Opens in a new tab. The class votes by show of hands at every decision; click the majority. About 10–12 minutes, ten possible endings.
After the game we put names on what the class saw, then turn it into a table and a graph.
After the game · what you just ran
Production: a farm turns inputs into output
Production is the process of combining inputs to produce outputs—ideally output worth more than the inputs.
A farm is a firm: it decides what to grow, how, how much, and how many people to hire. You just made that last decision.
Natural resources
The field, already planted with sweet potatoes
Labor
Maria, Jamal, Kenji… the harvest crew
Capital
The digger, the truck and its ramp
Technology
The method: dig with a machine, not by hand
Entrepreneurship
You, the boss who decided whom to hire
In the game only one input changed: the number of workers. The field, the digger and the truck stayed the same.
A production function shows how much output a firm gets from its inputs—here, bushels per day for each crew size.
You met the factors of production in Unit 2. “Technology” means any method of combining inputs, not only gadgets.
LO 8a.2 · name what you saw
Marginal product: what one more worker adds
Marginal product of labor (MP): the extra output from hiring one more worker, holding the other inputs fixed.
Total product (TP) is total output: Pine Hollow’s bushels per day.
MP =change in total productchange in workers
Each step adds one worker, so the bottom of the fraction is 1: MP is simply the change in total product.
Jamal, the 2nd worker: 40 → 100 bushelsMP = 100 − 40 = 60. Jamal added more than Maria.
Maria drives, picks, boxes and hauls. While she carries a crate to the truck, the digger sits still.
Maria drives and Jamal picks right behind the digger. Nobody runs back and forth, so the digger never stops.
LO 8a.2 · your turn · computing marginal product
Pine Hollow’s production table
One digger · bushels per day
Workers (L)
Total product (TP)
Marginal product (MP)
0
0
—
1
40
40
2
100
60
3
150
50
4
180
30
5
200
20
6
210
10
7
200
−10
MP =change in total productchange in workers
?
Fill in the MP column, starting with worker #4Worker #4 is Priya. In the game, three workers dug 150 and four dug 180. Answer before we reveal.
1
4th worker: 180 − 150 = 30 bushelsNow the rest of the column.
2
MP column: 40, 60, 50, 30, 20, 10, −10Each MP is one TP minus the TP just above it.
3
Seven workers dig 200, not 280The 7th worker even lowers output.
Back to the game’s first bet
Seven workers dig 200, not 280
280if every worker added 40
200what 7 workers dig
Output does not grow in proportion to workers, because the digger does not grow.
Every worker shares the same machine and the same rows.
The game asked this before anyone was hired: 280, more, or less? Seven workers dig less.
LO 8a.1 · the pattern has a name
Diminishing marginal returns: Unit 3 named it
Diminishing marginal returns occur when, with technology and other inputs held constant, successive units of one input
eventually generate smaller additions to total output.
1
Hold everything else fixedSame land, same machines, same know-how. Only one input changes.
2
Add that input one unit at a timeOne more worker, one more acre, one more bag of fertilizer.
3
Each new unit eventually adds lessThe first few may even add more. But sooner or later the additions shrink. Total output still grows, just more slowly.
Why do the additions shrink? Two everyday pictures next: a farm that runs out of good land, and a checkout lane that runs out of room.
Unit 3 named the idea. Today we measure it, and at the end of class we put a price on it.
Example 1 · farming · no numbers needed
Expand onto poorer land
A farmer plants the best land first. Every new acre is a little drier, rockier or steeper than the last,
so each one adds a smaller harvest.
Before each click: will this acre add as much as the last one? The silo keeps filling, but each band is thinner.
Here the later acres are worse land. Next: a case where every new worker is just as good as the last, and each still adds less.
Example 2 · crowding a fixed input · no numbers needed
One checkout lane, more and more baggers
Fixed: one register and one bagging counter. Variable: baggers.
The first bagger frees the cashier to just scan. After that, every bagger has to share the same small counter.
Every bagger is just as good as the last. Each one adds less because the counter does not grow.
Pine Hollow is the same story: one digger, more and more workers.
LO 8a.1 · game debrief
Game debrief: where—and why—MP fell
Workers in hiring order: Maria 40 · Jamal 60 · Kenji 50 · Priya 30 · Luis 20 · Hannah 10 · Omar −10
1
Where did diminishing returns begin?Worker #3, Kenji: MP fell 60 → 50, the first MP smaller than the one before. On the graph, that is where TP starts to flatten.
2
Why did MP rise, then fall?Jamal let Maria specialize, so MP rose. After that everyone shared one digger, a fixed input—not lazier workers. Any hiring order gives the same numbers.
