Lecture 4 © copyright ： qinwang 2012 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 ---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 quite 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 function 2.Short run production Marginal revenue 3.Long run production returns to scale 4.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)

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)

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 technology  Given the condition of other input fixed  Marginal 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 $ 0 14,000 22,000 4,000 6,000 9,000 34,000 $ 6,000 20,000 28,000 10,000 12,000 15,000 40,000

Total Cost Curves (Figure 8.3)

Average Costs Average variable cost (AVC) Average fixed cost (AFC) Average total cost (ATC)

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

Average & Marginal Cost Schedules Outpu t (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) $ $ $ $

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 & AVC  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, short-run costs are related to the production function by two relations 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 & isoquants are used to study production decisions An isoquant is a curve showing all possible input 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 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 As labor is substituted for capital, MP L declines & MP K 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) 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 unit 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

Output Maximization for Given Cost

Optimization & Cost  Expansion path gives the efficient (least-cost) input combinations for every level of output Derived for a specific set of input prices Along expansion path, input-price ratio is constant & 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 yuan/month ； if add a car, can increase total revenue for 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

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

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 （ $10 9 ） TR of the world companies （ $10 9 ） Bao steel （ 86 ） 22,6.634ThyssenKrupp （ 338 ） China National Petroleum Corporation (CNPC) （ 415 ） Exxon Mobil （ 1916 ） Industrial and Commercial Bank of China Limited, ICBC （ 198 ） Citibank （ 1120 ） China Mobile Communications Corporation （ 158 ） Nippon Telegraph & Telephone, NTT （ 934 ） 91,9.983 FAW Group Corporation （ 63 ） GM （ 1773 ） 207,3.49 Lianhua （ 23 ） walmart （ 2198 ） Lenovo china （ 30 ） 166IBM （ 860 ）

4.Innovation and technology progress  Joseph Alois Schumpeter: creative destruction 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 technology beat the other The more application of one technology, the more improvement opportunity for it.