Technical Reference

Model Formulas, Parameters, and Code Documentation

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Return to: Interactive Cost Model | New to this topic? How Cultured Chicken is Made

Overview

This document provides complete technical documentation for the cultured chicken cost model:

Model Formulas — Mathematical structure and equations
Parameter Definitions — All inputs with distributions and sources
Code Reference — Implementation details
Limitations — Known caveats and recommendations

Model Formulas

This section presents the model structure top-down: starting with the final output and unpacking each component.

1. Total Unit Cost

The model estimates unit production cost ($/kg) by summing four components:

\[\boxed{\text{Unit Cost} = \underbrace{\text{VOC}}_{\text{variable}} + \underbrace{\text{CAPEX}_{/\text{kg}}}_{\text{capital}} + \underbrace{\text{Fixed OPEX}_{/\text{kg}}}_{\text{overhead}} + \underbrace{\text{Downstream}_{/\text{kg}}}_{\text{optional}}}\]

What does each term mean?

Term	Description	Typical range
VOC	Variable operating costs — inputs that scale with production	$5–100/kg
CAPEX/kg	Annualized capital costs (bioreactors, facilities)	$1–20/kg
Fixed OPEX/kg	Labor, maintenance, overhead	$1–10/kg
Downstream/kg	Scaffolding, texturization (for structured products)	$2–15/kg if enabled

2. Variable Operating Costs (VOC)

VOC is the sum of four input categories:

\[\text{VOC} = \text{Media} + \text{Micronutrients} + \text{Growth Factors} + \text{Other}\]

2a. Media Cost

Media is the liquid nutrient broth that feeds growing cells. Media cost depends on how much liquid you need per kg of meat:

\[\text{Media Cost} = \underbrace{\left(\frac{1000}{\text{density}}\right)}_{\text{L per kg wet cells}} \times \underbrace{\text{turnover}}_{\text{media changes}} \times \underbrace{\text{price}}_{\text{\$/L}}\]

Variable definitions:

Cell density (g/L): Final concentration of cells at harvest. Higher density = less media needed per kg. The 1000 converts g/L to L/kg (since 1 kg = 1000 g).
Media turnover: How many times the media volume is replaced during a production run. Batch systems (turnover = 1) use one fill; perfusion systems (turnover = 3–10) continuously flow fresh media through.
Price ($/L): Cost per liter of complete media formulation.

Example calculation:

Cell density: 50 g/L → need 1000/50 = 20 L per kg
Media turnover: 3× (perfusion system) → 20 × 3 = 60 L total per kg
Media price: $0.50/L (hydrolysates) → 60 × 0.50 = $30/kg

Why does density vary? Achievable density depends on cell type, bioreactor design, and operating mode. Batch cultures typically reach 30–50 g/L; perfusion cultures with optimized conditions can reach 100–200 g/L (Humbird 2021).

Hydrolysates vs. pharma-grade amino acids:

Scenario	Price range ($/L)	What it means
With hydrolysates	$0.20 – $1.20	Amino acids from digested plant/yeast proteins (soy, wheat, etc.)
Pharma-grade amino acids	$1.00 – $4.00	Individual purified amino acids, as used in pharmaceutical manufacturing

Hydrolysates cost less because they’re produced from commodity feedstocks via enzymatic digestion, rather than synthetic chemistry or purification.

2b. Growth Factor Cost

Growth factors (FGF-2, IGF-1, TGF-β) are signaling proteins that tell cells to proliferate. They are the most price-volatile component:

\[\text{GF Cost} = \underbrace{g_{\text{GF}}}_{\text{grams/kg meat}} \times \underbrace{P_{\text{GF}}}_{\text{\$/gram}}\]

The GF Progress Slider

The dashboard’s GF Technology Progress slider lets you explore scenarios between today’s research prices and potential future breakthroughs:

\[P_{\text{GF}} = P_{\text{current}} \times (0.01)^{\text{progress}}\]

Where progress is the slider value (0 to 1):

Progress	Calculation	Effective price multiplier
0% (today)	$P \times 0.01^0 = P \times 1$	100% of current prices
50%	$P \times 0.01^{0.5} = P \times 0.1$	10% of current prices
100% (breakthrough)	$P \times 0.01^1 = P \times 0.01$	1% of current prices

This creates a smooth exponential interpolation: at 50% progress, prices are ~10× lower; at 100%, ~100× lower.

Why a Binary “Cheap vs. Expensive” Scenario?