3
When MP fell, did total output fall?No. TP kept rising (150 → 210) while MP shrank. Only a negative MP—Omar’s −10—made TP fall, 210 → 200.
4
Does MP always rise first?No. Rise-then-fall is the typical shape; the law only says MP eventually falls—sometimes from the very first unit, like a bag of fertilizer on an already-rich field.
Why MP fell · one input was fixed · guess first
Fixed inputs vs. variable inputs
Fixed input
Your guess: what does it mean?
Cannot be changed quickly. The farm has the same amount whether it digs a lot or a little.
Variable input
Your guess: what does it mean?
Can be changed quickly. Dig more, and the farm uses more of it.
At Pine Hollow this harvest season, which inputs are fixed? Which are variable? The digger and the leased field stay the same however many people dig; workers, diesel and boxes go up and down with the digging.
Each input brings a cost: fixed inputs bring fixed costs, variable inputs bring variable costs. We put dollars on them after the next few slides.
Hands up · your turn
Fixed or variable at Pine Hollow?
Time span: this harvest season. Vote on each card, then reveal.
The digger’s lease for the season
FixedPaid whether 1 or 7 people dig.
The digger’s lease for the season
VariableLease a second digger, or none at all.
Daily wages of the harvest workers
VariableMore workers, more wages.
Diesel for the tractor
VariableMore digging, more fuel.
The farm’s insurance premium
FixedSet for the year.
The farm’s insurance premium
VariableChange the policy, or drop it if the farm is sold.
Cardboard boxes for the sweet potatoes
VariableOne box per bushel shipped.
Land rent already signed for the year
FixedOwed no matter the harvest.
Land rent already signed for the year
VariableRent more acres, fewer, or none.
Now make the time span five years. Judge every card again: which ones change?
All of them are variable now. In five years the farm can lease more diggers or none, rent more land or less, change its insurance—or sell the farm.
The time horizon
Short run vs. long run
The last slide’s two answers have names.
Short run
A period so short that at least one input is fixed.
Pine Hollow, this harvest season: the digger and the leased field are fixed. Only workers, diesel and boxes can change.
Long run
A period long enough that every input is variable.
Pine Hollow, five years out: lease a second digger (the game’s last screen), rent more acres, build a bigger curing room—or sell the farm.
The long run is not a date on the calendar. It is “long enough to change every input.”
For a food truck that might be weeks; for an orchard, years.
Diminishing returns are a short-run story: they happen because something is fixed. Pine Hollow’s MP fell because the digger could not grow.
Production in three lines
Production: three ideas to take away
1
MP = ΔTP ÷ ΔLThe extra output from one more worker, holding the other inputs fixed.
2
Diminishing returns begin with the first MP that is smaller than the one beforeOn the graph: where TP starts to flatten. The cause: a fixed input.
3
Short run: at least one input is fixed. Long run: every input can change.The same input can be fixed this season and variable over five years.
Everything so far is in bushels. Next: what those bushels cost.
From inputs to costs · LO 8a.3 · guess first
Fixed costs vs. variable costs
Fixed cost (FC)
Your guess: what does it mean?
The cost of the fixed inputs.
It stays the same however much the farm produces in the short run, and is paid even if nothing is produced.
Variable cost (VC)
Your guess: what does it mean?
The cost of the variable inputs.
It rises when the farm produces more, and is zero when nothing is produced.
FC = $400 + $350 + $150 = $900 a day, even if nobody digs.
VC = $120 a day per worker
(diesel and boxes folded in): 3 workers → $360; nobody → $0. Total cost: TC = FC + VC.
Illustrative numbers. The test for any cost: does it change if the farm digs one more bushel? Next: the daily cost table.
LO 8a.3 · the total cost table
Pine Hollow’s daily costs
For now, labor is the only variable cost. VC = $120 × the number of workers; diesel and boxes are folded into the $120.
FC = $900 · wage = $120
Workers
Output Q (bu)
FC
VC
TC
0
0
$900
$0
$900
1
40
$900
$120
$1,020
2
100
$900
$240
$1,140
3
150
$900
$360
$1,260
4
180
$900
$480
$1,380
5
200
$900
$600
$1,500
6
210
$900
$720
$1,620
1
VC = $120 × workersThree workers: $360.
2
TC = FC + VCThree workers: $900 + $360 = $1,260.
3
At zero output, TC = FC = $900That is how quiz questions hide FC: it is the TC when Q = 0.
The 7th worker is left out: he would raise cost and lower output. No farm hires him.
LO 8a.3 · the same table as a graph
Total cost = variable cost shifted up by $900
Read the axes first
The horizontal axis is now output (bushels), not workers. Production graphs put workers on the axis; cost graphs put output.
