Lecture 3 Lecture 3 Production and Production and

CostsCosts

OutlineOutline

Production Theory: BasicsProduction Theory: Basics Cost Theory: BasicsCost Theory: Basics Economies and Diseconomies of ScaleEconomies and Diseconomies of Scale Production With Multiple InputsProduction With Multiple Inputs Time and Costs: Observations on Time and Costs: Observations on

Fixed CostsFixed Costs Ideas That MatterIdeas That Matter Complications Complications

Production Theory: Production Theory: Basics Basics

Production FunctionProduction Function: The relationship : The relationship describing the most output possible with a describing the most output possible with a given quantity of an input.given quantity of an input. (Or the least amount inputs necessary to (Or the least amount inputs necessary to

produce some given level of output.)produce some given level of output.) Marginal Product:Marginal Product: The change in total The change in total

product when one of the inputs is changed.product when one of the inputs is changed. Approximation: MPx =Change in Approximation: MPx =Change in

output/change in inputoutput/change in input Exact (calculus): MPx =dq/dxExact (calculus): MPx =dq/dx Average Product:Average Product: Output per unit of input Output per unit of input

APx =Q/XAPx =Q/X

ExampleExample

Hours of Labor Quantity of Output Marginal Product Average Product

0 0    

1 1 1 1

2 3 2 1.5

3 6 3 2

4 8 2 2

5 9 1 1.8

EXTRA Q PER EXTRA

L

The GraphThe Graph

0

1

2

3

4

0 1 2 3 4 5 6

Labor

MP increase and then decreases

Max AC occurs when

MC=AC

Useful StuffUseful Stuff

MP increases and then decreasesMP increases and then decreases Think about what an odd world it would be if MP Think about what an odd world it would be if MP

did not decrease.did not decrease. (This is commonly defined as (This is commonly defined as diminishing diminishing

marginal returnsmarginal returns). ). AP begins to decrease only when MP<APAP begins to decrease only when MP<AP

Techies can prove this using about two lines of Techies can prove this using about two lines of calculus, but it has a common sense explanation calculus, but it has a common sense explanation as wellas well

Application: Optimal Application: Optimal Choice of Input Choice of Input

Hours of Labor Quantity of Output Marginal Product

0 0

1 5 5

2 9 4

3 12 3

4 14 2

5 15 1

Suppose that the output is worth $10 per unit and labor Suppose that the output is worth $10 per unit and labor costs $15 per hour. Total value (value of output – cost costs $15 per hour. Total value (value of output – cost

of inputs) is as follows.of inputs) is as follows.

Hours of Labor

Quantity of Output

Marginal Product

Total Value

0 0 $ -

1 5 5 $35

2 9 4 $60

3 12 3 $75

4 14 2 $80

5 15 1 $75

More MarginalsMore Marginals

Marginal revenue product: Marginal revenue product: the the revenue obtained from the extra revenue obtained from the extra output produced when another unit output produced when another unit of the input is employed. Formally, of the input is employed. Formally, MRP = Marginal Product x Price of MRP = Marginal Product x Price of

outputoutput

Output price=$10Output price=$10Input price =$15Input price =$15

Hours of Labor

Quantity of Output

Marginal Product

MRP

0 0

1 5 5 $50

2 9 4 $40

3 12 3 $30

4 14 2 $20

5 15 1 $10

MRP=10*MPIf MRP > Input

price, buy more input

Cost Function: BasicsCost Function: Basics

Cost Function:Cost Function: The relationship describing the least The relationship describing the least expensive way producing a given quantity of output. expensive way producing a given quantity of output. (Or, equivalently, the most output that can be (Or, equivalently, the most output that can be produced for a given level of expenditure.)produced for a given level of expenditure.)

““Costs” are simply of way of expressing Costs” are simply of way of expressing economically important information about what the economically important information about what the firm does. As such, when we describe costs, we are firm does. As such, when we describe costs, we are really summarizing two kinds of thingsreally summarizing two kinds of things The production technology (e.g., what sorts of inputs are The production technology (e.g., what sorts of inputs are

able to produce what sorts of outputs)able to produce what sorts of outputs) The cost of the inputsThe cost of the inputs

Thus, if we have described the technology by writing Thus, if we have described the technology by writing out the production function, we need only to know out the production function, we need only to know the price of the inputs before we can describe costs. the price of the inputs before we can describe costs.

