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MICROECONOMICSFrom bread ovens to budget lines
One bakery stall and one student's monthly budget. A firm deciding how many bakers to hire and a consumer deciding how to spend $160 turn out to be asking the same question: is one more unit worth it?
Cost theory and consumer theory usually arrive in separate chapters, and students tend to file them in separate drawers. That is a shame, because they run on one idea. A firm compares the revenue from one more unit with what it costs to make. A consumer compares what one more unit of a good is worth to them with what they give up to buy it. Both are decisions at the margin, and both have a graph whose slope is the whole story.
This post works one example from each side, end to end, with numbers you can check. Every figure is drawn to scale, and the interactive versions of both examples are in the Cost & Choice Lab.
Part 1: Riverside Sourdough
Riverside Sourdough sells loaves at a weekend farmers' market alongside dozens of other bakers. It cannot set its own price; loaves go for the market rate of $7.00, and if it asked for more, shoppers would walk to the next stall. That makes it a price taker, the defining feature of a perfectly competitive firm. It pays $40 a day in fixed costs (stall fee and oven rental) and $150 a day for each baker it hires.
Build the table first
Every column comes from a short formula. The thing to watch is which ones use changes and which use totals:
MPL = ΔQ ÷ ΔL · MC = ΔTC ÷ ΔQ = W ÷ MPL · ATC = TC ÷ Q · AVC = VC ÷ Q · MR = P
| Bakers | Loaves | TC | MPL | MC | ATC | AVC | Profit |
|---|---|---|---|---|---|---|---|
| 0 | 0 | $40 | — | — | — | — | −$40 |
| 1 | 20 | $190 | 20 | $7.50 | $9.50 | $7.50 | −$50 |
| 2 | 45 | $340 | 25 | $6.00 | $7.56 | $6.67 | −$25 |
| 3 | 75 | $490 | 30 | $5.00 | $6.53 | $6.00 | $35 |
| 4 | 95 | $640 | 20 | $7.50 | $6.74 | $6.32 | $25 |
| 5 | 105 | $790 | 10 | $15.00 | $7.52 | $7.14 | −$55 |
One row in full, the way it should be written out. Adding the 3rd baker takes output from 45 to 75 loaves, so MPL = (75 − 45) ÷ 1 = 30 loaves. Total cost rises by that baker's $150, so MC = 150 ÷ 30 = $5.00 a loaf. The shortcut W ÷ MPL gives the same $5.00, which is a free check on your arithmetic. And the sentence that turns numbers into economics: each of those 30 loaves costs $5.00 to make and sells for $7.00, so each one adds $2.00 to profit.
The output decision: the MC rule
A competitive firm produces where P = MR = MC. Table data almost never lands on that equality exactly, so use the working version: keep expanding while MR ≥ MC, and stop before MC climbs above MR.
- From 45 to 75 loaves (the 3rd baker), MC is $5.00, below MR of $7.00. Those loaves add to profit.
- From 75 to 95 loaves (the 4th baker), MC is $7.50, above $7.00. Each of those loaves loses $0.50.
So the stall should bake 75 loaves with 3 bakers, and the profit column confirms it: $35 is the highest number there.
Stopping at the first row where MC is above price. The 1st baker's MC ($7.50) is higher than $7.00, yet the stall should keep hiring, because MC is still falling. The 2nd and 3rd bakers are much more productive. The MC rule bites where MC is rising through the price line. When in doubt, read the profit column.
Lowest average cost is not highest profit. Producing at the bottom of ATC is the most efficient scale, not the most profitable one. Profit is decided at the margin.
The same decision in the labour market: the hiring rule
A firm hires workers up to the point where the value of the marginal product of labour equals the wage, VMPL = P × MPL = W. With table data, hire while VMPL ≥ W.
| Baker | MPL | VMPL = P × MPL | Wage | Decision |
|---|---|---|---|---|
| 3rd | 30 | $7 × 30 = $210 | $150 | Hire, adds $60 |
| 4th | 20 | $7 × 20 = $140 | $150 | Don't hire, loses $10 |
Both rules give the same answer, and that is not a coincidence. MC = W ÷ MPL ≤ P rearranges to P × MPL ≥ W. They are one condition written two ways: one counted in loaves, the other in workers.
