the firm’s production and selling decisions

4

The Firm’s Production and Selling Decisions

Copyright© 2006 South-Western/Thomson Learning. All rights reserved.

● Production and Input Choice, with One Variable Input

● Multiple Input Decisions: The Choice of Optimal Input Combinations

● Cost and Its Dependence on Output

● Economies of Scale

● Production and Input Choice, with One Variable Input

● Multiple Input Decisions: The Choice of Optimal Input Combinations

● Cost and Its Dependence on Output

● Economies of Scale

OutlineOutline


● Price and Quantity: One Decision, Not Two

● Total Profit: Keep your Eye on the Goal

● Marginal Analysis and Maximization of Total Profit

● Generalization: The Logic of Marginal Analysis and Maximization

● Price and Quantity: One Decision, Not Two

● Total Profit: Keep your Eye on the Goal

● Marginal Analysis and Maximization of Total Profit

● Generalization: The Logic of Marginal Analysis and Maximization

OutlineOutline


Production and Input Choice, with 1 Variable InputProduction and Input Choice, with 1 Variable Input

● Arkansas chicken farmer named Florence, who owns a small poultry business. ♦ She knows Q corn she feeds her chickens will impact

Q meat. ♦ She could also buy more T, growth hormones, and L

to ↑Q meat. But for now, let’s focus on the relationship between poultry meat and corn.

● Arkansas chicken farmer named Florence, who owns a small poultry business. ♦ She knows Q corn she feeds her chickens will impact

Q meat. ♦ She could also buy more T, growth hormones, and L

to ↑Q meat. But for now, let’s focus on the relationship between poultry meat and corn.

TABLE 1. TPP, MPP, and APP for Flo’s Chicken Farm

TABLE 1. TPP, MPP, and APP for Flo’s Chicken Farm

Corn in bags TPP in lbs. MPP in lbs. APP in lbs.

0 0.0 ----- -----

1 14.0 14.0 14.0

2 36.0 22.0 18.0

3 66.0 30.0 22.0

4 100.0 34.0 25.0

5 130.0 30.0 26.0

6 156.0 26.0 26.0

7 175.0 19.0 25.0

8 184.0 9.0 23.0

9 185.4 1.4 20.6

10 180.0 -5.4 18.0

11 165.0 -15.0 15.0

12 144.0 -21.0 12.0

FIGURE 1. TPP with Different Quantities of Corn

FIGURE 1. TPP with Different Quantities of Corn

Total Physical Product (TPP) in lbs.

01

2

3

4

5

67

8 9 1011

12

020406080

100120140160180200

0 2 4 6 8 10 12 14

Quantity of Corn (bags per week)

To

tal O

utp

ut

of

Po

ult

ry M

ea

t



● Total Physical Product (TPP) = amount of output that can be produced as 1 input changes, with all other inputs held constant.♦ Table 1 shows TPP or how much chicken Flo can

produce with different Q corn, holding all other inputs fixed.

♦ If Q corn = 0 → Q meat = 0. Each add. bag of corn yields more poultry. 4 bags → 100 lbs. After 9 bags, ↑corn → ↓output –chickens are so overfed they become ill.

● Total Physical Product (TPP) = amount of output that can be produced as 1 input changes, with all other inputs held constant.♦ Table 1 shows TPP or how much chicken Flo can

produce with different Q corn, holding all other inputs fixed.

♦ If Q corn = 0 → Q meat = 0. Each add. bag of corn yields more poultry. 4 bags → 100 lbs. After 9 bags, ↑corn → ↓output –chickens are so overfed they become ill.



● Average Physical Product (APP) = TPP/(Q of input) = measures output per unit of input. ♦ E.g., 4 bags corn → 100 lbs meat, so APP = 25.

● Marginal Physical Product (MPP) = additional output resulting from a 1 unit increase in the

input, holding all other inputs constant. ♦ E.g., ↑corn from 4 to 5 bags, the 5th bag yields an

add. 30 lbs of meat.

● Average Physical Product (APP) = TPP/(Q of input) = measures output per unit of input. ♦ E.g., 4 bags corn → 100 lbs meat, so APP = 25.

● Marginal Physical Product (MPP) = additional output resulting from a 1 unit increase in the

input, holding all other inputs constant. ♦ E.g., ↑corn from 4 to 5 bags, the 5th bag yields an

add. 30 lbs of meat.

FIGURE 2. Flo’s MPP Curve FIGURE 2. Flo’s MPP Curve

MPP

Bags of corn

00

9

14

34

4 120

-21

NegativeFallingRising

MPP


Graph of MPPGraph of MPP

● Marginal returns to an input typically rise and then fall.

● Area of ↑MPP (1 to 4 bags) → each add. bag of corn adds more to TPP than previous bag. ↑TPP rapidly.

● Area of ↓MPP (between 4 and 9 bags) → each add. bag of corn adds less to TPP than previous bag. ↑TPP at a dim. rate.

● Area of (-)MPP (beyond 9 bags) → each add. bag of corn reduces TPP by more than previous bag. ↓TPP.

● Marginal returns to an input typically rise and then fall.

● Area of ↑MPP (1 to 4 bags) → each add. bag of corn adds more to TPP than previous bag. ↑TPP rapidly.