ExampleExample: Given the production function : Given the production function suppose that cost of the fixed input=$10 suppose that cost of the fixed input=$10

and wage rate=$5)and wage rate=$5)

Cost Function

Hours of Labor

Quantity of Output Total Cost MC AC

0 0 $ 10

1 1 $ 15 5 15

2 3 $ 20 2.5 6.7

3 6 $ 25 1.67 4.17

4 8 $ 30 2.5 3.75

5 9 $ 35 5.0 3.89

Economies and Economies and diseconomies of scalediseconomies of scale

Economies of scaleEconomies of scale the tendency for the tendency for AC to decrease when output AC to decrease when output increasesincreases MC<ACMC<AC

Diseconomies of Scale: Diseconomies of Scale: The The tendency for AC to increase when tendency for AC to increase when output increasesoutput increases MC>ACMC>AC

Why Economies of Scale? Why Economies of Scale?

Learning by doing/gains from Learning by doing/gains from specializationspecialization

The presence of fixed costsThe presence of fixed costs Pure technological factorsPure technological factors Pecuniary Economies: Reduction in Pecuniary Economies: Reduction in

input prices by purchasing in input prices by purchasing in volume.volume.

Why Diseconomies of Why Diseconomies of Scale?Scale?

Managerial complexitiesManagerial complexities Pecuniary diseconomiesPecuniary diseconomies

Production with multiple Production with multiple inputs inputs

There is more than one way to do most There is more than one way to do most things. (Think of examples where this is things. (Think of examples where this is and isn’t the case.) Thus, the essential and isn’t the case.) Thus, the essential problem is how to find the optimal mix problem is how to find the optimal mix of inputs. This can be stated formally of inputs. This can be stated formally in either of two ways.in either of two ways. Minimize the cost of producing a given Minimize the cost of producing a given

quantity of outputquantity of output Maximize the output from a given level of Maximize the output from a given level of

expenditures. expenditures.

IsoquantIsoquant: various combinations of : various combinations of inputs that will produce a given level of inputs that will produce a given level of output. (equivalent to an indifference output. (equivalent to an indifference

curve)curve)Ways of Producing Q=5

Method Capital Labor

A 11 1

B 7 2

C 4 3

D 2 4

E 1 5

Marginal Rate of Technical Substitution: The Marginal Rate of Technical Substitution: The rate at which one input can be substituted for rate at which one input can be substituted for

another without any change in outputanother without any change in output

Capital Labor Capital MRTS

11 1 11

7 2 7 -4

4 3 4 -3

2 4 2 -2

1 5 1 -1

Optimal Input Mix (Price of labor = $10, Price Optimal Input Mix (Price of labor = $10, Price of Labor =$25)of Labor =$25)

Q=5

Capital Labor TC MRTS

11 1 135

7 2 120 -4

4 3 115 -3

2 4 120 -2

1 5 135 -1

What is the Marginal

Condition That Makes This

Optimal

MRTS measures the relative MRTS measures the relative productivity of the two inputs productivity of the two inputs

The ratio of their prices measures The ratio of their prices measures their relative coststheir relative costs

If an input’s relative productivity is If an input’s relative productivity is greater than its relative cost, buy greater than its relative cost, buy more of that input and less of the more of that input and less of the other other

Time and Costs: Time and Costs: Observations on Fixed CostsObservations on Fixed Costs

““Long run”, “short run” and fixed Long run”, “short run” and fixed costscosts

Long Run: Period of time sufficiently long Long Run: Period of time sufficiently long to vary all costs.to vary all costs.

Short Run: Any period less than the long Short Run: Any period less than the long run.run.

Fixed Costs: Those costs that cannot be Fixed Costs: Those costs that cannot be varied in the short run.varied in the short run.

