Production and Costs A simple production function is:

Q = f (K,L), where K is capital, L is labor

Here we assume K is “fixed” at K*

This creates “short run” in contrast to “long run”

Long run: all factors are variable Short run: some factors (K) are fixed,

locked in place

With fixed K*, we vary L and observe changes in output, Q

Some definitionsSome definitions Total productTotal product: total output in a given time: total output in a given time

Average productAverage product: total product (Q), : total product (Q), divided by the amount of an input (L) used divided by the amount of an input (L) used to produce it:to produce it:– It is a ratio, such as Q/LIt is a ratio, such as Q/L

Marginal productMarginal product: the change in output : the change in output (Q) as the amount of an input (L) changes:(Q) as the amount of an input (L) changes:– It is a derivative, such as dQ/dLIt is a derivative, such as dQ/dL

Diminishing marginal product:Diminishing marginal product: the decline the decline in marginal product that takes place as in marginal product that takes place as use of an input rises (a fact of nature)use of an input rises (a fact of nature)

Let’s start a simple business:pizza production per hour in pizza shop (L) (Q) (dQ/dL = MPL)Laborers Pizzas Change in pizzas APL (Q/L)

0 0 - -1 8 8 8 2 22 14 113 29 7 9.674 31 2 7.755 29 -2 5.86 20 -9 3.33

Note how labor productivity rises then falls in fixed Note how labor productivity rises then falls in fixed

production scale.production scale.

How many pizzas do you produce?

(assume sale price is $3 each) (L) (Q) (dQ/dL = MPL)(L) (Q) (dQ/dL = MPL)LaborersLaborers PizzasPizzas Change in pizzasChange in pizzas APL (Q/L)APL (Q/L) TR = TR =

PxQPxQ00 0 0 -- - -11 8 8 8 $24 8 8 8 $242 22 14 11 $662 22 14 11 $6633 29 7 9.67 $87 29 7 9.67 $874 31 2 7.754 31 2 7.75 $93 $935 29 -2 5.85 29 -2 5.8 $87 $876 20 -9 3.33 $606 20 -9 3.33 $60

New

Where TR (total revenue) equals price times quantity sold.

Components of CostsComponents of Costs

In the short run, some inputs (“capital” or K) are In the short run, some inputs (“capital” or K) are fixed—here, the size of the pizza shop is fixed.fixed—here, the size of the pizza shop is fixed.

Total cost has two components:Total cost has two components:– Fixed or unavoidable (“sunk”) costsFixed or unavoidable (“sunk”) costs– Variable or avoidable (“incremental”) costsVariable or avoidable (“incremental”) costs

Accounting “costs” are only relevant when they can Accounting “costs” are only relevant when they can be avoided, i.e., when they are be avoided, i.e., when they are economiceconomic costs costs– Fixed costs cannot be avoided; thus, fixed costs Fixed costs cannot be avoided; thus, fixed costs

are accounting notions onlyare accounting notions only– Fixed costs do not affect production decisions Fixed costs do not affect production decisions in in

the short runthe short run

CostsCosts Total costs = Fixed costs + Variable costsTotal costs = Fixed costs + Variable costs

– C = F + VC = F + V

F is a constant, independent of output and F is a constant, independent of output and unavoidable in the short rununavoidable in the short run

V depends on inputs, and thus outputs:V depends on inputs, and thus outputs:– V = (L * w) + (I * p)V = (L * w) + (I * p)– Where w is the wage rate paid per unit Where w is the wage rate paid per unit

of Lof L– Where I are ingredients and p their priceWhere I are ingredients and p their price

RememberRemember

““A sunk cost is an unrecoverable A sunk cost is an unrecoverable past expenditure. Such costs should past expenditure. Such costs should seldom be taken into account when seldom be taken into account when determining what to do in the future determining what to do in the future because … they are irrelevant to because … they are irrelevant to what can be recovered.”what can be recovered.”

Charles Koch, CEO Koch Industries,Charles Koch, CEO Koch Industries,p.33, “The Science of Success”p.33, “The Science of Success”

How many pizzas do you produce?How many pizzas do you produce?Suppose ingredients cost per pizza Suppose ingredients cost per pizza $1.$1. (L) (Q) (L) (Q) LaborersLaborers PizzasPizzas TR = PxQ – Cost of pizza TR = PxQ – Cost of pizza

supplies supplies 00 0 0 --11 8 8 $24 - $8 = $16$24 - $8 = $162 222 22 $66 - $22 = $44$66 - $22 = $4433 29 29 $87 - $29 = $58$87 - $29 = $584 314 31 $93 - $31 = $62$93 - $31 = $625 295 29 $87 - $29 = $58$87 - $29 = $586 206 20 $60 - $20 = $40$60 - $20 = $40

Pizza ingredients (tomato, etc.) are what Pizza ingredients (tomato, etc.) are what kind of costs? kind of costs?