FC is flat; TC and VC are parallel
The gap between TC and VC is always $900.
From totals to cost per bushel · guess first
Which day digs cheaper bushels?
Same farm, two days. Day B’s bill is bigger. Does that mean its bushels cost more? Vote first.
Split each day’s bill over its bushels: every crate carries its share.
Day B’s bill is bigger, but twice as many bushels share it,
so each bushel carries less. That share is the average cost of a bushel.
The total tells you the size of the bill; the average tells you what each bushel carries, the number to hold up against the $8 a bushel the packing house pays.
LO 8a.3 · cost per bushel
Four ways to measure cost per unit
Average fixed cost
AFC = FC ÷ Q
The $900 spread over every bushel. Falls as Q rises.
Average variable cost
AVC = VC ÷ Q
Wages per bushel. Next unit (8b) uses AVC to decide when to shut down.
Average total cost
ATC = TC ÷ Q = AFC + AVC
The full cost of a typical bushel.
Marginal cost
MC = ΔTC ÷ ΔQ
The cost of the next bushel only.
Divide by the change in output, not by 1. Going from 2 to 3 workers adds 50 bushels for $120: MC = $120 ÷ 50 = $2.40.
That is MC = wage ÷ MP: one more worker costs the wage and adds MP bushels.
Quiz tables that add one unit at a time make MC look like a plain difference in TC—because ΔQ = 1.
Reading: Lumen “Costs in the Short Run” and “Average Costs and Curves.” One correction: where it says the ATC of 80 haircuts is $8, the table gives $560 ÷ 80 = $7.
Cost per bushel, one at a time · 1 of 4
AFC: one bill, more and more bushels
The $900 bill is the same every day, however many people dig. AFC spreads it over all the bushels the crew digs.
The bill never changes, but more bushels share it, so AFC keeps falling: fast at first, then more and more slowly. It never turns up.
Cost per bushel, one at a time · 2 of 4
MC: what the next bushel costs
Hiring one more worker costs $120 and adds that worker’s pile. MC spreads the $120 over the new pile only.
A big new pile makes the next bushel cheap; a small one makes it dear. MC is lowest with Jamal and shoots up as the new piles shrink: the mirror image of MP.
Cost per bushel, one at a time · 3 of 4
AVC: why does it dip, then rise?
Every worker costs $120 a day. AVC spreads that $120 over the bushels the average worker digs: a bigger pile means a cheaper bushel.
The newest worker pulls the average toward their own number. Digs more than the average: the pile grows, AVC falls. Digs less: the pile shrinks, AVC rises. Diminishing returns start with Kenji, but AVC rises only from Priya, the first worker below the average.
Cost per bushel, one at a time · 4 of 4
ATC = AFC + AVC
ATC is the whole cost of a typical bushel: its share of the $900 bill (AFC, purple) plus its share of the wages (AVC, green).
At first the shrinking purple part wins, so ATC falls. Later the growing green part wins, so ATC turns up. The bottom, $7.50 at 200 bushels, is where the two pulls balance.
LO 8a.4 · marginal pulls the average
MC and ATC work like your quiz average
Your quiz average
After 4 quizzes your average is 85.
↑
Quiz 5 = 90 → average 86(4 × 85 + 90) ÷ 5. Above the average pulls it up.
↓
Quiz 5 = 70 → average 82Below the average pulls it down.
Pine Hollow
At 180 bushels, ATC is $7.67.
↓
Next 20 bushels: MC = $6.00 < ATCBelow the average pulls it down: ATC falls to $7.50.
↑
Then 10 more: MC = $12.00 > ATC $7.50Above the average pulls it up: ATC rises to $7.71.
The newest unit (the marginal one) pulls the average toward itself—whether it is a quiz score or a cost.
LO 8a.4 · the rule
Where MC crosses ATC, ATC is at its lowest
MC < ATC
ATC falls.
Pine Hollow, 180 → 200 bu: MC $6.00 < ATC $7.67, so ATC falls to $7.50.
MC = ATC
ATC is at its minimum.
MC crosses ATC from below near 200 bushels, where ATC bottoms out at $7.50.
MC > ATC
ATC rises.
200 → 210 bu: MC $12.00 > ATC $7.50, so ATC rises to $7.71.
The same holds for AVC, as the money-bag slide showed: a new worker who digs more than the average pulls AVC down, less pulls it up. Kenji digs exactly the average, so his MC of $2.40 (100 → 150 bu) equals the lowest AVC, $2.40.
Trap: “MC is rising, so ATC must be rising.” No—at Pine Hollow MC rises from $2 to $6 while ATC keeps falling,
because MC is still below ATC. Compare the levels, not the direction.
