Production & Costs: Review
Pine Hollow Farm, one digger, more and more workers
Diminishing returns in one slide
Where it begins
At the first MP smaller than the one before.
Pine Hollow: MP = 40, 60, 50, … Kenji, the 3rd worker.
Why
A fixed input: every worker shares the same digger and the same rows.
Not lazier workers. A short-run story.
Trap
MP falling ≠ output falling.
TP keeps rising while MP > 0. Only a negative MP makes TP fall.
Does total output fall?
“The principle of diminishing returns implies that total production decreases when more units of a variable input are added.”
Answer: False.
Diminishing returns means each extra unit adds less output, not that total output falls. TP keeps rising as long as MP > 0.
Why do diminishing returns happen?
Which of the following is the primary reason for experiencing diminishing returns to labor?
Answer: C · fixed inputs.
Workers share a fixed input (land, a machine), so each extra worker eventually adds less. Demand has nothing to do with the production function.
Hiring more laborers on fixed acres
You have a fixed amount of acres to harvest. As you hire more laborers, what does the law of diminishing returns predict?
Answer: D · the best option offered.
The key point is that MP falls. “Rises, then falls” is the typical shape; the law only requires that MP eventually falls. C is wrong: MP turns negative only when total output starts to fall.
Which bagel shop shows diminishing returns?
Which of the following is true about the law of diminishing returns? A small bagel shop hires more people for its busiest shift.
Answer: A.
MP = 10, 6, 2, then negative: each hire adds less. B shows rising MP; C shows constant MP.
Too much pesticide
A farmer sprays pesticides to repel insects. The first spraying keeps insects from harming the crop. As the farmer sprays more and more, he eventually kills the crop. What economic principle does this best represent?
Answer: A.
Each extra spraying adds less protection; eventually its marginal product is negative and output falls.
No diminishing returns at all
A production function always doubles output when the input doubles, with no diminishing returns to any input. With output on the vertical axis and input on the horizontal axis, what does it look like?
Answer: C · a straight line through the origin.
Constant MP means every unit adds the same amount, so TP rises in a straight line. B is what diminishing returns look like.
Where do diminishing returns begin?
At which point do we first witness diminishing returns to labor?
| Workers | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Toy production | 0 | 10 | 22 | 30 | 35 |
Answer: C · the 3rd worker.
MP = 10, 12, 8, 5. The first MP smaller than the one before is the 3rd worker’s (8 < 12).
From marginal product back to total output
Pine Hollow: start at 0 bushels with 0 workers. MP = 40, 60, 50, 30, …
Watch the starting point
If output is not zero when the input is zero, start from that number. A field with no fertilizer still grows some corn.
Quiz format
“Here is the MP of each worker. What is total output with n workers?” Add the first n MPs.
How many workers to fill an order?
A grocery chain wants 170 bushels from Pine Hollow today. MP of each worker: 40, 60, 50, 30, 20, 10. What is the smallest crew that fills the order?
“Minimum workers to reach a target” is just the running total from the last slide, read from the other side.
Nitrogen fertilizer on one acre of corn
| 40-lb unit of nitrogen | 1st | 2nd | 3rd | 4th | 5th | 6th |
|---|---|---|---|---|---|---|
| Marginal product (bushels) | 40 | 30 | 20 | 10 | 0 | −5 |
With no fertilizer the acre yields 100 bushels (the soil already holds some nitrogen).
- (a) Total yield with 3 units?
- (b) With which unit do diminishing returns begin?
- (c) Highest yield, and how many units reach it?
- (d) What does the 6th unit do?
(a) 100 + 40 + 30 + 20 = 190
(b) The 2nd unit: 30 < 40. MP falls from the very first unit.
(c) 200, with 4 or 5 units (the 5th adds 0)
(d) Yield drops to 195: MP < 0
Becky’s Boutique Bakery
Becky owns a commercial oven, dough mixers and utensils. Other inputs: flour, yeast, salt, water and skilled bakers. Flour and the other ingredients are adjusted with the number of bakers.
| Bakers | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| Loaves of bread | 0 | 50 | 120 | 180 | 230 | 270 | 300 |
(a) Which are fixed costs? Select all: oven, dough mixers, bakers, flour.