Why MC eventually rises: diminishing returns
Diminishing marginal returns happen when at least one input is fixed (here, the oven and the stall), so each additional unit of the variable input adds less output than the one before. At Riverside Sourdough it starts with the 4th baker, whose MPL of 20 is below the 3rd's 30. Total output is still rising; it just rises by less each time, which is why the word is diminishing and not negative. And because MC = W ÷ MPL, a falling MPL is a rising MC. That is where the upward slope of the marginal cost curve comes from.
The Sourdough Stall lab has this exact table. Slide the number of bakers and watch both rules, the profit column and the diminishing-returns marker update. Then switch to Curve Kitchen and drag the price to see where P = MC lands.
Open the Sourdough Stall →Part 2: Devon's monthly fun budget
Devon, a college student, sets aside $160 a month for two things: dinners out with friends at $40 each (the vertical axis) and climbing-gym visits at $8 each (the horizontal axis).
The budget line
- Vertical intercept: everything on dinners, $160 ÷ $40 = 4 dinners, the point (0, 4).
- Horizontal intercept: everything on climbing, $160 ÷ $8 = 20 visits, the point (20, 0).
- Equation: start from 40Y + 8X = 160 and solve for Y: Y = 4 − (1/5)X.
The slope, −PX/PY = −8/40 = −1/5, is an opportunity cost: every climbing visit costs Devon a fifth of a dinner out. It is the same idea as the slope of a production possibilities frontier, covered in The shape of scarcity. There the trade-off is between two things an economy can make; here it is between two things one person can afford.
A pricing threshold puts a corner in the line
The climbing gym rewards regulars: the first 10 visits each month cost the usual $8, and every visit after the 10th costs $4. Whenever a price changes at a threshold, the budget line gets a kink. Work it point by point:
- Vertical intercept. If Devon never climbs, the deal never applies. It stays at (0, 4).
- The kink. The threshold is 10 visits, which cost 10 × $8 = $80. The other $80 buys $80 ÷ $40 = 2 dinners, so the kink sits at (10, 2). Because those first 10 visits are full price, the kink lies right on the original line.
- New horizontal intercept. Past the kink, the remaining $80 buys $80 ÷ $4 = 20 more visits, for 10 + 20 = 30 visits at (30, 0).
| Segment | Price ratio | Rise ÷ run check | Slope |
|---|---|---|---|
| Visits 1–10 at $8 | −8 ÷ 40 | (2 − 4) ÷ (10 − 0) | −1/5 |
| Visits 11+ at $4 | −4 ÷ 40 | (0 − 2) ÷ (30 − 10) | −1/10 |
Why do the slopes differ? Because the slope is the relative price, and the relative price changes at the threshold. For the first 10 visits, one visit costs a fifth of a dinner. After that, one visit costs a tenth of a dinner. Devon's income has not changed, and neither has the price of dinners. Only the relative price of climbing has, and only past the 10th visit.
Calculate every slope twice: once as a price ratio, once as rise over run between the points you labelled. If they disagree, one of your points is wrong. And before you draw anything, ask which units get the special price. That alone tells you whether the line gets flatter or steeper after the kink.
Budget Builder draws Devon's line with and without the loyalty price. Click any combination of dinners and visits and it tells you whether it's affordable, exactly on the line, or a dream basket.
Open Budget Builder →When a price rises: two effects at once
Now drop the loyalty deal, and suppose the gym raises its price from $8 to $10 a visit. Devon's horizontal intercept falls from 20 to 16 visits; the vertical intercept stays at 4, because dinners still cost $40. The line pivots inward around that vertical intercept and gets steeper. Economists split Devon's response into two parts:
- The substitution effect is the change caused only by the shift in relative prices, holding Devon's real income (or satisfaction) constant. A visit used to cost a fifth of a dinner; now it costs a quarter ($10 ÷ $40). Climbing is relatively dearer, so Devon substitutes toward dinners out. The substitution effect always moves consumption away from the good whose relative price rose.