The model also includes a Bernoulli toggle (coin flip) that switches between two price regimes. This is a simplification, but reflects real industry dynamics:

The breakthrough technologies are substitutes, not complements:

Autocrine cell lines — cells engineered to produce their own FGF2 → GF cost ≈ $0
Plant molecular farming — GFs expressed in tobacco/rice → target $1-10/g
Precision fermentation — microbial production at scale → target $10-100/g

If any one of these succeeds at commercial scale, the “cheap” price regime applies. The model doesn’t sum their effects because they’re alternative solutions to the same problem.

The uncertainty is discrete, not continuous:

At the pivotal question level, we’re asking: “Will at least one breakthrough technology reach commercial viability by 2036?” This is more naturally modeled as a probability (50%) than a continuous distribution.

The slider complements this by letting users explore “what if progress is partial?” scenarios.

3. Annualized Capital Costs

Capital costs are annualized using the Capital Recovery Factor (CRF):

\[\text{CAPEX}_{/\text{kg}} = \frac{\text{Total CAPEX} \times \text{CRF}}{\text{Annual Output (kg)}}\]

Where CRF converts a lump sum to annual payments:

\[\text{CRF} = \frac{r \cdot (1+r)^n}{(1+r)^n - 1}\]

What is CRF?

Capital Recovery Factor answers: “If I borrow $X at interest rate r for n years, what’s my annual payment?”

WACC	Asset Life	CRF	Meaning
10%	15 years	13.1%	Pay 13.1% of capital cost annually
15%	10 years	19.9%	Pay 19.9% of capital cost annually
20%	8 years	26.1%	Pay 26.1% of capital cost annually

Higher WACC or shorter asset life → higher annual capital charge.

4. Technology Adoption & Maturity

The model uses a maturity factor to create realistic correlations between different aspects of industry development. Without this, the Monte Carlo simulation would generate unrealistic scenarios (e.g., breakthrough growth factor technology but prohibitively expensive financing).

The Maturity Factor ($m$)

The maturity factor is a single number between 0 and 1 representing overall industry development:

$m = 0$: Nascent industry — early R&D stage, no scale-up
$m = 0.5$: Moderate development — pilots running, some commercial activity
$m = 1$: Mature industry — established supply chains, proven technology

Each simulation draws $m$ from a Beta distribution (default: mean 0.5, stdev 0.2).

How Maturity Adjusts Adoption Probabilities

Each technology’s adoption probability is adjusted based on the maturity draw:

\[P_{\text{adopted}} = \text{bound}\Big(P_{\text{base}} + k \cdot (m - 0.5),\; 0,\; 1\Big)\]

Where:

$P_{\text{base}}$ = base adoption probability for that technology (e.g., 0.75 for hydrolysates)
$k$ = sensitivity coefficient (how much maturity affects this technology; typically 0.20–0.30)
$m$ = maturity factor drawn for this simulation (0–1)
$\text{bound}(\cdot, 0, 1)$ = clips result to valid probability range [0, 1]

Example: If hydrolysates have $P_{\text{base}} = 0.75$ and $k = 0.25$:

In a “bad world” ($m = 0.2$): $P = 0.75 + 0.25 \times (0.2 - 0.5) = 0.675$
In a “good world” ($m = 0.8$): $P = 0.75 + 0.25 \times (0.8 - 0.5) = 0.825$

What does “bound” mean?

bound(x, 0, 1) ensures the result stays between 0 and 1. Also called “clip” or “clamp” in programming.

If x < 0, return 0
If x > 1, return 1
Otherwise, return x

This prevents impossible probabilities like -0.2 or 1.3.

What Gets Correlated

The maturity factor simultaneously adjusts:

Component	Effect when $m$ is high	Justification
Technology adoption rates	Higher probability of hydrolysates, cheap GFs	More R&D investment, proven pilots
Custom reactor share	More facilities use food-grade equipment	Supply chain development
WACC (financing cost)	Lower interest rates	Reduced investor risk perception

Why this matters: In a world where growth factor technology succeeds, it’s more plausible that: 1. Other technologies also succeed (shared R&D ecosystem) 2. Investors see lower risk (proven technology → cheaper capital) 3. Custom reactor suppliers exist (developed supply chain)

The maturity factor captures this “worlds come in bundles” intuition without requiring us to specify every pairwise correlation.