● Area of ↓MPP (between 4 and 9 bags) → each add. bag of corn adds less to TPP than previous bag. ↑TPP at a dim. rate.

● Area of (-)MPP (beyond 9 bags) → each add. bag of corn reduces TPP by more than previous bag. ↓TPP.


● ↑ Q of any one input, holding Q of all other inputs constant, leads to lower marginal returns to the expanding input.♦ E.g., Flo feeds chickens more and more, without

giving them extra water, cleaning up after them more, or buying add. chickens. Eventually overfed and become sick.

● Law of dim. marginal returns should hold for most activities.

Can you think of one?

● ↑ Q of any one input, holding Q of all other inputs constant, leads to lower marginal returns to the expanding input.♦ E.g., Flo feeds chickens more and more, without

giving them extra water, cleaning up after them more, or buying add. chickens. Eventually overfed and become sick.

● Law of dim. marginal returns should hold for most activities.

Can you think of one?

The “Law” of Diminishing Marginal Returns The “Law” of Diminishing Marginal Returns


Optimal Purchase Rule for a Single InputOptimal Purchase Rule for a Single Input

● How does a firm decide on the quantity of an input?♦ Assume P corn = $10/40-lb bag and P chicken = $0.75/lb.

Consider purchasing just 1 bag of corn. Does this max profits?● 1 bag produces 14 lbs of chicken.

TR: $0.75 x 14 = $10.50TC: $10 x 1 = $10.00Profit: = $0.50

● Shouldn't stop at 1 bag because 2 bags yield more profit.TR: $0.75 x 36 = $27.00TC: $10 x 2 = $20.00Profit: = $7.00

● How does a firm decide on the quantity of an input?♦ Assume P corn = $10/40-lb bag and P chicken = $0.75/lb.

Consider purchasing just 1 bag of corn. Does this max profits?● 1 bag produces 14 lbs of chicken.

TR: $0.75 x 14 = $10.50TC: $10 x 1 = $10.00Profit: = $0.50

● Shouldn't stop at 1 bag because 2 bags yield more profit.TR: $0.75 x 36 = $27.00TC: $10 x 2 = $20.00Profit: = $7.00



● Easier way to proceed. Until 9 bags, each add. bag of corn ↑Q chicken. So each bag (1-9) raises TR, but also costs $10. To max profit, Flo should compare revenue that each bag generates against the cost of each bag.

● Marginal Revenue Product (MRP) = MPP x Price of output.

● MRP = add. revenue generated from ↑input by 1 unit.

● Easier way to proceed. Until 9 bags, each add. bag of corn ↑Q chicken. So each bag (1-9) raises TR, but also costs $10. To max profit, Flo should compare revenue that each bag generates against the cost of each bag.

● Marginal Revenue Product (MRP) = MPP x Price of output.

● MRP = add. revenue generated from ↑input by 1 unit.

Bags ofCorn

TPP MPP TR(P*TPP)

MRP(P*MPP)

P corn Profit

0 0.0 ----- $0.00 ----- $10.00 $0.00

1 14.0 14.0 10.50 $10.50 10.00 0.50

2 36.0 22.0 27.00 16.50 10.00 7.00

3 66.0 30.0 49.50 22.50 10.00 19.50

4 100.0 34.0 75.00 25.50 10.00 35.00

5 130.0 30.0 97.50 22.50 10.00 47.50

6 156.0 26.0 117.00 19.50 10.00 57.00

7 175.0 19.0 131.25 14.25 10.00 61.25

8 184.0 9.0 138.00 6.75 10.00 58.00

9 185.4 1.4 139.05 1.05 10.00 49.05

10 180.0 -5.4 135.00 -4.05 10.00 35.00

11 165.0 -15.0 123.75 -11.25 10.00 13.75

12 144.0 -21.0 108.00 -15.75 10.00 -12.00

Table 2. Flo’s TPP, MPP, and MRP Schedules



● Rule: If MRP > P of an input → use more of the input. If MRP < P of an input → use less of the input.

● Purchase an input where MRP = P of the input.♦ E.g., Flo should purchase 7 bags of corn.

Can you explain why she should not buy the 8th bag?

● Note: ↓MPP (bag 4 to 9) → ↓MRP. At 7 bags, Flo is producing where dim. MPP sets in. Flo should stop ↑corn purchases when MRP falls to = P of corn.

● Rule: If MRP > P of an input → use more of the input. If MRP < P of an input → use less of the input.

● Purchase an input where MRP = P of the input.♦ E.g., Flo should purchase 7 bags of corn.

Can you explain why she should not buy the 8th bag?

● Note: ↓MPP (bag 4 to 9) → ↓MRP. At 7 bags, Flo is producing where dim. MPP sets in. Flo should stop ↑corn purchases when MRP falls to = P of corn.


Multiple Input DecisionsMultiple Input Decisions

● Firms seek the method of production that is least costly.♦ Consider the choice between L and K in prod.

Compared with Mexico, in U.S., L is expensive and K is cheap. So (K/L) U.S. > (K/L) Mexico

● One input can often be substituted for another in production. ♦ E.g., shoes produced in Mexico are manufactured

using more L and less K than shoes in U.S.

