were $ If eggs cost 50 cents, how many eggs in each omelet?
AC=AVC+AFC
TC/Q=AVC+AFC
50/10=$1.50+AFC
$3.50=AFC

44. There were 7 eggs in each omelet.
Example
To make an omelet, one must crack a fixed number of eggs (E) and add a variable number of other ingredients (O). Total costs for 10 omelets were $50. Each omelet’s average variable costs were $ If eggs cost 50 cents, how many eggs in each omelet?
$3.50=AFC
$3.50=PE (E/Q)
$3.50=0.5 (E/Q)
7=E/Q
There were 7 eggs in each omelet.

45. $ Per Unit
Average fixed cost is constantly decreasing, as fixed costs don’t rise with output.
AFC
Q (units per
year)

46. $ Per Unit
Average variable cost generally decreases then increases due to economies of scale.
AVC
AFC
Q (units per
year)

47. SAC is the vertical sum of AVC and AFC
$ Per Unit
SAC
AVC
Equal
AFC
Q (units per
year)

48. • • SMC intersects SAC and AVC at their minimum points $ Per Unit SAC
AFC
Q (units per
year)

49. 8.4 Economies of Scope
Often a firm produces more than one product, and often these products are related:
-Pepsi Cola makes Pepsi and Diet Pepsi
-HP makes Computers and Cameras
-Denny’s Serves Breakfast and Dinner
Often a firm benefits from economies of scope by producing goods that are related; they share common inputs (or good A is an input for good B). Efficiencies often exist in producing related products (ie: no shipping between plants).

50. TC(Q1,Q2)<TC(Q1,0)+TC(0,Q2)
Economies of Scope
If a firm can produce 2 products at a lower total cost than 2 firms each producing their own product:
TC(Q1,Q2)<TC(Q1,0)+TC(0,Q2)
That firm experiences economies of scope.

51. Economies of Scope Example
If the cities maintains local roads, it costs are $15 million a year. If a private firm covers park maintenance, it costs are $12 million a year. If the city does both, it costs $25 million a year.
TC(Q1,Q2)=$25 million
TC(Q1,0)+TC(0,Q2)=$15 million + $12 million
TC(Q1,0)+TC(0,Q2)=$27 million
TC(Q1,Q2)<TC(Q1,0)+TC(0,Q2)
Economies of scope exist.

52. 8.5 Economies of Experience
Often with practice a firm “gets better” at producing a given output; it cuts costs by being able to produce the good faster and with fewer defects.
Ie: The first time you worked on elasticities, each question took you 10 minutes and 10% were wrong. By the end of the course you’ll be able to calculate elasticities in 4 minutes with only 5% error (for example).

53. Economies of Experience
Economies of experience are efficiencies (cost advantages) resulting from accumulated experience (learning-by-doing).
The experience curve shows the relationship between average variable cost and cumulative production volume.
-As more is produced (more experience is gained), average cost decreases.

54. The Experience Curve Eventually the curve Flattens out AVC
Cumulative Output

55. Economies of Experience
vs. Economies of Scale
Economies of experience occur once, while economies of scale are ongoing.
A large producer benefiting from economies of scale will increase average costs by decreasing production.
A large producer benefiting from economies of experience may safely decrease production

56. Chapter 8 Key Concepts Long-Run Costs:
TC=wL+rK (if labor and capital are the only inputs
AC=TC/Q
MC=∆TC/ ∆ Q
Economies of scale summarize how average cost changes as Q increases
Economies of scale = AC decreases as Q increases
Diseconomies of scale = AC increases as Q increases

57. Chapter 8 Key Concepts Short-Run Costs
TFC=All costs of the FIXED input
TVC=All total costs of the VARIABLE input
STC=TFC+TVC
SAC=STC/Q
SMC=∆STC/ ∆Q
AFC=TFC/Q
AVC=TVC/Q
SAC=AFC+AVC

58. Chapter 8 Key Concepts
If one firm has lower costs producing two goods than two firms producing the goods individually, that firm enjoys ECONOMIES OF SCOPE
If AC decreases as cumulative output increases, a firm enjoys ECONOMIES OF EXPERIENCE
This effect decreases over time
Calculators are important in Econ 281