5. Monte Carlo Simulation

The model runs 30,000 simulations, each time:

Draw random values for all uncertain parameters
Draw technology adoption outcomes (Bernoulli coin flips)
Calculate unit cost for that scenario
Collect results into a distribution

This produces the histograms and probability thresholds shown in the dashboard.

Parameter Definitions

This section defines all model inputs. Each parameter links back to where it appears in the cost equations.

Basic Parameters

Parameter	Symbol	Distribution	Default	Unit	Used in
Plant capacity	$Q$	Lognormal(p5, p95)	5–50	kTA/year	CAPEX/kg, Fixed OPEX
Utilization	$u$	Beta(mean, sd)	0.90	fraction	Annual output = $Q \times u$
Maturity index	$m$	Beta(mean, sd)	0.50	0–1	Technology adoption, WACC adjustment

Why these distributions?

Lognormal for plant capacity: Capacity is positive and right-skewed (most plants are medium-sized, few are very large). Lognormal naturally captures this. The p5/p95 parameterization lets us specify “90% of plants are between 5 and 50 kTA.”
Beta for utilization and maturity: Both are bounded between 0 and 1. Beta distributions are flexible for modeling proportions and can be parameterized with mean/stdev.

These choices follow standard practice in techno-economic assessments (Humbird 2021, Risner et al. 2021).

Technology Adoption

Each technology has a base adoption probability, adjusted by the maturity factor:

\[ P_{\text{adopted}} = \text{bound}(P_{\text{base}} + k \times (m - 0.5), 0, 1) \]

Technology	Base Prob	$k$	Effect on cost	Notes
Hydrolysates	75%	0.25	Reduces media $/L by ~70%	Plant/yeast protein digests replace purified amino acids
Food-grade micronutrients	65%	0.20	Reduces micronutrient $/g by ~90%	Commodity vitamins/minerals vs. pharma-grade
Scalable GF technology	50%	0.25	Switches to “cheap” GF prices	Any breakthrough: autocrine, plant farming, precision fermentation

Process Intensities

These parameters determine how much media is needed per kg of meat. See Media Cost equation.

Parameter	Range (p5–p95)	Unit	Definition	Cost impact
Cell density	30–200	g/L	Final biomass concentration at harvest	Higher → less media per kg
Cycle time	0.5–5	days	Duration of one production batch	Affects throughput, not directly in cost equation
Media turnover	1–10	×	Times media is replaced per batch	Higher → more media cost, but enables higher density

Media turnover explained: In batch mode (turnover = 1), the reactor is filled once and cells grow until nutrients deplete. In perfusion mode (turnover > 1), fresh media continuously flows in while spent media exits. Perfusion uses more media but achieves higher cell densities.

Growth Factor Price Scenarios

The model uses two discrete price scenarios, selected by a Bernoulli draw (see why binary above):

Scenario	Quantity (g/kg)	Price ($/g)	What it represents
Scalable tech achieved	0.0001 – 0.005	$1 – $100	At least one breakthrough reaches commercial scale
Limited progress	0.0005 – 0.02	$500 – $50,000	Incremental improvements only; no step-change

Why different quantities too? Breakthrough technologies often reduce both price and required amount:

Thermostable variants (e.g., FGF2-G3 from Enantis) have 20-day half-life vs. hours, reducing dosing frequency
Autocrine lines produce GFs continuously, maintaining optimal concentrations
Recycling systems recover GFs from spent media

Breakthrough technologies (any one could trigger “cheap”):

Technology	Mechanism	Current status	Target price
Autocrine cell lines	Cells engineered to produce own FGF2	Proof of concept	~$0/g
Plant molecular farming	GFs expressed in tobacco, rice	Pilot scale	$1–10/g
Precision fermentation	Microbial production at scale	Scaling up	$10–100/g
Small molecule substitutes	Chemicals that activate GF receptors	Research	<$1/g

Capital Cost Parameters

Reference Scale: Why 20 kTA?