● Firms seek the method of production that is least costly.♦ Consider the choice between L and K in prod.

Compared with Mexico, in U.S., L is expensive and K is cheap. So (K/L) U.S. > (K/L) Mexico

● One input can often be substituted for another in production. ♦ E.g., shoes produced in Mexico are manufactured

using more L and less K than shoes in U.S.


Multiple Input DecisionsMultiple Input Decisions

● A firm can produce same amount of a good with less of one input (say L) as long as it’s willing to use more of another input (like K).

● Actual combos of inputs (such as K and L) depend on relative P of inputs. Firms strive to produce a good using the least expensive method.

● A firm can produce same amount of a good with less of one input (say L) as long as it’s willing to use more of another input (like K).

● Actual combos of inputs (such as K and L) depend on relative P of inputs. Firms strive to produce a good using the least expensive method.


Marginal Rule for Optimal Input ProportionsMarginal Rule for Optimal Input Proportions

● E.g., Flo can feed chickens soymeal or cornmeal –they are substitutes in production. ♦ Not perfect substitutes. Soymeal has more protein but

fewer carbohydrates than corn. ♦ Best to feed some combo of 2 meals. ↓Q poultry if Flo

relies too much on 1 input. There are dim. returns to substitution among the inputs.

● E.g., Flo can feed chickens soymeal or cornmeal –they are substitutes in production. ♦ Not perfect substitutes. Soymeal has more protein but

fewer carbohydrates than corn. ♦ Best to feed some combo of 2 meals. ↓Q poultry if Flo

relies too much on 1 input. There are dim. returns to substitution among the inputs.



How much of each input should Flo purchase?● Feed ↑corn and ↓soy. Soy costs twice as much, but yields only

67% more meat.

● If Flo ↓soy by 1 bag → saves $20. But ↓output by 50 lbs. So buy 1.67 (or 50/30) bags of corn to make up for ↓output, cost = $16.70. She saves $3.30 while holding Q output fixed.

How much of each input should Flo purchase?● Feed ↑corn and ↓soy. Soy costs twice as much, but yields only

67% more meat.

● If Flo ↓soy by 1 bag → saves $20. But ↓output by 50 lbs. So buy 1.67 (or 50/30) bags of corn to make up for ↓output, cost = $16.70. She saves $3.30 while holding Q output fixed.

Price corn = $10 per 40 lb. bag MPP bag corn = 30 lbs. meat

Price soy = $20 per 40 lb. bag MPP bag soy = 50 lbs. meat



● Above: MPPsoy/Psoy < MPPcorn/Pcorn

i.e., 50/$20 < 30/$10♦ Soy yields 2.5 lbs. meat per $1 while corn yields 3 lbs. per $1.

More output from corn rather than soy at the margin.

● MPP of an input/P of an input = add. output from spending $1 on the input.

● By substituting input with lower output per $1 for input with higher output per $1; firm can reduce costs while holding Q output fixed.

● Above: MPPsoy/Psoy < MPPcorn/Pcorn

i.e., 50/$20 < 30/$10♦ Soy yields 2.5 lbs. meat per $1 while corn yields 3 lbs. per $1.

More output from corn rather than soy at the margin.

● MPP of an input/P of an input = add. output from spending $1 on the input.

● By substituting input with lower output per $1 for input with higher output per $1; firm can reduce costs while holding Q output fixed.



● Rule: if MPPb/Pb > MPPa/Pa → spend less on input a and more on input b.♦ Optimally, MPPa/Pa = MPPb/Pb

● Above: MPPcorn/Pcorn > MPPsoy/Psoy

♦ These ratios will equalize at an optimum because of dim. MPP. As Flo uses ↑corn and ↓soy → ↓MPP corn and ↑MPP soy, until two ratios are equal.

● Rule: if MPPb/Pb > MPPa/Pa → spend less on input a and more on input b.♦ Optimally, MPPa/Pa = MPPb/Pb

● Above: MPPcorn/Pcorn > MPPsoy/Psoy

♦ These ratios will equalize at an optimum because of dim. MPP. As Flo uses ↑corn and ↓soy → ↓MPP corn and ↑MPP soy, until two ratios are equal.



● Changes in Input Prices and Input Proportions:● Optimally, MPPcorn/Pcorn = MPPsoy/Psoy

● What if ↑P corn? ♦ Then ↑MPP corn to match ↑P corn. How? Flo will use ↓corn

and ↑soy until ratios are equal.

● As ↑P input → firms switch to cheaper inputs.

● Changes in Input Prices and Input Proportions:● Optimally, MPPcorn/Pcorn = MPPsoy/Psoy

● What if ↑P corn? ♦ Then ↑MPP corn to match ↑P corn. How? Flo will use ↓corn

and ↑soy until ratios are equal.

● As ↑P input → firms switch to cheaper inputs.


● 3 different cost curves –Total Cost (TC), Average Cost (AC), and Marginal Cost (MC).

● Flo’s costs depend on Q of inputs and on P of those inputs.

● To calculate costs, assume:♦ P corn is beyond Flo's control.♦ Q of all other inputs (except corn) are fixed.♦ P corn = $10 per 40 lb. bag

● 3 different cost curves –Total Cost (TC), Average Cost (AC), and Marginal Cost (MC).