Oven and dough mixers. Bakers and flour change with how much bread she makes.
(b) Calculate the marginal product of expanding from 2 to 3 bakers.
180 − 120 = 60 loaves. All MPs: 50, 70, 60, 50, 40, 30.
(c) When do diminishing returns begin?A. 2 → 3 bakers · B. the 1st baker · C. 1 → 2 bakers · D. after 3 → 4 bakers
A. MP rises to 70 with the 2nd baker, then first falls with the 3rd (60 < 70).
(d) Shape of the total product curve?A. straight line · B. declines after the 1st baker · C. rises steeply throughout · D. rises quickly at first, then at a decreasing rate
D. TP rises fastest from 1 to 2 bakers, then each step adds less: diminishing returns.
Wheat farm: from MPL to total output
The farm produces 0 bushels with no workers. Each worker is paid $50 a day.
| Worker | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| MPL (bushels) | 100 | 90 | 80 | 70 | 60 | 50 | 40 | 30 |
(a) Total wheat production after all 8 workers are hired?
100 + 90 + … + 30 = 520 bushels.
(b) The production target is 400 bushels. Minimum number of workers to meet or exceed it?
Running total: 100, 190, 270, 340, 400. Four give 340 < 400, so hire 5.
(c) Total wage cost of that minimum crew?
5 × $50 = $250.
(d) With which worker do diminishing returns begin?
The 2nd worker: 90 < 100. MP falls from the start—no rising stage here.
Wheat farm: MP, total cost and MC
One fixed input (land). Fixed cost is $400 a day; each worker costs $200 a day.
| Point | A | B | C | D | E | F | G | H | I |
|---|---|---|---|---|---|---|---|---|---|
| Workers | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Wheat (bushels) | 0 | 19 | 36 | 51 | 64 | 75 | 84 | 91 | 96 |
(a) Marginal product of the 3rd worker?
51 − 36 = 15 bushels. All MPs: 19, 17, 15, 13, 11, 9, 7, 5.
(b) As the farm hires more workers, what happens to MP?A. increases · B. decreases · C. stays the same
B. It decreases, from the very first worker.
(c) Total cost at point C?A. $400 · B. $800
B. $400 + 2 × $200 = $800. $400 is only the fixed cost.
(d) From B to C, what is the marginal cost of a bushel?
MC = wage ÷ MP = $200 ÷ 17 ≈ $11.76 per bushel.
Every cost formula on one page
Pine Hollow, cost per bushel
| Q (bu) | TC | AFC | AVC | ATC | MC |
|---|---|---|---|---|---|
| 40 | $1,020 | $22.50 | $3.00 | $25.50 | $3.00 |
| 100 | $1,140 | $9.00 | $2.40 | $11.40 | $2.00 |
| 150 | $1,260 | $6.00 | $2.40 | $8.40 | $2.40 |
| 180 | $1,380 | $5.00 | $2.67 | $7.67 | $4.00 |
| 200 | $1,500 | $4.50 | $3.00 | $7.50 | $6.00 |
| 210 | $1,620 | $4.29 | $3.43 | $7.71 | $12.00 |
Fixed or variable? A one-year view
For each cost, decide whether it is a fixed cost or a variable cost for an agricultural firm over a 1-year time span. Vote on each card.
Fuel for tractors
VariableInsurance premiums for the farm
FixedCost of pesticides
VariableWater usage for irrigation
VariableRent for farmland
FixedThe test: does this cost change if the farm produces more this year? Insurance and land rent do not.
Switching to egg production
In the context of farmers switching to egg production, which of the following is an example of a variable cost associated with this transition?
Answer: C · feed.
Feed rises directly with the number of hens. Barn upgrades and new facilities are fixed. A farm-wide utility bill is overhead here, so it is not the best answer.
Fill in the missing costs
The table shows variable and total costs for Good X.
| Quantity of X | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Variable cost (VC) | $0 | $20 | $40 | ? | $110 |
| Total cost (TC) | $80 | $100 | $120 | $150 | ? |
(a) What are fixed costs?
TC at Q = 0: $80. (Check: $100 − $20 = $80 at every row.)