The model defines CAPEX at a reference scale of 20 kTA (20,000 metric tons/year), then adjusts for actual plant size using economies of scale. We use 20 kTA because:

It matches the scale in Risner et al. (2021), enabling direct comparison
It represents a plausible first commercial-scale facility
Published cost estimates are most reliable around this scale

Economies of Scale: The $K \sim Q^s$ Relationship

Capital costs don’t scale linearly with capacity. A plant 10× larger doesn’t cost 10× more — it benefits from economies of scale:

\[\text{CAPEX} = \text{CAPEX}_{\text{ref}} \times \left(\frac{Q}{Q_{\text{ref}}}\right)^s\]

Where:

$K$ = total capital cost (we use $K$ as shorthand for CAPEX)
$Q$ = plant capacity; $Q_{\text{ref}}$ = reference capacity (20 kTA)
$s$ = scale exponent (0.6–0.9)

What the exponent means:

Scale exponent $s$	If capacity doubles…	Example industries
1.0	CAPEX doubles (no economies)	Modular, containerized systems
0.7	CAPEX increases 62%	Chemical plants, refineries
0.6	CAPEX increases 52%	Power plants, large bioreactors

The range 0.6–0.9 reflects uncertainty about whether cultured meat will achieve chemical-industry economies (0.6) or remain more modular (0.9).

Pharma-Grade vs. Food-Grade Equipment

Pharma-grade bioreactors are built to pharmaceutical manufacturing standards:

316L stainless steel, electropolished surfaces
Extensive validation, documentation
Designed for injectable drug production
Cost: $50–500 per liter installed capacity

Food-grade (or “custom”) equipment is simpler:

Standard stainless steel (304 or food-grade 316)
Less stringent validation
Similar to brewing or dairy equipment
Target cost: $10–50 per liter — comparable to beer brewing ($5–15/L)

The custom reactor ratio (0.35–0.85) represents the cost of food-grade equipment relative to pharma-grade. At 0.5, custom equipment costs half as much.

Parameter	Range	Definition	Where it appears
WACC	8–20%	Weighted average cost of capital	CRF equation — the $r$ term
Asset life	8–20 years	How long equipment lasts before replacement	CRF equation — the $n$ term
Scale exponent	0.6–0.9	Economies of scale (see above)	CAPEX scaling
Pharma-grade CAPEX	$5–25/kg capacity	At 20 kTA reference scale	Baseline capital cost
Custom reactor ratio	0.35–0.85	Food-grade cost ÷ pharma-grade cost	Equipment type mix

WACC Justification

WACC (Weighted Average Cost of Capital) represents the blended cost of debt and equity financing. Our 8–20% range reflects:

Benchmark	Typical WACC	Source
Established food companies	6–10%	Industry averages
Biotech startups (pre-revenue)	15–25%	VC expected returns
Cultured meat companies	12–20%	Humbird (2021) assumption

The high end (20%) reflects that most cultured meat companies are venture-backed with no revenue. As the industry matures (higher $m$), WACC should decline toward food-industry norms.

Code Reference

The full model implementation is available in multiple formats:

Format	Location	Notes
JavaScript (interactive)	Embedded in dashboard	Primary implementation
Python (reference)	dashboard/model.py	Standalone script
Squiggle (reference)	models/cm_cost_v0.2.squiggle	Synced with dashboard parameters

Key Functions

The JavaScript implementation includes:

simulate(n, seed, params) — Main Monte Carlo loop
sampleLognormalP5P95(rng, p5, p95, n) — Sample from lognormal given percentiles
sampleBetaMeanStdev(rng, mean, sd, n) — Sample from beta distribution
crf(wacc, years) — Capital Recovery Factor calculation
spearmanCorr(x, y) — Rank correlation for sensitivity analysis

View the page source for the complete implementation.

Limitations

Known Limitations

Static snapshot model — Projects costs for a single target year (adjustable 2026-2050). Does not model year-over-year learning curves; instead, the “maturity” parameter serves as a proxy for cumulative industry development.
Downstream is optional — Scaffolding, texturization, and forming costs can be included via toggle (+$2-15/kg for structured products).
No geography — Assumes generic global costs, not region-specific labor, energy, or regulatory factors.
Limited contamination modeling — No batch failure or contamination event distributions.
Some correlations may be underspecified — While the maturity factor induces correlation between technology adoption, reactor costs, and WACC, other potential correlations (e.g., between cell density and cycle time) are treated as independent.