● Flo’s costs depend on Q of inputs and on P of those inputs.

● To calculate costs, assume:♦ P corn is beyond Flo's control.♦ Q of all other inputs (except corn) are fixed.♦ P corn = $10 per 40 lb. bag

Cost Curves and Input QuantitiesCost Curves and Input Quantities

TABLE 3. TPP, TC, and AC for Flo’s Chicken Farm

TABLE 3. TPP, TC, and AC for Flo’s Chicken FarmTPP of chicken(lbs. per week)

Corn input(bags per week)

Total Cost(per week)

Average Cost(TC/Q output)

0 0 0 0.00

14 1 10 0.71

36 2 20 0.56

66 3 30 0.45

100 4 40 0.40

130 5 50 0.38

156 6 60 0.38

175 7 70 0.40

184 8 80 0.43

185.4 9 90 0.49


Cost Curves and Input QuantitiesCost Curves and Input Quantities

● TPP → Q output firm can produce given Q inputs. Q inputs and P inputs → firm can determine TC of producing any Q output.

● TC = P inputs x Q inputs● AC = TC/Q output

♦ E.g., TC 100 lbs = $40 → AC = $40/100 = $0.40● MC = TC when output increases by 1 unit

♦ E.g., if TC 100 lbs. = $40.00 TC 99 lbs. = $39.70

MC 100th lb. = $0.30♦ Note: table above doesn’t show this because ↑output > 1.

● TPP → Q output firm can produce given Q inputs. Q inputs and P inputs → firm can determine TC of producing any Q output.

● TC = P inputs x Q inputs● AC = TC/Q output

♦ E.g., TC 100 lbs = $40 → AC = $40/100 = $0.40● MC = TC when output increases by 1 unit

♦ E.g., if TC 100 lbs. = $40.00 TC 99 lbs. = $39.70

MC 100th lb. = $0.30♦ Note: table above doesn’t show this because ↑output > 1.

FIGURE 3. Flo’s Total Cost CurveFIGURE 3. Flo’s Total Cost Curve

Total Cost

0102030405060708090

100

0 50 100 150 200

Quantity of Chicken (lbs / week)

To

tal C

os

t ($

/ w

ee

k)

Total Cost

0102030405060708090

100

0 50 100 150 200

Quantity of Chicken (lbs / week)

To

tal C

os

t ($

/ w

ee

k)

FIGURE 4. Flo’s Average Cost and Marginal Cost Curves

FIGURE 4. Flo’s Average Cost and Marginal Cost Curves

0

AC and MC

Q of chicken

MC

AC

AC and MC typically ↓ and then ↑ as the ↑output level.


● TC, AC, and MC can be divided into 2 parts –fixed costs and variable costs.

● Fixed cost is the cost of an input whose Q does not ↑ when ↑output. Input that the firm requires to produce any output. Any other cost is a variable cost.♦ E.g., takes at least 1 taxi to run a cab co. and its cost is the

same whether 1 or 60 people ride in it. But gas use rises as more people ride. Taxi is a fixed cost and gas is a variable cost.

What are the fixed and variable costs where you work?

● TC, AC, and MC can be divided into 2 parts –fixed costs and variable costs.

● Fixed cost is the cost of an input whose Q does not ↑ when ↑output. Input that the firm requires to produce any output. Any other cost is a variable cost.♦ E.g., takes at least 1 taxi to run a cab co. and its cost is the

same whether 1 or 60 people ride in it. But gas use rises as more people ride. Taxi is a fixed cost and gas is a variable cost.

What are the fixed and variable costs where you work?

Fixed and Variable CostsFixed and Variable Costs


● TC = TVC + TFC

● AC = AVC + AFC♦ AC = TC/Q output♦ AVC = TVC/Q output♦ AFC = TFC/Q output

● TC = TVC + TFC

● AC = AVC + AFC♦ AC = TC/Q output♦ AVC = TVC/Q output♦ AFC = TFC/Q output

Fixed and Variable CostsFixed and Variable Costs

Table 4. Flo’s Total and Average Fixed Costs

Table 4. Flo’s Total and Average Fixed Costs

Output (20 lb pack)

TFC$ / week

AFC$ / week

0 5.0 ---

1 5.0 5.00

2 5.0 2.50

3 5.0 1.70

4 5.0 1.25

5 5.0 1.00

6 5.0 0.80

7 5.0 0.70

8 5.0 0.60

Flo pays rent of $5 per week for her chicken coop.

FIGURE 5. Graph of Flo’s Total Fixed CostFIGURE 5. Graph of Flo’s Total Fixed Cost

TFC

Q (20 lb. packages)

TFC$5

0 6 8 10

FIGURE 6. Graph of Flo’s Average Fixed CostFIGURE 6. Graph of Flo’s Average Fixed Cost

AFC

Q (20 lb. packages)

AFC

0 1

$5.00

4

$1.25

7

$0.70

If Flo produces 1 package, TFC is carried by 1. But if she produces 4, TFC gets divided between 4 packages. So

↓AFC as ↑output.