What about labor?What about labor?

How many pizzas do you How many pizzas do you produce?produce?Suppose Labor is $6 per hour.Suppose Labor is $6 per hour. (L) (Q) (L) (Q) LaborersLaborers PizzasPizzas TR = PxQ – Cost – Labor = NetTR = PxQ – Cost – Labor = Net

00 0 0 --11 8 8 $24 - $8 = $16 - $6 = $10$24 - $8 = $16 - $6 = $102 222 22 $66 - $22 = $44 - $12 = $32$66 - $22 = $44 - $12 = $3233 29 29$87 - $29 = $58 - $18 = $40$87 - $29 = $58 - $18 = $404 314 31 $93 - $31 = $62 - $24 = $38$93 - $31 = $62 - $24 = $385 295 29 $87 - $29 = $58 - $30 = $28$87 - $29 = $58 - $30 = $286 206 20 $60 - $20 = $40 - $36 = $4$60 - $20 = $40 - $36 = $4

But what about fixed costs (building, taxes, But what about fixed costs (building, taxes,

ovens)? Does that affect our decision?ovens)? Does that affect our decision?

How many pizzas do you How many pizzas do you produce?produce?Suppose Labor is $20 per hour.Suppose Labor is $20 per hour. (L) (Q) (L) (Q) LaborersLaborers PizzasPizzas TR = PxQ – Cost – Labor = NetTR = PxQ – Cost – Labor = Net

00 0 0 --11 8 8 $24 - $8 = $16 - $20 = $-4$24 - $8 = $16 - $20 = $-42 222 22 $66 - $22 = $44 - $40 = $4$66 - $22 = $44 - $40 = $433 29 29$87 - $29 = $58 - $60 = $-2$87 - $29 = $58 - $60 = $-24 314 31 $93 - $31 = $62 - $80 = $-18$93 - $31 = $62 - $80 = $-185 295 29 $87 - $29 = $58 - $100 = $-42$87 - $29 = $58 - $100 = $-426 206 20 $60 - $20 = $40 - $120 = $-80$60 - $20 = $40 - $120 = $-80

But what about fixed costs (building, etc.)?But what about fixed costs (building, etc.)?

Production and Costs:Production and Costs:The Long RunThe Long Run

The long runThe long run– A period of time (or set of contracts) sufficient to A period of time (or set of contracts) sufficient to

permit all inputs to be variable; all costs are permit all inputs to be variable; all costs are avoidableavoidable

– There is no distinction between “types” of costs There is no distinction between “types” of costs (fixed or variable); (fixed or variable); all costs are variable in the all costs are variable in the long runlong run

FormallyFormally– C = (K*r) + (L*w) + (I*p)C = (K*r) + (L*w) + (I*p)– Objective: choose a set of inputs (K,L,I) that Objective: choose a set of inputs (K,L,I) that

minimizes total costs at each rate of outputminimizes total costs at each rate of output– Although the algebra is tedious, the basic Although the algebra is tedious, the basic

geometry is quite simplegeometry is quite simple

Cost Curves in the Long Cost Curves in the Long RunRunMC goes through minimum of ATC. Now MC goes through minimum of ATC. Now ALLALL costs costs

are variable. Is Q where we should produce?are variable. Is Q where we should produce?

Output

Average andMarginal Costs

MC

ATC

Q

Economics of scaleEconomics of scaleThe behavior of The behavior of averageaverage costs as output costs as output variesvaries

For Q < Q m, AC is falling: “Increasing returns to scale”For Q < Q m, AC is falling: “Increasing returns to scale”For Q > Q m, AC is rising: “Decreasing returns to scale”For Q > Q m, AC is rising: “Decreasing returns to scale”At Q = Q m, AC is constant: “Constant returns to scale”At Q = Q m, AC is constant: “Constant returns to scale”

Average andMarginal Costs

Output (Q)Q m

MC

ATC

0

Scale Economy Scale Economy ExampleExample Study of hospitals in the U.S. found Study of hospitals in the U.S. found

that per unit cost of providing hospital that per unit cost of providing hospital services was minimized at 250 beds. services was minimized at 250 beds. Hospitals with only 50 beds have Hospitals with only 50 beds have costs 20-30% higher per bed service.costs 20-30% higher per bed service.