(b) Variable costs when quantity is 3?
$150 − $80 = $70.
(c) Total costs when quantity is 4?
$80 + $110 = $190.
A total cost table, quiz format
The table shows the total cost associated with each unit of production.
| Units produced | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| Total cost ($) | 500 | 750 | 1,050 | 1,400 | 1,800 | 2,250 | 2,750 |
(a) What is the fixed cost of this operation?
TC at Q = 0: 500.
(b) Average variable cost of the first unit?
(750 − 500) ÷ 1 = 250.
(c) Marginal cost of producing the fifth unit?
2,250 − 1,800 = 450.
(d) At what output is average total cost lowest?
ATC = 750, 525, 466.67, 450, 450, 458.33: lowest at Q = 4 and 5. The 5th unit’s MC (450) equals ATC, so ATC stays flat; the 6th unit’s MC (500) is above it, so ATC rises.
A farmer’s total cost
The table shows a farmer’s total cost of producing their crop.
| Output | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| Total cost ($) | 1,000 | 1,500 | 1,800 | 2,000 | 2,200 | 2,500 |
(a) Fixed cost?
$1,000 (TC at zero output).
(b) Variable cost at 4 units?
2,200 − 1,000 = $1,200.
(c) Average total cost at 3 units? (2 decimal places)
2,000 ÷ 3 = $666.67.
(d) Average variable cost at 5 units?
(2,500 − 1,000) ÷ 5 = $300.
(e) Marginal cost of going from 3 to 4 units?
2,200 − 2,000 = $200.
Working backward from AVC
Terry plants corn. She produces 100 bushels, her average variable cost is $5 per bushel, and total fixed costs are $100.
(a) What is her variable cost?
VC = AVC × Q = $5 × 100 = $500.
(b) What is her total cost?
TC = FC + VC = $100 + $500 = $600.
(c) What is her average total cost?
ATC = $600 ÷ 100 = $6. Check: AFC $1 + AVC $5.
Spreading the same fixed cost
In both parts, total fixed cost stays the same.
(a) The AFC of producing 600 eggs is $12. What is the AFC of producing 1,200 eggs?
FC = $12 × 600 = $7,200; $7,200 ÷ 1,200 = $6. Double the output, halve the AFC.
(b) A chocolate company’s AFC is $3 per bar at 100 bars. What is AFC at 600 bars?
FC = $3 × 100 = $300; $300 ÷ 600 = $0.50. Six times the output, one-sixth the AFC.
Read the cost curves
The graph shows cost curves for a typical firm. Choose from MC, ATC, AFC, AVC.
(a) Which curve is Curve 1 (red)? Curve 2 (blue)?
Curve 1 = MC, Curve 2 = AVC (Curve 3 = ATC). MC is the steep curve through the bottoms of both U’s; AVC is the lower U.
(b) Average variable cost at 2 units? At 3 units?
Read Curve 2: $7 at Q = 2, $8 at Q = 3.
(c) At what price does MC intersect AVC?
$7, at AVC’s minimum (Q = 2).
(d) True or false: the gap between ATC and AVC is always larger at lower quantities.
True. The gap is AFC = FC ÷ Q, which shrinks as Q grows.
Name the curves: M, N and O
Curves M, N and O are a firm’s cost curves.
(a) Which curve represents marginal cost?
M: the steep curve that passes through the lowest points of N and O.
(b) Which curve represents average variable cost?
O: the lower U. N is ATC; the gap between them is AFC, and it narrows as Q grows.
Tip: MC crosses AVC first (at a smaller Q), then ATC.
If fixed costs were zero
If fixed costs equal 0, what is true about the ATC and AVC curves?
Answer: A.
ATC = AFC + AVC. With FC = 0, AFC = 0 at every output, so ATC and AVC coincide.
Can AFC be above ATC?
“The average fixed cost curve can never be above the average total cost curve.”
Answer: True.
ATC = AFC + AVC, and AVC is never negative, so ATC ≥ AFC everywhere.
The marginal unit pulls the average
MC < ATC
ATC falls.
Quiz average 85, next quiz 70 → average 82.
MC = ATC
ATC is at its minimum.