FIGURE 7. Flo’s Total Variable Cost CurveFIGURE 7. Flo’s Total Variable Cost Curve

TVC

Q

TVC

$125

0

$57

6 10

TVC has same shape as TC because ↑variable costs as ↑output.


● Marginal Cost = Marginal Variable Cost (MVC)

Why doesn't MC have a fixed component (i.e., MC = MVC + MFC)?

● Marginal Cost = Marginal Variable Cost (MVC)

Why doesn't MC have a fixed component (i.e., MC = MVC + MFC)?

Fixed and Variable Costs Fixed and Variable Costs


● AC is generally U shaped –it initially declines and eventually rises with the level of output.

● AC declines for 2 reasons:1. Changing input proportions: at first, Flo feeds

chickens more corn while holding all other inputs constant. Output rises rapidly when ↑MPP corn, which tends to ↓AC.

2. ↓Average fixed costs as ↑output.

● AC is generally U shaped –it initially declines and eventually rises with the level of output.

● AC declines for 2 reasons:1. Changing input proportions: at first, Flo feeds

chickens more corn while holding all other inputs constant. Output rises rapidly when ↑MPP corn, which tends to ↓AC.

2. ↓Average fixed costs as ↑output.

Shape of the Average Cost CurveShape of the Average Cost Curve


● AC eventually rises for 2 reasons:1. Dim MPP: ↑output more slowly as ↓MPP corn,

which tends to ↑AC.2. Bureaucratic mess: as firms grow in size they lose

personal touch of management and become increasingly bureaucratic, which drives up costs.

● Point where ↑AC varies by industry. AC in auto industry begins ↑ after more units of output than farming. Huge K investment → AFC↓ dramatically.

● AC eventually rises for 2 reasons:1. Dim MPP: ↑output more slowly as ↓MPP corn,

which tends to ↑AC.2. Bureaucratic mess: as firms grow in size they lose

personal touch of management and become increasingly bureaucratic, which drives up costs.

● Point where ↑AC varies by industry. AC in auto industry begins ↑ after more units of output than farming. Huge K investment → AFC↓ dramatically.

Shape of the Average Cost CurveShape of the Average Cost Curve


Short-run versus Long-run CostsShort-run versus Long-run Costs

● Cost of changing a firm's output level depends on period of time under consideration. Many input choices are precommitted by past decisions.

● Sunk cost = a cost to which a firm is precommitted for some limited period of time. ♦ E.g., a 2-year-old machine with a 9-year economic life is a

variable cost after 7 years because the machine would have to be replaced anyway.

● Cost of changing a firm's output level depends on period of time under consideration. Many input choices are precommitted by past decisions.

● Sunk cost = a cost to which a firm is precommitted for some limited period of time. ♦ E.g., a 2-year-old machine with a 9-year economic life is a

variable cost after 7 years because the machine would have to be replaced anyway.



● SR = period of time when some of the firm's cost commitments end.

● LR = period of time when all of the firm's cost commitments end.

● There are no fixed costs in LR –all costs are variable.♦ E.g., if # of workers can be altered daily, and # of machines

altered yearly, and size of plant every 10 years. Then 10 years is the LR.

● SR = period of time when some of the firm's cost commitments end.

● LR = period of time when all of the firm's cost commitments end.

● There are no fixed costs in LR –all costs are variable.♦ E.g., if # of workers can be altered daily, and # of machines

altered yearly, and size of plant every 10 years. Then 10 years is the LR.



● Size of a firm may be fixed in SR because it has purchased or leased a particular plant, but firm can alter size of its plant in LR.♦ E.g., Flo has already built a chicken coop, which

restricts her ability to ∆ output level in SR. In LR, Flo can build a new larger coop to produce more.

● Size of a firm may be fixed in SR because it has purchased or leased a particular plant, but firm can alter size of its plant in LR.♦ E.g., Flo has already built a chicken coop, which

restricts her ability to ∆ output level in SR. In LR, Flo can build a new larger coop to produce more.


● LR AC curve differs from SR AC curve because all inputs are variable in LR.♦ E.g., In SR, Flo can only chose how many chickens to

squeeze into coop. In LR, she can chose among different coop sizes.

● LR AC curve differs from SR AC curve because all inputs are variable in LR.♦ E.g., In SR, Flo can only chose how many chickens to

squeeze into coop. In LR, she can chose among different coop sizes.

Average Cost Curve in the Short and Long RunAverage Cost Curve in the Short and Long Run

FIGURE 8. Flo’s SR and LR Average Cost Curves

FIGURE 8. Flo’s SR and LR Average Cost Curves

S$16

AC (per package)

Q (20 lb. packages)40 100

G

BL

VUT

$12

$9


Average Cost Curve in the Short and Long RunAverage Cost Curve in the Short and Long Run

● If Flo expects to sell 40 → she buys a small coop with AC of SL. If Q = 40 → AC = $12 (pt U).

● She is surprised by strong D and can sell 100 with AC = $12 (pt V).

● Now she needs a bigger coop with AC of BG with its lower AC of $9 for Q = 100.

● In SR, Flo is stuck with AC of SL. In LR, she can replace coop and the relevant AC is STG.

● LR AC curve shows the lowest possible SR AC for each output level.

