Lecture 4 © copyright ： qinwang 2012 [email protected] SHUFE school of international business.

Lecture 4

© copyright ： qinwang 2012

[email protected]  

SHUFE  school of international business

Production economics

How to allocate your resources to produce goods or provide service? There are a lot of decisions about operation, marketing, finance and HR in a firm.

The product process: input ---outputThe product process: input ---output

Inputs are considered variable or fixed depending on how readily their usage can be changed

Variable input An input for which the level of usage may be changed quit

e readily Fixed input

An input for which the level of usage cannot readily be changed and which must be paid even if no output is produced

Quasi-fixed input A “lumpy” or indivisible input for which a fixed amount

must be used for any positive level of output None is purchased when output is zero

Basic Concepts of Production Theory

Case: what happed to power plant

In 1970s, investors and regulators were prefer large scale power plants. They established a lot of nuclear power plants and coal-fired power plants. They want to gain economic efficiency by large scale.

In 1980s, more and more investors began to set up small power plants that using gas as energy. Such kind of plants are of larger Variable input but relatively smaller fixed input.

Short run At least one input is fixed All changes in output achieved by

changing usage of variable inputs Long run

All inputs are variable Output changed by varying usage of all

inputs

Basic Concepts of Production Theory

Basic theory

1. Production and production function2. Short run production

• Marginal revenue 3. Long run production

• returns to scale4.Innovation and technological progress

Production and production function

Production: create valuable goods or serves to consumers or other producers.

production includes tangible goods and intangible goods/serves, such as consultant, logistics, finance, education and creation.

Production function

Production function Maximum amount of output that can be

produced from any specified set of inputs, given existing technology

Q=f(X1,X2,X3……)Example: Q=f(K,L)

K\L 1 2 3 4 5 6 7 8 9 101 5 12 35 48 56 55 53 50 46 402 15 31 48 59 67 72 73 72 70 673 35 49 59 68 76 83 89 91 90 894 47 58 68 77 85 91 97 100 102 1035 55 66 75 84 92 99 104 107 109 1106 62 72 82 91 99 107 111 114 116 117

K\L 1 2 3 4 5 6 7 8 9 101 5 12 35 48 56 55 53 50 46 402 15 31 48 59 67 72 73 72 70 673 35 49 59 68 76 83 89 91 90 894 47 58 68 77 85 91 97 100 102 1035 55 66 75 84 92 99 104 107 109 1106 62 72 82 91 99 107 111 114 116 117

Example:

Short Run Production

In the short run, capital is fixed Only changes in the variable labor input can

change the level of output Short run production function

Q = f (L, K) = f (L)

Short-run production

TP 、 AP and MP Law of diminishing marginal product Three stage of production Short-run decision

Average & Marginal Products

Average product of labor AP = Q/L

Marginal product of labor MP = Q/L

When AP is rising, MP is greater than AP When AP is falling, MP is less than AP When AP reaches it maximum, AP = MP

Total, Average & Marginal Products of Labor, K = K

Number of workers (L)

Total product (Q)

Average product (AP=Q/L)

Marginal product (MP=Q/L)

0 0

1 52

2 112

3 170

4 220

5 258

6 286

7 304

8 314

9 318

10 314

--

55

51.6

5256

56.7

47.7

43.4

39.3

35.3

31.4

--

50

38

5260

58

28

18

104

-4

Total, Average, & Marginal Products

Total, Average & Marginal Product Curves

Law of diminishing marginal product

As usage of a variable input increases, a point is reached beyond which its marginal product decreases

MP curve is usually rising first and then falling.

Premise of Law of diminishing marginal product

Given the condition of technologyGiven the condition of other input fixedMarginal product is diminishing when the

input is over some quantity.

Rice production/mu:33000 (half a kilo) ，four children can stand on it.

Information is different??

Physical product VS. information The ownership of physical product is

changed after sale; information may not be and the owner could sell it several times.

The copy cost of physical goods is high; but marginal cost of information is zero.

……

Short Run Production Costs

Total variable cost (TVC) Total amount paid for variable inputs Increases as output increases

Total fixed cost (TFC) Total amount paid for fixed inputs Does not vary with output

Total cost (TC)

TC = TVC + TFC

Short-Run Total Cost Schedules

Output (Q) Total fixed cost (TFC)

Total variable cost (TVC)

Total Cost (TC=TFC+TVC)

0 $6,000

100 6,000200 6,000300 6,000400 6,000500 6,000600 6,000

$ 0

14,000

22,000

4,0006,000

9,000

34,000

$ 6,000

20,000

28,000

10,00012,000

15,000

40,000

Total Cost Curves (Figure 8.3)

Average Costs

• Average variable cost (AVC)

• Average fixed cost (AFC)

• Average total cost (ATC)

TVCAVC

Q

TFCAFC

Q

TCATC AVC AFC

Q

Short Run Marginal Cost

Short run marginal cost (SMC) measures rate of change in total cost (TC) as output varies

TC TVCSMC

Q Q

Average & Marginal Cost Schedules

Output (Q)

Average fixed cost (AFC=TFC/Q)

Average variable cost (AVC=TVC/Q)

Average total cost (ATC=TC/Q= AFC+AVC)

Short-run marginal cost (SMC=TC/Q)

0

100

200

300

400

500

600

--

15

12

$6030

20

10

--

35

44

$403030

56.7

--

50

56

$1006050

66.7

--

50

80

$402030

120

Average & Marginal Cost Curves

Short Run Average & Marginal Cost Curves

Short Run Cost Curve Relations

AFC decreases continuously as output increases Equal to vertical distance between ATC & A