That is, AC drops and drops until Q is That is, AC drops and drops until Q is about 250 beds. Then is stable but about 250 beds. Then is stable but begins to rise again eventually.begins to rise again eventually.

What Is Best Level of What Is Best Level of Output?Output?

If our output sells at price P* we will keep producing units (Q) If our output sells at price P* we will keep producing units (Q) so long as we cover the cost of producing added units. so long as we cover the cost of producing added units. Difference between MC and ATC is profit for those units.Difference between MC and ATC is profit for those units.

Price/Costs

Output (Q)

MC

ATC

0

P*

Q*

AC*

Profits per unit

An Example: Making Olive Oil (short An Example: Making Olive Oil (short run)run)

Marcello owns (or rents) the olive trees; he hires migrant Marcello owns (or rents) the olive trees; he hires migrant workers at $4 per hour to pick olives and press oil.workers at $4 per hour to pick olives and press oil.

Labor Input (hours)Labor Input (hours) Olive Oil Output (gallons)Olive Oil Output (gallons)100100 30 30200200 100 100300300 200 200400400 350 350500500 800 800600600 12001200700700 14001400800800 15751575900900 17001700 10001000 18001800 11001100 18501850

Production and Cost of Production and Cost of Olive OilOlive Oil

Calculate total labor cost at various levels of Calculate total labor cost at various levels of output.output.

Calculate average cost per gallon.Calculate average cost per gallon. Calculate marginal cost per gallon —Calculate marginal cost per gallon —

since data are not gallon by gallon, calculate it since data are not gallon by gallon, calculate it based on the jumps from one level to the next.based on the jumps from one level to the next.

Then, draw the cost curves: total on one Then, draw the cost curves: total on one diagram, average and marginal on another.diagram, average and marginal on another.

Cost Measures Cost Measures [Output in [Output in gallons. Input in hours of labor.]gallons. Input in hours of labor.]

Input Output Input Output TCTC __ __ AC AC MC MC100100 30 30 $ $ 400400 $13.33$13.33 $13.33$13.33200200 100 100 800800 8.00 8.00 5.71 5.71300300 200 200 12001200 6.00 6.00 4.00 4.00400400 350 350 16001600 4.57 4.57 2.67 2.67500500 800 800 20002000 2.50 2.50 0.89 0.89600600 12001200 24002400 2.00 2.00 1.00 1.00700700 14001400 28002800 2.00 2.00 2.00 2.00800800 15751575 32003200 2.03 2.03 2.28 2.28900900 17001700 36003600 2.12 2.12 3.20 3.2010001000 18001800 40004000 2.22 2.22 4.00 4.0011001100 18501850 44004400 2.37 2.37 8.00 8.00

Draw the cost curves (approximately)Draw the cost curves (approximately)

Cost curvesCost curves

$ TotalCost

Total, Average and Marginal Costs. Is point of lowest Total, Average and Marginal Costs. Is point of lowest average cost where we should produce?average cost where we should produce?

OutputLowestAverageCost

$/gallon

Output

MCAC

LowestAverageCost

$2

QuestionsQuestions

Suppose the market price of olive oil is Suppose the market price of olive oil is $2.30 per gallon. How much oil does $2.30 per gallon. How much oil does Marcello produce to maximize profits? Marcello produce to maximize profits?

Does he make a profit?Does he make a profit?

Answer Answer Remember the Golden Remember the Golden RuleRule

MR = MCMR = MC Produce where MR ($2.30) equals MC. Produce where MR ($2.30) equals MC.

The golden rule! MR = MCThe golden rule! MR = MCThat would be 1575 gallons, where MC is $2.28 That would be 1575 gallons, where MC is $2.28

per gallon. If he increased production to 1700 per gallon. If he increased production to 1700 gallons by hiring another 100 hours of labor, his gallons by hiring another 100 hours of labor, his MC would rise to $3.20 for the additional MC would rise to $3.20 for the additional gallons. 1575 gallons at $2.30 equals $3622 gallons. 1575 gallons at $2.30 equals $3622 revenue minus cost of $3200 for a profit of revenue minus cost of $3200 for a profit of $422. $422.

But—is that really his profit?But—is that really his profit?

Fixed Cost QuestionFixed Cost Question

In the 1920s there were British ships that burned coal for power. Not as efficient as newer oil burning ships. Their owners made enough money carrying cargo to pay variable costs—labor, fuel, etc.—but not enough revenue to cover all repayment costs (interest and principal) on the ships.

Was it foolish to continue to use the ships? What should the banks do about the loans?