● If Flo expects to sell 40 → she buys a small coop with AC of SL. If Q = 40 → AC = $12 (pt U).

● She is surprised by strong D and can sell 100 with AC = $12 (pt V).

● Now she needs a bigger coop with AC of BG with its lower AC of $9 for Q = 100.

● In SR, Flo is stuck with AC of SL. In LR, she can replace coop and the relevant AC is STG.

● LR AC curve shows the lowest possible SR AC for each output level.


Economies of ScaleEconomies of Scale

● Returns to scale indicates how the output level changes when all the firm's inputs are doubled.

1. Increasing Returns to Scale (IRTS): Q output more than doubles.● IRTS gives a cost advantage to larger firms. Found in

industries like telecommunications, electricity, automobiles, and aircraft.

2. Constant Returns to Scale (CRTS): Q output doubles.3. Decreasing Returns to Scale (DRTS): Q output less than

doubles. ● Gives a cost advantage to smaller firms. Most U.S. industries

have DRTS.

● Returns to scale indicates how the output level changes when all the firm's inputs are doubled.

1. Increasing Returns to Scale (IRTS): Q output more than doubles.● IRTS gives a cost advantage to larger firms. Found in

industries like telecommunications, electricity, automobiles, and aircraft.

2. Constant Returns to Scale (CRTS): Q output doubles.3. Decreasing Returns to Scale (DRTS): Q output less than

doubles. ● Gives a cost advantage to smaller firms. Most U.S. industries

have DRTS.



● Returns to scale impacts the shape of the AC curve.

● AC = TC/Q output = (P input x Q input)/Q output♦ E.g., if Q inputs doubles and Q output doubles, then

AC is constant.

● Returns to scale impacts the shape of the AC curve.

● AC = TC/Q output = (P input x Q input)/Q output♦ E.g., if Q inputs doubles and Q output doubles, then

AC is constant.

FIGURE 9. 3 Possible Shapes for the AC CurveFIGURE 9. 3 Possible Shapes for the AC Curve

Lo

ng

-Ru

n A

ve

rag

e C

os

t

(c) Quantity of Output

Decreasing returns to scale

Lo

ng

-Ru

n A

ve

rag

e C

os

t

(b) Quantity of Output

Constant returns to scale

Lo

ng

-Ru

n A

ve

rag

e C

os

t

(a) Quantity of Output

Increasing returns to scale

AC

AC

AC



● Law of dim. marginal returns and IRTS may seem contradictory, but they are unrelated.

● Dim. marginal returns refers to increasing a single input. Returns to scale refers to a doubling of all inputs.

● A firm with dim. returns to a single input could have IRTS, CRTS, or DRTS.

● Law of dim. marginal returns and IRTS may seem contradictory, but they are unrelated.

● Dim. marginal returns refers to increasing a single input. Returns to scale refers to a doubling of all inputs.

● A firm with dim. returns to a single input could have IRTS, CRTS, or DRTS.


Price and Quantity: One Decision, Not TwoPrice and Quantity: One Decision, Not Two

● Critical decision -when Apple decides how many ipods to produce and P it will charge.

● P affects how consumers respond and Q affects K and L costs.

● When firms chose P and Q to max profits → they can pick only one –P or Q.♦ Chose P → customers decide Q

♦ Chose Q → market determines P at which this Q can be sold

● Critical decision -when Apple decides how many ipods to produce and P it will charge.

● P affects how consumers respond and Q affects K and L costs.

● When firms chose P and Q to max profits → they can pick only one –P or Q.♦ Chose P → customers decide Q

♦ Chose Q → market determines P at which this Q can be sold

FIGURE 10. Demand Curve for Flo’s Poultry Meat

FIGURE 10. Demand Curve for Flo’s Poultry Meat

D

Quantity of Chicken (20 lb-packages per week)

Pric

e pe

r pa

ckag

e A

1

$19

B

9

$11

Flo faces a local D curve.

If she picks P = $19 → Qd = 1.

If she picks Q = 9 → P = $11 to find required # of customers.


Price and Quantity: One Decision, Not TwoPrice and Quantity: One Decision, Not Two

● Each pt on D curve corresponds to a (P,Q) pair. A firm can pick 1 pair, but it can never pick P from 1 pt on D and a different Q from another pt on D.

● Economists assume that firms pick (P,Q) pair that maximizes profits.

● Each pt on D curve corresponds to a (P,Q) pair. A firm can pick 1 pair, but it can never pick P from 1 pt on D and a different Q from another pt on D.

● Economists assume that firms pick (P,Q) pair that maximizes profits.


Total Profit: Keep Your Eye on the GoalTotal Profit: Keep Your Eye on the Goal

● Total profit (or economic profit) = TR – TC (including opportunity cost)♦ Opportunity costs include any K or L supplied by the firm’s

owners.

● Economic profit = Accounting profit – opportunity cost.♦ E.g., if a talented attorney, gives up her salary of $120,000 to

start her own law firm and earns $150,000 after paying for all operating costs → accounting profit = $150,000 but economic profit = $30,000

♦ E.g., if you start a business and earn 6% on money you invested but could have earned 4% in T-Bills → economic profit = 2%.