Recommendations for Use

Recommendation	What it means	Why
Use for relative comparisons	Compare scenarios: “How much does cheap GF technology reduce costs?” rather than “Costs will be $X/kg”	Parameter uncertainty is wide; the difference between scenarios is more robust than absolute values
Focus on probability thresholds	Ask “What’s P(cost < $10/kg)?” not “What’s the expected cost?”	Probabilities integrate over uncertainty and map to decisions (“Is this worth pursuing?”)
Validate parameters with experts	Before publishing, check that ranges match current industry knowledge	Published literature lags industry by 1–3 years; some parameters (GF costs) change rapidly
Report uncertainty ranges	Always show 90% CI, not just median	Wide intervals reflect genuine uncertainty; suppressing them gives false confidence
Explore correlated scenarios	Use the maturity slider to see “good world” vs “bad world” bundles	Technologies, financing, and supply chains develop together — independent draws miss this

What “relative comparisons” means in practice:

✅ Good use: “Achieving 150 g/L cell density instead of 50 g/L would reduce costs by 40–60%”

❌ Risky use: “Cultured chicken will cost $8.50/kg by 2030”

The model is better at estimating how much a technology improvement helps than what the final cost will be, because relative effects are less sensitive to baseline assumptions.

Sources

Risner et al. (2021) - UC Davis ACBM Calculator — Original academic cost model
Humbird (2021) - Scale-Up Economics — Independent TEA analysis
Good Food Institute - State of the Industry Reports — Annual industry overview
The Unjournal - Cultured Meat Evaluations — Independent research evaluations

Changelog

Version	Date	Changes
v0.3	2026-02	Separated Learn page, consolidated technical docs
v0.2	2026-02	Explicit scale/uptime, beta distributions, maturity factor
v0.1	2026-01	Initial Squiggle model based on UC Davis