LO 8a.3–8a.4 · putting the four together
Pine Hollow’s four cost curves
Bushels per day on the horizontal axis. AFC and ATC start off the chart at small output.
1
AFC keeps fallingThe same $900 split over more and more bushels, like the split bills on Day A and Day B.
2
AVC dips, then rises$120 per worker spread over the average worker’s pile: the pile grows while new workers dig more than the average, then shrinks.
3
ATC = AFC + AVC: a UIt falls while the $900 is still being spread thin, then rises once crowding wins. The gap above AVC is AFC.
4
MC dips, then climbs steeplyThe cost of the next bushel, wage ÷ MP: it mirrors MP, so it shoots up as MP falls.
5
MC crosses ATC and AVC at their lowest pointsThe marginal pulls the average: it falls while MC is below, rises once MC is above.
LO 8a.4 · concept check
Quick check
“When marginal cost is above average total cost, average total cost must be falling.”
FalseMC above ATC pulls ATC up.
“A rise in fixed cost raises marginal cost.”
FalseMC counts only what changes with one more unit; FC does not.
A firm makes 10 units at ATC = $20. The 11th unit has MC = $9. Does ATC rise or fall, and to what?
Falls($200 + $9) ÷ 11 = $19.
“The gap between ATC and AVC is largest at small output.”
TrueThe gap is AFC, which shrinks as Q grows.
Your turn · LO 8a.3 · quiz format
A kettle corn stand at the State Fair
Output in hundreds of bags per day
Output Q
0
1
2
3
4
5
6
Total cost
$120
$180
$220
$270
$340
$430
$540
(a) What is the fixed cost?
(b) What is AVC at Q = 3?
(c) What is the MC of the 5th unit?
(d) At what Q is ATC lowest? What is it?
(a) TC at Q = 0: $120 (the booth fee)
(b) ($270 − $120) ÷ 3 = $50
(c) $430 − $340 = $90
(d) Q = 4: $340 ÷ 4 = $85
Q
1
2
3
4
5
6
MC
$60
$40
$50
$70
$90
$110
ATC
$180
$110
$90
$85
$86
$90
AVC
$60
$50
$50
$55
$62
$70
LO 8a.3 & 8a.5 · cost curves can move
What moves, and what stays put?
Pine Hollow’s curves were drawn for one wage, one lease and one season’s weather. Change one of them:
What changes
MC
AVC
AFC
ATC
A variable input costs morewages, diesel, fertilizer, cocoa
↑
↑
—
↑
A fixed input costs morerent, a lease, insurance, equipment
—
—
↑
↑
Productivity falls, input prices unchangeddrought, disease, storm damage
↑
↑
↑
↑
One question sorts them: does this cost change when the farm digs one more bushel? If not, MC and AVC stay put.
Next: sort real farm and food events into these rows.
LO 8a.5 · farm and food events · hands up
Fixed, variable, or productivity?
1Cocoa prices double. A chocolate maker’s main ingredient costs twice as much.
Variable inputMC, AVC, ATC ↑
2Nitrogen fertilizer prices spike before corn planting.
Variable inputMC, AVC, ATC ↑
3Proposition 12 requires a hog farm to rebuild its sow pens—a one-time renovation.
Fixed inputAFC, ATC ↑ · MC unchanged*
4A hurricane floods part of a sweet potato field. Same crew, same digger, fewer bushels.
Productivity ↓all four ↑
5A new digger attachment lets the same crew dig 25% more each day.
Productivity ↑MC, AVC, ATC ↓
6The farm’s property insurance premium goes up.
Fixed inputAFC, ATC ↑
* If the new rules also mean fewer sows per barn, productivity falls too, and MC rises. The answer depends on what the rule changes.
Back to Unit 4 · ahead to 8b
Why higher costs shift supply to the left
Unit 4 said
“Input prices: higher wages or materials costs → supply left.”
Higher input prices or lower MP push the MC curve up.
At any given price, the farm now finds fewer bushels worth digging.
Coming in 8b: in perfect competition, a firm’s supply curve is its MC curve—the part above AVC.
That is why today we also learned AVC.
And why a rise in fixed cost (the lease, insurance) does not shift that MC curve at all.
Optional · a peek at the long run
In the long run, every input can change
Economies of scale
When a firm grows all its inputs together, its long-run average cost can fall. A large hog farm spreads a Prop 12 renovation over many more pigs than a small one.
Not the same as today’s curves
Today’s rising MC is a short-run story: one digger, more workers. Economies of scale are a long-run story: everything grows together.
Trap: “Demand for cage-free eggs jumps, so in the short run marginal cost falls because of economies of scale.”
No—with barns fixed, producing more raises MC.
We return to economies of scale when we study market structure.