● Total profit (or economic profit) = TR – TC (including opportunity cost)♦ Opportunity costs include any K or L supplied by the firm’s

owners.

● Economic profit = Accounting profit – opportunity cost.♦ E.g., if a talented attorney, gives up her salary of $120,000 to

start her own law firm and earns $150,000 after paying for all operating costs → accounting profit = $150,000 but economic profit = $30,000

♦ E.g., if you start a business and earn 6% on money you invested but could have earned 4% in T-Bills → economic profit = 2%.



● Total, Average, and Marginal Revenue:♦ Total Revenue (TR) = P Q

■ Calculated from D curve

♦ Average Revenue (AR) = TR/Q = (P Q)/Q = P■ AR curve = D curve

♦ Marginal Revenue (MR) = TR when ↑output by 1 unit.

■ Slope of TR curve

● Total, Average, and Marginal Revenue:♦ Total Revenue (TR) = P Q

■ Calculated from D curve

♦ Average Revenue (AR) = TR/Q = (P Q)/Q = P■ AR curve = D curve

♦ Marginal Revenue (MR) = TR when ↑output by 1 unit.

■ Slope of TR curve

TABLE 5. Schedule of Flo’s Total, Average, and Marginal Revenue

TABLE 5. Schedule of Flo’s Total, Average, and Marginal Revenue

Chicken

(20 lb-pack)

Price (or AR)

($ per package)

Total Revenue

(P x Q)

Marginal Revenue

0 ----- 0 -----

1 $19 $19 $19

2 18 36 17

3 17 51 15

4 16 64 13

5 15 75 11

6 14 84 9

7 13 91 7

8 12 96 5

9 11 99 3

10 10 100 1

FIGURE 11. Flo’s Total Revenue CurveFIGURE 11. Flo’s Total Revenue Curve

Total Revenue

$0

$20

$40

$60

$80

$100

0 2 4 6 8 10

Quantity of Chicken (20-lb packages)

To

tal R

eve

nu

e



● Total, Average, and Marginal Cost:♦ TC = P inputs x Q inputs

♦ AC = TC/Q output■Per unit costs

♦ MC = ∆TC when ↑output by 1 unit.■Slope of TC curve

● Total, Average, and Marginal Cost:♦ TC = P inputs x Q inputs

♦ AC = TC/Q output■Per unit costs

♦ MC = ∆TC when ↑output by 1 unit.■Slope of TC curve

TABLE 6. Flo’s Total, Average, and Marginal Cost

TABLE 6. Flo’s Total, Average, and Marginal Cost

Chicken

(20 lb-pack)

Total Cost Marginal Cost Average Cost

0 $0.0 ----- -----

1 17.0 $17.0 $17.0

2 26.0 9.0 13.0

3 33.0 7.0 11.0

4 40.0 7.0 10.0

5 48.0 8.0 9.6

6 57.0 9.0 9.5

7 67.2 10.2 9.6

8 80.0 12.8 10.0

9 99.0 19.0 11.0

10 125.0 26.0 12.5

FIGURE 12(a). Flo’s Total Cost CurveFIGURE 12(a). Flo’s Total Cost Curve

Total Cost

$0.00

$20.00

$40.00

$60.00

$80.00

$100.00

$120.00

0 2 4 6 8 10

Quantity of Chicken (20-lb packages per week)

To

tal C

os

t

FIGURE 12(b). Flo’s Average and Marginal Cost Curves

FIGURE 12(b). Flo’s Average and Marginal Cost Curves

Average and Marginal Cost

0

5

10

15

20

25

30

1 2 3 4 5 6 7 8 9 10 11

Quantity of Chicken (20-lb packages per week)

Av

era

ge

an

d m

arg

ina

l co

st

MC

AC



● Maximization of Total Profits:♦ Profits typically increase with output, then fall.

♦ Some intermediate level of output generates max profit.

● Maximization of Total Profits:♦ Profits typically increase with output, then fall.

♦ Some intermediate level of output generates max profit.

TABLE 7. TR, TC, and Profit for FloTABLE 7. TR, TC, and Profit for Flo

Chicken

(20 lb-pack)

Total Revenue

(P x Q)

Total Cost Total Profit

0 $0 $0.0 $0.0

1 19 17.0 2.0

2 36 26.0 10.0

3 51 33.0 18.0

4 64 40.0 24.0

5 75 48.0 27.0

6 84 57.0 27.0

7 91 67.2 23.8

8 96 80.0 16.0

9 99 99.0 0.0

10 100 125.0 -25.0



● In our example:

♦ Total profit (Π) is max at 5 or 6 packages, where farm earns its highest profits of $27 per week.

♦ Any other Q level → ↓Π■E.g., if Q = 3 → Π = $18 or if Q = 8 → Π = $16

● In our example:

♦ Total profit (Π) is max at 5 or 6 packages, where farm earns its highest profits of $27 per week.

♦ Any other Q level → ↓Π■E.g., if Q = 3 → Π = $18 or if Q = 8 → Π = $16


Marginal Analysis and Maximization of Total ProfitMarginal Analysis and Maximization of Total Profit

● Use marginal analysis to find Q that max profits.● Marginal profit = ∆ total profit when ↑Q by 1 unit.