--- title: "Technical Reference" subtitle: "Model Formulas, Parameters, and Code Documentation" toc: true format: html: include-after-body: text: | <script src="https://hypothes.is/embed.js" async></script> --- ::: {.callout-tip} **Return to:** [Interactive Cost Model](index.qmd) | **New to this topic?** [How Cultured Chicken is Made](learn.qmd) ::: ## Overview This document provides complete technical documentation for the cultured chicken cost model: - [Model Formulas](#model-formulas) — Mathematical structure and equations - [Parameter Definitions](#parameter-definitions) — All inputs with distributions and sources - [Code Reference](#code-reference) — Implementation details - [Limitations](#limitations) — Known caveats and recommendations --- ## Model Formulas {#model-formulas} This section presents the model structure **top-down**: starting with the final output and unpacking each component. ### 1. Total Unit Cost The model estimates **unit production cost** ($/kg) by summing four components: $$\boxed{\text{Unit Cost} = \underbrace{\text{VOC}}_{\text{variable}} + \underbrace{\text{CAPEX}_{/\text{kg}}}_{\text{capital}} + \underbrace{\text{Fixed OPEX}_{/\text{kg}}}_{\text{overhead}} + \underbrace{\text{Downstream}_{/\text{kg}}}_{\text{optional}}}$$ <details> <summary>What does each term mean?</summary> | Term | Description | Typical range | |------|-------------|---------------| | **VOC** | Variable operating costs — inputs that scale with production | $5–100/kg | | **CAPEX/kg** | Annualized capital costs (bioreactors, facilities) | $1–20/kg | | **Fixed OPEX/kg** | Labor, maintenance, overhead | $1–10/kg | | **Downstream/kg** | Scaffolding, texturization (for structured products) | $2–15/kg if enabled | </details> ### 2. Variable Operating Costs (VOC) VOC is the sum of four input categories: $$\text{VOC} = \text{Media} + \text{Micronutrients} + \text{Growth Factors} + \text{Other}$$ <details> <summary>2a. Media Cost</summary> Media is the liquid nutrient broth that feeds growing cells. Media cost depends on **how much liquid** you need per kg of meat: $$\text{Media Cost} = \underbrace{\left(\frac{1000}{\text{density}}\right)}_{\text{L per kg wet cells}} \times \underbrace{\text{turnover}}_{\text{media changes}} \times \underbrace{\text{price}}_{\text{\$/L}}$$ **Variable definitions:** - **Cell density (g/L)**: Final concentration of cells at harvest. Higher density = less media needed per kg. The 1000 converts g/L to L/kg (since 1 kg = 1000 g). - **Media turnover**: How many times the media volume is replaced during a production run. Batch systems (turnover = 1) use one fill; perfusion systems (turnover = 3–10) continuously flow fresh media through. - **Price ($/L)**: Cost per liter of complete media formulation. **Example calculation:** - Cell density: 50 g/L → need 1000/50 = 20 L per kg - Media turnover: 3× (perfusion system) → 20 × 3 = 60 L total per kg - Media price: $0.50/L (hydrolysates) → 60 × 0.50 = **$30/kg** **Why does density vary?** Achievable density depends on cell type, bioreactor design, and operating mode. Batch cultures typically reach 30–50 g/L; perfusion cultures with optimized conditions can reach 100–200 g/L ([Humbird 2021](https://www.sciencedirect.com/science/article/pii/S2589014X21000026)). **Hydrolysates vs. pharma-grade amino acids:** | Scenario | Price range ($/L) | What it means | |----------|-------------------|---------------| | With hydrolysates | $0.20 – $1.20 | Amino acids from digested plant/yeast proteins (soy, wheat, etc.) | | Pharma-grade amino acids | $1.00 – $4.00 | Individual purified amino acids, as used in pharmaceutical manufacturing | Hydrolysates cost less because they're produced from commodity feedstocks via enzymatic digestion, rather than synthetic chemistry or purification. </details> <details> <summary>2b. Growth Factor Cost</summary> Growth factors (FGF-2, IGF-1, TGF-β) are signaling proteins that tell cells to proliferate. They are the most price-volatile component: $$\text{GF Cost} = \underbrace{g_{\text{GF}}}_{\text{grams/kg meat}} \times \underbrace{P_{\text{GF}}}_{\text{\$/gram}}$$ #### The GF Progress Slider The dashboard's **GF Technology Progress** slider lets you explore scenarios between today's research prices and potential future breakthroughs: $$P_{\text{GF}} = P_{\text{current}} \times (0.01)^{\text{progress}}$$ Where **progress** is the slider value (0 to 1): | Progress | Calculation | Effective price multiplier | |----------|-------------|---------------------------| | 0% (today) | $P \times 0.01^0 = P \times 1$ | 100% of current prices | | 50% | $P \times 0.01^{0.5} = P \times 0.1$ | 10% of current prices | | 100% (breakthrough) | $P \times 0.01^1 = P \times 0.01$ | 1% of current prices | This creates a smooth exponential interpolation: at 50% progress, prices are ~10× lower; at 100%, ~100× lower. #### Why a Binary "Cheap vs. Expensive" Scenario? The model also includes a **Bernoulli toggle** (coin flip) that switches between two price regimes. This is a simplification, but reflects real industry dynamics: **The breakthrough technologies are substitutes, not complements:** - **Autocrine cell lines** — cells engineered to produce their own FGF2 → GF cost ≈ $0 - **Plant molecular farming** — GFs expressed in tobacco/rice → target $1-10/g - **Precision fermentation** — microbial