MC crosses ATC (and AVC) at the bottom of the U.
MC > ATC
ATC rises.
Quiz average 85, next quiz 90 → average 86.
A fifth toy
You produce toys. Currently you produce 4 toys at a total cost of $40.
(a) What is your average total cost?
$40 ÷ 4 = $10.
(b) You produce a fifth toy, and its marginal cost is $5. What is ATC now?
($40 + $5) ÷ 5 = $9.
(c) Why did ATC change?A. The MC of the fifth toy was lower than the previous ATC · B. The price of materials fell
A. A marginal unit below the average pulls the average down. Nothing happened to input prices.
Which statements are correct?
Select all of the following statements that are correct.
Answer: C and D.
A: MC counts only costs that change with one more unit; FC does not. B has the direction backward. D: MC = wage ÷ MP, so a falling MP means a rising MC.
Where MC crosses the averages
“The marginal cost curve always intersects the ATC and AVC curves at their minimum points.”
Answer: True.
Left of the crossing MC < average, so the average falls; right of it MC > average, so the average rises. The crossing is the bottom. Same for AVC.
Which curves move?
| What changes | MC | AVC | AFC | ATC |
|---|---|---|---|---|
| A variable input costs morewages, feed, fertilizer, cocoa, flour | ↑ | ↑ | — | ↑ |
| A fixed input costs moreland rent, a lease, insurance, equipment | — | — | ↑ | ↑ |
| Productivity fallsdrought, disease, fewer gallons per cow | ↑ | ↑ | — | ↑ |
Variable costs rise
If variable costs increase, which of the following is true?
Answer: A.
Variable costs enter MC, AVC and ATC. AFC = FC ÷ Q does not change.
Fixed costs fall
If fixed costs decrease:
Answer: A.
Lower FC lowers AFC and therefore ATC. MC and AVC contain no fixed cost. (AFC also shifts down, but C wrongly adds MC and AVC.)
The landowner cuts your lease
You lease several plots from a landowner each year. Recently, the landowner reduced the leasing rate. How would your cost curves be affected? (Select all that apply.)
Answer: A and D.
The lease is a fixed cost: AFC and ATC fall. AVC and MC do not change—and nothing here would make them rise.
Egg equipment costs more
Suppose the price of egg production equipment increases. How would this affect the cost curves of egg production?
Answer: B.
Equipment is a fixed input: AFC and ATC shift up. C has the wrong direction; AVC and MC do not change.
Cheaper flour at Jenny’s bakery
The price of flour, Jenny’s primary input, has fallen because of a surplus in wheat production. All else equal, how will this affect her average total cost (ATC) curve?
Answer: C.
Flour is a variable input: a lower price shifts MC, AVC and ATC down. A and B invent other changes; “all else equal” rules them out.
Organic feed doubles in price
How does a rise in organic input prices, such as the price of organic soybean meal doubling, affect the marginal cost (MC) of producing organic products?
Answer: A.
Soybean meal is feed, a variable input. Fixed costs never enter MC, so B has the right direction for the wrong reason.
No growth hormones
Organic dairy farms may not use synthetic growth hormones. How does this most directly affect the marginal cost (MC) of producing milk?
Answer: B.
Less milk per cow is lower productivity: more inputs per gallon, so MC rises (the third row of the recap table).
Cage-free eggs in the short run
Demand for cage-free eggs increases significantly, and farmers increase their production in the short run. What is likely to happen to the marginal cost of producing those eggs?
Answer: B.
In the short run the barns are fixed, so producing more runs into diminishing returns and MC rises. Economies of scale are a long-run idea.
Organic vs. nonorganic production functions
How would you compare the production function of an organic farm to that of a nonorganic farm?
Answer: A.
With the same inputs, organic rules (no synthetic fertilizer or hormones) give less output, so the organic production function lies below. Same land does not mean same output.
Back to supply: fertilizer costs more
Fertilizer, an input for corn production, becomes more expensive. Due to higher fertilizer prices, ____ for corn ____.
Answer: A · supply decreases.
A higher input price raises MC, so the supply curve shifts left. “Quantity supplied” would be a movement along the curve, caused only by a change in the corn price.