♦ Slope of total profit curve

● Rule: if marginal Π > 0 → ↑Q

if marginal Π < 0 → ↓Q ♦ Profit-max Q is reached when marginal Π = 0.

● Graphically, only reach top of total profit “hill” when marginal profit (its slope) = 0.

● Use marginal analysis to find Q that max profits.● Marginal profit = ∆ total profit when ↑Q by 1 unit.

♦ Slope of total profit curve

● Rule: if marginal Π > 0 → ↑Q

if marginal Π < 0 → ↓Q ♦ Profit-max Q is reached when marginal Π = 0.

● Graphically, only reach top of total profit “hill” when marginal profit (its slope) = 0.

FIGURE 13(a). Profit MaximizationFIGURE 13(a). Profit Maximization

5

Output, Packages per week

10 9 8 7 6 4 3 2 1

–30

–20

0

20

27

To

tal

Pro

fit

pe

r w

ee

k (

$)

Total Profit “hill”

Total profit has a “hill” shape. At Q = 0, Π = 0. At larger Q levels, firm floods the market, and ↓Π. Only at intermediate Q levels is Π > 0.



● Like marginal Π, MR and MC can guide us to Q output where total profit is maximized.

● MR = slope of TR and MC = slope of TC ● Total profit is max when TR and TC are farthest apart.

♦ Occurs when their slopes are equal, so they are not growing closer together (Π↓) or growing further apart (Π↑).

● Rule: if MR > MC → Q

if MR < MC → Q♦ Profit maximizing Q is where MR = MC.

● Like marginal Π, MR and MC can guide us to Q output where total profit is maximized.

● MR = slope of TR and MC = slope of TC ● Total profit is max when TR and TC are farthest apart.

♦ Occurs when their slopes are equal, so they are not growing closer together (Π↓) or growing further apart (Π↑).

● Rule: if MR > MC → Q

if MR < MC → Q♦ Profit maximizing Q is where MR = MC.

FIGURE 13(b). Profit MaximizationFIGURE 13(b). Profit Maximization

TC

TR

Profit

Output, packages per week

5

To

tal R

even

ue,

To

tal C

ost

per

wee

k ($

)

10 9 8 7 6 4 3 2 1 0

99 84

57

20 $27

125

Total Π = vertical distance between TR and TC curves

TABLE 8. Maximization of Flo’s Total Profits

TABLE 8. Maximization of Flo’s Total Profits

Output

(packages)

Marginal Revenue

Marginal Cost

Marginal Profit

Total Profit

0 ----- ----- ----- $0.0

1 $19 $17.0 $2.0 2.0

2 17 9.0 8.0 10.0

3 15 7.0 8.0 18.0

4 13 7.0 6.0 24.0

5 11 8.0 3.0 27.0

6 9 9.0 0.0 27.0

7 7 10.2 -3.2 23.8

8 5 12.8 -7.8 16.0

9 3 19.0 -16.0 0.0

10 1 26.0 -25.0 -25.0



● Finding the Optimal P from Optimal Q:

● Optimal Q is where MR = MC (and marg. Π = 0).♦ E.g., at Q = 6; MR = MC = $9.

● Producer picks Q then demand curve P buyers will pay to purchase that level of output.♦ E.g., at Q = 6 → P = $14 –only P at which this Q is

purchased by consumers.

● Finding the Optimal P from Optimal Q:

● Optimal Q is where MR = MC (and marg. Π = 0).♦ E.g., at Q = 6; MR = MC = $9.

● Producer picks Q then demand curve P buyers will pay to purchase that level of output.♦ E.g., at Q = 6 → P = $14 –only P at which this Q is

purchased by consumers.


Logic of Marginal Analysis & MaximizationLogic of Marginal Analysis & Maximization

● Decision makers constantly faced with problem of choosing the magnitude of some variable. ♦ E.g., how many cars to produce; how many workers to hire, or

how many pints of ice cream to buy.

● Generally, larger the number selected → higher the total benefit. However, costs ↑ as number chosen ↑.

● Optimally, decision makers chose Q of some variable where difference between total benefit and total cost is greatest.

● Decision makers constantly faced with problem of choosing the magnitude of some variable. ♦ E.g., how many cars to produce; how many workers to hire, or

how many pints of ice cream to buy.

● Generally, larger the number selected → higher the total benefit. However, costs ↑ as number chosen ↑.

● Optimally, decision makers chose Q of some variable where difference between total benefit and total cost is greatest.

Logic of Marginal Analysis & MaximizationLogic of Marginal Analysis & Maximization

● Decide about Q of some variable, then max net benefit = total benefit – total cost by choosing the Q where marginal benefit = marginal cost.

● Rule is true regardless of who the decision maker is.

● Decide about Q of some variable, then max net benefit = total benefit – total cost by choosing the Q where marginal benefit = marginal cost.

● Rule is true regardless of who the decision maker is.

Decision maker

Marginal benefit

Marginal

cost

Choice variable

Objective

consumer MU P good Q of good Max CS

firm MRP input P input Q of 1 input Max Π

firm MR output MC output Q of output Max Π

the firm’s production and selling decisions

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