production at scale → target $10-100/g If **any one** of these succeeds at commercial scale, the "cheap" price regime applies. The model doesn't sum their effects because they're alternative solutions to the same problem. **The uncertainty is discrete, not continuous:** At the pivotal question level, we're asking: "Will at least one breakthrough technology reach commercial viability by 2036?" This is more naturally modeled as a probability (50%) than a continuous distribution. The slider complements this by letting users explore "what if progress is partial?" scenarios. </details> ### 3. Annualized Capital Costs Capital costs are **annualized** using the Capital Recovery Factor (CRF): $$\text{CAPEX}_{/\text{kg}} = \frac{\text{Total CAPEX} \times \text{CRF}}{\text{Annual Output (kg)}}$$ Where CRF converts a lump sum to annual payments: $$\text{CRF} = \frac{r \cdot (1+r)^n}{(1+r)^n - 1}$$ <details> <summary>What is CRF?</summary> **Capital Recovery Factor** answers: "If I borrow $X at interest rate r for n years, what's my annual payment?" | WACC | Asset Life | CRF | Meaning | |------|------------|-----|---------| | 10% | 15 years | 13.1% | Pay 13.1% of capital cost annually | | 15% | 10 years | 19.9% | Pay 19.9% of capital cost annually | | 20% | 8 years | 26.1% | Pay 26.1% of capital cost annually | Higher WACC or shorter asset life → higher annual capital charge. </details> ### 4. Technology Adoption & Maturity {#maturity-factor} The model uses a **maturity factor** to create realistic correlations between different aspects of industry development. Without this, the Monte Carlo simulation would generate unrealistic scenarios (e.g., breakthrough growth factor technology but prohibitively expensive financing). #### The Maturity Factor ($m$) The maturity factor is a single number between 0 and 1 representing overall industry development: - **$m = 0$**: Nascent industry — early R&D stage, no scale-up - **$m = 0.5$**: Moderate development — pilots running, some commercial activity - **$m = 1$**: Mature industry — established supply chains, proven technology Each simulation draws $m$ from a Beta distribution (default: mean 0.5, stdev 0.2). #### How Maturity Adjusts Adoption Probabilities Each technology's adoption probability is adjusted based on the maturity draw: $$P_{\text{adopted}} = \text{bound}\Big(P_{\text{base}} + k \cdot (m - 0.5),\; 0,\; 1\Big)$$ Where: - $P_{\text{base}}$ = base adoption probability for that technology (e.g., 0.75 for hydrolysates) - $k$ = sensitivity coefficient (how much maturity affects this technology; typically 0.20–0.30) - $m$ = maturity factor drawn for this simulation (0–1) - $\text{bound}(\cdot, 0, 1)$ = clips result to valid probability range [0, 1] **Example:** If hydrolysates have $P_{\text{base}} = 0.75$ and $k = 0.25$: - In a "bad world" ($m = 0.2$): $P = 0.75 + 0.25 \times (0.2 - 0.5) = 0.675$ - In a "good world" ($m = 0.8$): $P = 0.75 + 0.25 \times (0.8 - 0.5) = 0.825$ <details> <summary>What does "bound" mean?</summary> **bound(x, 0, 1)** ensures the result stays between 0 and 1. Also called "clip" or "clamp" in programming. - If x < 0, return 0 - If x > 1, return 1 - Otherwise, return x This prevents impossible probabilities like -0.2 or 1.3. </details> #### What Gets Correlated The maturity factor simultaneously adjusts: | Component | Effect when $m$ is high | Justification | |-----------|------------------------|---------------| | Technology adoption rates | Higher probability of hydrolysates, cheap GFs | More R&D investment, proven pilots | | Custom reactor share | More facilities use food-grade equipment | Supply chain development | | WACC (financing cost) | Lower interest rates | Reduced investor risk perception | **Why this matters:** In a world where growth factor technology succeeds, it's more plausible that: 1. Other technologies also succeed (shared R&D ecosystem) 2. Investors see lower risk (proven technology → cheaper capital) 3. Custom reactor suppliers exist (developed supply chain) The maturity factor captures this "worlds come in bundles" intuition without requiring us to specify every pairwise correlation. ### 5. Monte Carlo Simulation The model runs **30,000 simulations**, each time: 1. Draw random values for all uncertain parameters 2. Draw technology adoption outcomes (Bernoulli coin flips) 3. Calculate unit cost for that scenario 4. Collect results into a distribution This produces the histograms and probability thresholds shown in the dashboard. --- ## Parameter Definitions {#parameter-definitions} This section defines all model inputs. Each parameter links back to where it appears in the [cost equations](#model-formulas). ### Basic Parameters | Parameter | Symbol | Distribution | Default | Unit | Used in | |-----------|--------|--------------|---------|------|---------| | Plant capacity | $Q$ | Lognormal(p5, p95) | 5–50 | kTA/year | [CAPEX/kg](#annualized-capital-costs), Fixed OPEX | | Utilization | $u$ | Beta(mean, sd) | 0.90 | fraction | Annual output = $Q \times u$ | | Maturity index | $m$ | Beta(mean, sd) | 0.50 | 0–1 | [Technology adoption](#maturity-factor), WACC adjustment | **Why these distributions?