Distinguishing fixed and Distinguishing fixed and sunk costssunk costs

Fixed costs: Costs that don’t vary with Fixed costs: Costs that don’t vary with outputoutput

an airplanean airplane Sunk costs: Costs that can’t be recoveredSunk costs: Costs that can’t be recovered

a railroad tracka railroad track

Opportunity Cost:Opportunity Cost: The total The total value of what must be given value of what must be given up to get something (which up to get something (which

is often more than the is often more than the measured monetary cost)measured monetary cost) Economic profit: Revenues-Opportunity Economic profit: Revenues-Opportunity

CostCost As distinguished from accounting cost: The As distinguished from accounting cost: The

dollars that must be given up to get dollars that must be given up to get something else. and accounting profit: something else. and accounting profit: Revenues-accounting costRevenues-accounting cost

Examples of Opportunity CostExamples of Opportunity Cost Retained earnings (was Coca Cola’s great cash Retained earnings (was Coca Cola’s great cash

flow free?)flow free?) Make vs buy (Was Valuejet really wrong to Make vs buy (Was Valuejet really wrong to

outsource maintenance?)outsource maintenance?) Time (Who gets the keys to the company jet?)Time (Who gets the keys to the company jet?)

Ideas That Matter: Relevant Ideas That Matter: Relevant Costs Costs

When do fixed costs matter? As we’ve already When do fixed costs matter? As we’ve already seen, certainly not in any decision involving seen, certainly not in any decision involving production levels, or pricing. Consider these production levels, or pricing. Consider these examplesexamples

R&D: “We’ve come too far to stop now.R&D: “We’ve come too far to stop now. Buildings: “We built in the wrong location, but we’re Buildings: “We built in the wrong location, but we’re

there nowthere now Eternal problem: Managers who are given the Eternal problem: Managers who are given the

power to make fixed investments need to be held power to make fixed investments need to be held accountable for those decisions. But how do you accountable for those decisions. But how do you get them to ignore the investment once it’s made?get them to ignore the investment once it’s made?

Ideas That Matter: Defining Ideas That Matter: Defining and measuring efficiencyand measuring efficiency

Pure Waste: not obtaining maximum Pure Waste: not obtaining maximum output from a given amount of output from a given amount of inputs inputs

Allocative Efficiency: Employing the Allocative Efficiency: Employing the wrong mix of inputs wrong mix of inputs

Caution: Is waste really waste if it Caution: Is waste really waste if it would cost more to eliminate than would cost more to eliminate than would be saved by eliminatingwould be saved by eliminating

Ideas That Matter: Ideas That Matter: Comparative Advantage Comparative Advantage

Suppose:Suppose: Attilla can produce 4 units of clean room or 2 units of clean Attilla can produce 4 units of clean room or 2 units of clean

dog per hourdog per hour Godzilla can produce 1 unit of clean room or 1 unit of Godzilla can produce 1 unit of clean room or 1 unit of

clean dog per hour.clean dog per hour. Note: Godzilla is, by one measure, less productive.Note: Godzilla is, by one measure, less productive. Can It Ever Be Efficient to Use a Less Productive Asset? Can It Ever Be Efficient to Use a Less Productive Asset?

Sure :Sure : Suppose both kids spent 1 hour on each chore (4 hours of Suppose both kids spent 1 hour on each chore (4 hours of

total work), producing 5 units of clean room and 3 units of total work), producing 5 units of clean room and 3 units of clean dog.clean dog.

They could produce the same output with less effort. Godzilla They could produce the same output with less effort. Godzilla could spend 2 hours on dog (producing 2 units of clean dog). could spend 2 hours on dog (producing 2 units of clean dog). Attilla could spend 1.25 hours on room (producing 5 units of Attilla could spend 1.25 hours on room (producing 5 units of clean room) and 0.5 hours on dog (producing 1 unit of clean clean room) and 0.5 hours on dog (producing 1 unit of clean dog). They get the same output with only 3.75 hours of labordog). They get the same output with only 3.75 hours of labor

Conclusion: The Value of Comparative AdvantageConclusion: The Value of Comparative Advantage An input is said to have a comparative advantage over An input is said to have a comparative advantage over

another input if the relative cost of producing one good is another input if the relative cost of producing one good is lower (Godzilla has a comparative advantage in the lower (Godzilla has a comparative advantage in the production of clean dog since she only has to give up one production of clean dog since she only has to give up one unit of clean room to get an extra unit of clean dog.) unit of clean room to get an extra unit of clean dog.)

