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Chapter 8 – Production & Cost

in the Short Run

Basic Concepts of Production Theory

� Production function� Maximum amount of output that can be produced from any

specified set of inputs, given existing technology

� The relationship between labor, capital, and output

� Technical efficiency� Achieved when maximum amount of output is produced

with a given combination of inputs

� Economic efficiency� Achieved when firm is producing a given output at the

lowest possible total cost

Basic Concepts of Production Theory

� 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� An input employed in a fixed amount for any positive level of

output that need not be paid if output is zero

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Basic Concepts of Production Theory

� Short run� At least one input is fixed

� Generally capital

� 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

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 )= =

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� Law of diminishing marginal product

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

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Total, Average, and Marginal Products of

Labor

435.33189

1039.33148

1843.43047

2847.72866

3851.62585

50552204

5856.71703

60561122

5252521

--00

Marginal Product (MP = ∆Q/∆L

Average Product (AP = Q/L)

Total Product (Q)# Workers (L)

TP, AP, and MP Graphs

� Total Product – Increasing at a decreasing rate

TP, AP, and MP Graphs

� AP increases if MP>AP� AP decreases if MP<AP

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Increase in Capital

� An increase in K will increase MP and AP

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 Costs

40000340006000600

28000220006000500

20000140006000400

1500090006000300

1200060006000200

1000040006000100

6000060000

Total Costs (TC = TFC + TVC)

Total Variable Costs (TVC)

Total Fixed Costs (TFC)

Output (Q)

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Total Costs

� Total Variable Costs as� TVC = w*L

� Where w is the wage rate and L is amount of labor

� Total Fixed Costs as� TFC = r*K

� Where r is the rental rate and K is amount of capital

� Total Costs as� TC = w*L + r*K

TC, TVC, and TFC

� Notice the difference between TC and TVC is TFC

Average Costs

� Average Variable Costs (AVC)� = TVC/Q

� Average Fixed Costs (AFC)� = TVC/Q

� Average Total Costs (ATC)� = TC/Q or ATC = AFC + AVC

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Short Run Total Costs

66.756.710600

564412500

503515400

503020300

603030200

1004060100

---0

Average Costs (ATC = AFC + AVC)

Average Variable Costs (AVC)

Average Fixed Costs (AFC)

Output (Q)

Short Run Marginal Cost

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

∆ ∆= =∆ ∆TC TVC

SMCQ Q

Short Run Marginal Costs

(40000-28000)/(600-500) = 12040000600

(28000-20000)/(500-400) = 8028000500

(20000-15000)/(400-300) = 5020000400

(15000-12000)/(300-200) = 3015000300

(12000-10000)/(200-100) = 2012000200

(10000-6000)/(100-0) = 4010000100

-60000

Short-Run Marginal CostTotal Costs (TC = TFC + TVC)

Output (Q)

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Cost Curves

� What do we notice about SMC, ATC, and AVC?

Cost Curves

� AVC and ATC increase when SMC is greater. SMC intersects both lines at their minimum point

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

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Short Run Cost Curve Relations

� 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

� In the case of a single variable input, short-run costs are related to the production function by two relations� AVC = TVC/Q = (w*L)/(AP*L) = w/AP

� SMC = ∆TVC/∆Q= ∆(w*L)/∆Q = w/MP� Remember MP = ∆Q/∆L

Relations Between Short-Run Costs &

Production

Production and Costs (w=$1000)

12056.678.3317.6560034

804412.5022.7350022

50352028.5740014

303033.3333.333009

20305033.332006

404025251004

----00

SMC=w/MPAVC=w/APMP=∆Q/∆LAP=Q/LQ Labor

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Production Curves

� When MP>AP what is true about costs?

� When MP<AP?

Cost Curves

� When MP>AP each worker is producing more, thus AVC is decreasing

� When MP<AP each worker produces less and AVC is increases

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