VC AVC is U-shaped

Equals SMC at AVC’s minimum ATC is U-shaped

Equals SMC at ATC’s minimum

SMC is U-shaped Intersects AVC & ATC at their minimum

points Lies below AVC & ATC when AVC &

ATC are falling Lies above AVC & ATC when AVC &

ATC are rising

Short Run Cost Curve Relations

Relations Between Short-Run Costs & Production In the case of a single variable input, sho

rt-run costs are related to the production function by two relations

and w w

AVC SMCAP MP

Where w is the price of the variable input

Short-Run Production & Cost Relations (Figure 8.6)

Relations Between Short-Run Costs & Production When marginal product (average

product) is increasing, marginal cost (average cost) is decreasing

When marginal product (average product) is decreasing, marginal cost (average variable cost) is increasing

When marginal product = average product at maximum AP, marginal cost = average variable cost at minimum AVC

Long-run production

Production Isoquants Marginal Rate of Technical Substitution returns to scale

Production Isoquants In the long run, all inputs are variable & is

oquants are used to study production decisions An isoquant is a curve showing all possible i

nput combinations capable of producing a given level of output

Isoquants are downward sloping; if greater amounts of labor are used, less capital is required to produce a given output

A Typical Isoquant Map

Different Production Isoquants

Unsubstituted Completely substituted

Incompletely substituted

Marginal Rate of Technical Substitution

The MRTS is the slope of an isoquant & measures the rate at which the two inputs can be substituted for one another while maintaining a constant level of output

KMRTS

L

The minus sign is added to make MRTS a positive number since ∆K / ∆L, the slope of the isoquant, is negative

The MRTS can also be expressed as the ratio of two marginal products:

Marginal Rate of Technical Substitution

L

K

MPMRTS

MP

L

K

MPKMRTS

L MP

As labor is substituted for capital, MPL declines & MPK rises causing MRTS to diminish

Isocost Curves• Show various combinations of inputs that may be purchased for given level of expenditure (C) at given input prices (w, r)

C wK L

r r

• Slope of an isocost curve is the negative of the input price ratio (-w/r)• K-intercept is C/r

• Represents amount of capital that may be purchased if zero labor is purchased

Isocost Curves

Optimal Combination of Inputs

Two slopes are equal in equilibrium Implies marginal product per dollar spent on last un

it of each input is the same

• Minimize total cost of producing Q by choosing the input combination on the isoquant for which Q is just tangent to an isocost curve

or L L K

K

MP MP MPw

MP r w r

Output Maximization for Given Cost

Optimization & Cost Expansion path gives the efficient (least-c

ost) input combinations for every level of output Derived for a specific set of input prices Along expansion path, input-price ratio is con

stant & equal to the marginal rate of technical substitution

Expansion Path

example

• Taxi renting:• The company have 100 buses and 15 cars.

If add a bus, then can increase total revenue 10000 yuan/month ； if add a car, can increase total revenue for 30000 yuan/M.

• The rental fee of bus is 2500 yuan/M ；the rental fee of car is 1250 yuan/M 。

• What would you do? To rent bus or car?

Long-Run Costs

Long-run total cost (LTC) for a given level of output is given by: LTC = wL* + rK*

Where w & r are prices of labor & capital, respectively, & (L*, K*) is the input combination on the expansion path that minimizes the total cost of producing that output

Long-Run Costs

Long-run average cost (LAC) measures the cost per unit of output when production can be adjusted so that the optimal amount of each input is employed LAC is U-shaped Falling LAC indicates economies of scale Rising LAC indicates diseconomies of scale

LTCLAC

Q

Long-Run Costs

Long-run marginal cost (LMC) measures the rate of change in long-run total cost as output changes along expansion path LMC is U-shaped LMC lies below LAC when LAC is falling LMC lies above LAC when LAC is rising LMC = LAC at the minimum value of LAC

LTCLMC

Q

Long-Run Average & Marginal Cost Curves

Returns to scale

when we increase all inputs by a multiplier of m. Suppose our inputs are capital or labor, and we double each of these (m = 2), we want to know if our output will more than double, less than double, or exactly double ？

Returns to scale

Increasing Returns to Scale Decreasing Returns to Scale Constant Returns to Scale

Why??

Theodore W. Schultz

1979 Nobel Laureate in Economics small is beautiful

Large Scale or small scale?

Advantages of large scale Disadvantages of large scale?

Advantages of small scale? Disadvantages of small scale?

TR of China companies （ $109 ） TR of the world companies （ $109

）Bao steel （ 86 ） 22,6.634 ThyssenKrupp （ 338 ） 579.27 China National Petroleum Corporation (CNPC) （ 415 ） 1105.2

Exxon Mobil （ 1916 ） 3472.54

Industrial and Commercial Bank of China Limited, ICBC （ 198 ） 368.329

Citibank （ 1120 ） 1467.77

China Mobile Communications Corporation （ 158 ） 359.137

Nippon Telegraph & Telephone, NTT （ 934 ） 91,9.983

FAW Group Corporation（ 63 ） 187.107

GM （ 1773 ） 207,3.49

Lianhua （ 23 ） walmart （ 2198 ） 3511.39

Lenovo china （ 30 ） 166 IBM （ 860 ） 914.24

4.Innovation and technology progress Joseph Alois Schumpeter: creative destr

uction The question is not “how capitalism administers existing

structures, ... [but] how it creates and destroys them.” This creative destruction, he believed, causes continuous progress and improves the standards of living for everyone.

Innovation: the new commodity, the new technology, the new source of supply, the new type of organization .

lock-in path dependence （ WB·Arthur ） Innovation under network externality Small historical events lead to one techn

ology beat the other The more application of one technology, t

he more improvement opportunity for it.