As long as there is a comparative advantage, specialization As long as there is a comparative advantage, specialization increases outputincreases output

Implications of Comparative AdvantageImplications of Comparative Advantage What do “menial” workers really produce?What do “menial” workers really produce? Trade is good: the U.S. might benefit from trade with Trade is good: the U.S. might benefit from trade with

developing countries that are not as absolutely productive developing countries that are not as absolutely productive but that have a comparative advantage in the production but that have a comparative advantage in the production of some goodsof some goods

Complications:Multiple Complications:Multiple OutputsOutputs

Most production processes produce more Most production processes produce more than one outputthan one output Cars and SUV’s. Consulting services and Cars and SUV’s. Consulting services and

audits. Finance majors and marketing majorsaudits. Finance majors and marketing majors Economies of ScopeEconomies of Scope are said to exist when are said to exist when

it is less expensive to produce more than it is less expensive to produce more than one output jointly than separately.one output jointly than separately.

Why economies of scope?Why economies of scope? The most likely source of economies of The most likely source of economies of

scope is common overheadscope is common overhead

Complications: Multiple Complications: Multiple PlantsPlants

: Some firms have several plants : Some firms have several plants that produce the same output. This that produce the same output. This raises two kinds of issues.raises two kinds of issues. Why?Why?

If it is efficient to have more than If it is efficient to have more than one plant, how much output should one plant, how much output should be assigned to each plantbe assigned to each plant

Transfer PricingTransfer Pricing

Many firms use a separate division to produce some intermediate input. What Many firms use a separate division to produce some intermediate input. What “price’ should the division charge for its input.? “price’ should the division charge for its input.?

The “customer” would like to have a low price (zero is nice) but this creates The “customer” would like to have a low price (zero is nice) but this creates incentives to produce too much .incentives to produce too much .

The “seller” would like to have a high price (it is in the position of being a The “seller” would like to have a high price (it is in the position of being a monopolist with a captive customer) but this creates incentives to produce too monopolist with a captive customer) but this creates incentives to produce too littlelittle

Principle: transferring at marginal cost requires the end user to recognize the Principle: transferring at marginal cost requires the end user to recognize the true cost of the good.true cost of the good.ComplicationsComplicationsHow do you measure marginal cost (especially when the manager of the How do you measure marginal cost (especially when the manager of the intermediate division has incentives to inflate costs).intermediate division has incentives to inflate costs).What if marginal costs are below average costs meaning that the intermediate What if marginal costs are below average costs meaning that the intermediate division operates at a loss (Certainly a possibility and if so, how do you assure the division operates at a loss (Certainly a possibility and if so, how do you assure the manager of the intermediate division that its good to run a losing operation.)manager of the intermediate division that its good to run a losing operation.)What if the intermediate good can also be sold on an open marketWhat if the intermediate good can also be sold on an open marketActually a blessing since the cost of transfering the intermediate good to the final Actually a blessing since the cost of transfering the intermediate good to the final producer is really just the price at which it could be sold on the marketproducer is really just the price at which it could be sold on the marketBut this may create real hard feelings if the outside customers of the intermediate But this may create real hard feelings if the outside customers of the intermediate good compete with the final manufacturer.good compete with the final manufacturer.

ComplicationsComplications

How do you measure marginal cost (especially when the manager How do you measure marginal cost (especially when the manager of the intermediate division has incentives to inflate costs).of the intermediate division has incentives to inflate costs).

What if marginal costs are below average costs meaning that the What if marginal costs are below average costs meaning that the intermediate division operates at a loss (Certainly a possibility intermediate division operates at a loss (Certainly a possibility and if so, how do you assure the manager of the intermediate and if so, how do you assure the manager of the intermediate division that its good to run a losing operation.)division that its good to run a losing operation.)

What if the intermediate good can also be sold on an open marketWhat if the intermediate good can also be sold on an open market Actually a blessing since the cost of transfering the Actually a blessing since the cost of transfering the

intermediate good to the final producer is really just the price intermediate good to the final producer is really just the price at which it could be sold on the marketat which it could be sold on the market

But this may create real hard feelings if the outside customers of But this may create real hard feelings if the outside customers of the intermediate good compete with the final manufacturerthe intermediate good compete with the final manufacturer..