- The income effect is the change caused by the fall in purchasing power. Devon still has $160, but it buys less than it did. If both activities are normal goods, less real income means less of both. For climbing, both effects point the same way, so visits clearly fall. For dinners, they pull in opposite directions, so the net change depends on which is larger.
"Devon's income fell." It didn't: Devon still has $160. What fell is real income, meaning what $160 can buy. Keeping money income and purchasing power apart is the difference between a good answer and a great one.
Effect Splitter gives you eight short scenarios and asks which effect each one describes. Listen for the tells: "instead" usually means substitution; "doesn't stretch as far" means income.
Open Effect Splitter →The through-line
The stall and the student are making the same kind of decision. The stall keeps hiring while the next baker brings in more than they cost. Devon chooses along a line whose slope is the price of one more visit in dinners given up. In both cases the graph is a picture of a trade-off, and its slope is the trade-off rate. Get the slope right and most of the answer follows.
Five questions to test yourself
Work each one through before opening the answer. Change one number, and see whether you can predict the result before you calculate it.
01A better price for bread
Loaves start selling for $8 instead of $7. How many bakers should Riverside Sourdough hire now? Check your answer with both rules.
Answer
Four bakers, 95 loaves. The 4th baker's MC is $7.50, which is now below the $8 price, so those 20 loaves are worth making. The 5th baker's MC is $15, far above it.
The hiring rule agrees: the 4th baker's VMPL is $8 × 20 = $160, more than the $150 wage; the 5th's is $8 × 10 = $80, less. Profit at 95 loaves is $760 − $640 = $120, the highest in the column.
02The stall fee doubles
The market doubles its daily stall fee from $40 to $80. Does the profit-maximizing number of loaves change?
Answer
No. A fixed cost is the same whatever you produce, so it never enters marginal cost. MC still crosses the $7 price at the same place: 3 bakers, 75 loaves.
What changes is profit: $525 − ($80 + $450) = −$5. The stall now loses money, but it still covers its variable costs (AVC is $6.00 at 75 loaves, below the $7 price), so it should keep baking in the short run. Closing would lose the whole $80.
03How low can the price go?
Roughly how far could the price of a loaf fall before Riverside Sourdough should shut down in the short run?
Answer
To about $6.00, the minimum of average variable cost, reached at 75 loaves. Above that, every loaf at least pays for the labour that made it, and the surplus chips away at the fixed cost. Below it, each loaf loses money even before the stall fee is counted, so producing nothing is the cheaper option.
04A deeper discount
Suppose visits after the 10th cost $2 instead of $4. Where would Devon's budget line now meet the horizontal axis? Does the kink move?
Answer
The kink stays at (10, 2): the first 10 visits are still $8 each, so they still cost $80 and leave $80 for 2 dinners.
From there, $80 ÷ $2 = 40 more visits, so the line meets the axis at 10 + 40 = 50 visits. The segment past the kink gets flatter again (slope −2/40 = −1/20). A bigger discount bends the line further out without moving the corner.
05Name the effect
Climbing goes up from $8 to $10 a visit. Which effect pushes Devon toward more dinners out, and which pushes toward fewer?
Answer
The substitution effect pushes toward more dinners. Climbing is now relatively dearer, so dinners are relatively cheaper, and Devon shifts toward them.
The income effect pushes toward fewer dinners, if dinners are a normal good. Devon's $160 buys less than before, so Devon cuts back on normal goods across the board. Which effect wins for dinners can't be known without more information. For climbing itself, both effects point the same way, so visits clearly fall.
A short checklist for cost and budget questions
- Every column built from its formula, with changes (Δ) kept separate from totals.
- MC checked two ways: ΔTC ÷ ΔQ and W ÷ MPL.
- Output chosen with MR and MC on both sides of your answer, not with the lowest ATC.
- VMPL calculated for the last worker hired and compared with the wage, and with the next worker's too.
- Diminishing returns identified from the MPL column: the first worker who adds less than the one before.
- Budget intercepts given as numbers and as points, and the equation solved for the vertical-axis good.
- For a kink, the threshold located first, then which side of it is cheaper, then both slopes checked two ways.
- Substitution and income effects each defined and applied to both goods, with money income kept separate from purchasing power.