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4. The Firm’s Production and Selling Decisions. Outline. 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. Outline. Price and Quantity: One Decision, Not Two

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slide1

4

The Firm’s Production and Selling Decisions

outline
Outline
  • 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
outline1
Outline
  • 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
production and input choice with 1 variable input
Production 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.
production and input choice with 1 variable input1
Production and Input Choice, with 1 Variable Input
  • 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.
production and input choice with 1 variable input2
Production and Input Choice, with 1 Variable Input
  • 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.
graph of mpp
Graph 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.
the law of diminishing marginal returns
The “Law” of Diminishing Marginal Returns
  • ↑ 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?

optimal purchase rule for a single input
Optimal 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 = $10.50

TC: $10 x 1 = $10.00

Profit: = $0.50

  • Shouldn't stop at 1 bag because 2 bags yield more profit.

TR: $0.75 x 36 = $27.00

TC: $10 x 2 = $20.00

Profit: = $7.00

optimal purchase rule for a single input1
Optimal Purchase Rule for a Single Input
  • 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.
optimal purchase rule for a single input2
Optimal Purchase Rule for a Single Input
  • 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 decisions
Multiple 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.
multiple input decisions1
Multiple 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.
marginal rule for optimal input proportions
Marginal 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.
marginal rule for optimal input proportions1
Marginal Rule for Optimal Input Proportions

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 ↓outputby 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.
marginal rule for optimal input proportions2
Marginal Rule for Optimal Input Proportions
  • 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.
marginal rule for optimal input proportions3
Marginal Rule for Optimal Input Proportions
  • 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.
marginal rule for optimal input proportions4
Marginal Rule for Optimal Input Proportions
  • 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.
cost curves and input quantities
Cost Curves and Input Quantities
  • 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 quantities1
Cost 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.
figure 4 flo s average cost and marginal cost curves
FIGURE 4. Flo’s Average Cost and Marginal Cost Curves

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

fixed and variable costs
Fixed and Variable Costs
  • 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 costs1
Fixed and Variable Costs
  • TC = TVC + TFC
  • AC = AVC + AFC
    • AC = TC/Q output
    • AVC = TVC/Q output
    • AFC = TFC/Q output
table 4 flo s total and average fixed costs
Table 4. Flo’s Total and Average Fixed Costs

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

figure 6 graph of flo s average fixed cost
FIGURE 6. Graph of Flo’s Average Fixed Cost

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 curve
FIGURE 7. Flo’s Total Variable Cost Curve

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

fixed and variable costs2
Fixed and Variable Costs
  • Marginal Cost = Marginal Variable Cost (MVC)

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

shape of the average cost curve
Shape of the Average Cost Curve
  • AC is generally U shaped –it initially declines and eventually rises with the level of output.
  • AC declines for 2 reasons:
    • 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.
    • ↓Average fixed costs as ↑output.
shape of the average cost curve1
Shape of the Average Cost Curve
  • AC eventually rises for 2 reasons:
    • Dim MPP: ↑output more slowly as ↓MPP corn, which tends to ↑AC.
    • 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.
short run versus long run costs
Short-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.
short run versus long run costs1
Short-run versus Long-run Costs
  • 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.
short run versus long run costs2
Short-run versus Long-run Costs
  • 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.
average cost curve in the short and long run
Average Cost Curve in the Short and Long Run
  • 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 run1
Average 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.
economies of scale
Economies of Scale
  • Returns to scale indicates how the output level changes when all the firm's inputs are doubled.
  • 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.
  • Constant Returns to Scale (CRTS): Q output doubles.
  • Decreasing Returns to Scale (DRTS): Q output less than doubles.
    • Gives a cost advantage to smaller firms. Most U.S. industries have DRTS.
economies of scale1
Economies of Scale
  • 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 curve

AC

Increasing returns

Constant returns

Decreasing returns

to scale

to scale

to scale

AC

AC

FIGURE 9. 3 Possible Shapes for the AC Curve

Long-Run Average Cost

Long-Run Average Cost

Long-Run Average Cost

Quantity of Output

Quantity of Output

Quantity of Output

(a)

(b)

(c)

economies of scale2
Economies of Scale
  • 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 two
Price 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
figure 10 demand curve for flo s poultry meat
FIGURE 10. Demand Curve for Flo’s Poultry Meat

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.

A

$19

Price per package

B

$11

D

1

9

Quantity of Chicken (20 lb-packages per week)

price and quantity one decision not two1
Price 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.
total profit keep your eye on the goal
Total 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 keep your eye on the goal1
Total Profit: Keep Your Eye on the Goal
  • 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 profit keep your eye on the goal2
Total Profit: Keep Your Eye on the Goal
  • 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 profit keep your eye on the goal3
Total Profit: Keep Your Eye on the Goal
  • Maximization of Total Profits:
    • Profits typically increase with output, then fall.
    • Some intermediate level of output generates max profit.
total profit keep your eye on the goal4
Total Profit: Keep Your Eye on the Goal
  • 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 profit
Marginal 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.
figure 13 a profit maximization
FIGURE 13(a). Profit Maximization

Total Profit “hill”

27

20

0

2

3

4

5

6

7

8

9

10

Total Profit per week ($)

1

–20

–30

Output, Packages per week

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.

marginal analysis and maximization of total profit1
Marginal Analysis and Maximization of Total Profit
  • 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 maximization

TC

TR

Profit

FIGURE 13(b). Profit Maximization

Total Π= vertical distance between TR and TC curves

125

99

84

Total Revenue, Total Cost per week ($)

57

$27

20

0

1

2

3

4

5

6

7

8

9

10

Output, packages per week

marginal analysis and maximization of total profit2
Marginal Analysis and Maximization of Total Profit
  • 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 maximization
Logic 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.
logic of marginal analysis maximization1
Logic 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.