** - **Lognormal** for plant capacity: Capacity is positive and right-skewed (most plants are medium-sized, few are very large). Lognormal naturally captures this. The p5/p95 parameterization lets us specify "90% of plants are between 5 and 50 kTA." - **Beta** for utilization and maturity: Both are bounded between 0 and 1. Beta distributions are flexible for modeling proportions and can be parameterized with mean/stdev. These choices follow standard practice in techno-economic assessments ([Humbird 2021](https://www.sciencedirect.com/science/article/pii/S2589014X21000026), [Risner et al. 2021](https://www.mdpi.com/2304-8158/10/1/3)). ### Technology Adoption Each technology has a base adoption probability, adjusted by the [maturity factor](#maturity-factor): $$ P_{\text{adopted}} = \text{bound}(P_{\text{base}} + k \times (m - 0.5), 0, 1) $$ | Technology | Base Prob | $k$ | Effect on cost | Notes | |------------|-----------|-----|----------------|-------| | [Hydrolysates](learn.qmd#hydrolysates-the-big-win-for-amino-acids) | 75% | 0.25 | Reduces media $/L by ~70% | Plant/yeast protein digests replace purified amino acids | | [Food-grade micronutrients](learn.qmd#media-composition) | 65% | 0.20 | Reduces micronutrient $/g by ~90% | Commodity vitamins/minerals vs. pharma-grade | | [Scalable GF technology](learn.qmd#growth-factors-the-pivotal-challenge) | 50% | 0.25 | Switches to "cheap" GF prices | Any breakthrough: autocrine, plant farming, precision fermentation | ### Process Intensities These parameters determine how much media is needed per kg of meat. See [Media Cost equation](#variable-operating-costs-voc). | Parameter | Range (p5–p95) | Unit | Definition | Cost impact | |-----------|----------------|------|------------|-------------| | Cell density | 30–200 | g/L | Final biomass concentration at harvest | Higher → less media per kg | | Cycle time | 0.5–5 | days | Duration of one production batch | Affects throughput, not directly in cost equation | | Media turnover | 1–10 | × | Times media is replaced per batch | Higher → more media cost, but enables higher density | **Media turnover explained:** In **batch mode** (turnover = 1), the reactor is filled once and cells grow until nutrients deplete. In **perfusion mode** (turnover > 1), fresh media continuously flows in while spent media exits. Perfusion uses more media but achieves higher cell densities. ### Growth Factor Price Scenarios {#gf-scenarios} The model uses two discrete price scenarios, selected by a Bernoulli draw (see [why binary](#why-a-binary-cheap-vs-expensive-scenario) above): | Scenario | Quantity (g/kg) | Price ($/g) | What it represents | |----------|----------------|-------------|-------------------| | **Scalable tech achieved** | 0.0001 – 0.005 | $1 – $100 | At least one breakthrough reaches commercial scale | | **Limited progress** | 0.0005 – 0.02 | $500 – $50,000 | Incremental improvements only; no step-change | **Why different quantities too?** Breakthrough technologies often reduce both price and required amount: - **Thermostable variants** (e.g., [FGF2-G3 from Enantis](https://www.enantis.com/)) have 20-day half-life vs. hours, reducing dosing frequency - **Autocrine lines** produce GFs continuously, maintaining optimal concentrations - **Recycling systems** recover GFs from spent media **Breakthrough technologies (any one could trigger "cheap"):** | Technology | Mechanism | Current status | Target price | |------------|-----------|----------------|--------------| | Autocrine cell lines | Cells engineered to produce own FGF2 | [Proof of concept](https://pmc.ncbi.nlm.nih.gov/articles/PMC10153192/) | ~$0/g | | Plant molecular farming | GFs expressed in tobacco, rice | Pilot scale | $1–10/g | | Precision fermentation | Microbial production at scale | Scaling up | $10–100/g | | Small molecule substitutes | Chemicals that activate GF receptors | Research | <$1/g | ### Capital Cost Parameters {#capex-parameters} #### Reference Scale: Why 20 kTA? The model defines CAPEX at a **reference scale of 20 kTA** (20,000 metric tons/year), then adjusts for actual plant size using economies of scale. We use 20 kTA because: 1. It matches the scale in [Risner et al. (2021)](https://www.mdpi.com/2304-8158/10/1/3), enabling direct comparison 2. It represents a plausible first commercial-scale facility 3. Published cost estimates are most reliable around this scale #### Economies of Scale: The $K \sim Q^s$ Relationship Capital costs don't scale linearly with capacity. A plant 10× larger doesn't cost 10× more — it benefits from **economies of scale**: $$\text{CAPEX} = \text{CAPEX}_{\text{ref}} \times \left(\frac{Q}{Q_{\text{ref}}}\right)^s$$ Where: - $K$ = total capital cost (we use $K$ as shorthand for CAPEX) - $Q$ = plant capacity; $Q_{\text{ref}}$ = reference capacity (20 kTA) - $s$ = scale exponent (0.6–0.9) **What the exponent means:** | Scale exponent $s$ | If capacity doubles... | Example industries | |--------------------|------------------------|-------------------| | 1.0 | CAPEX doubles (no economies) | Modular, containerized systems | | 0.7 | CAPEX increases 62% | Chemical plants, refineries | | 0.6 | CAPEX increases 52% | Power plants, large bioreactors | The range 0.6–0.9 reflects uncertainty about whether cultured meat will achieve chemical-industry economies (0.6) or remain more modular (0.9). #### Pharma-Grade vs. Food-Grade Equipment **Pharma-grade** bioreactors are built to pharmaceutical manufacturing standards: - 316L stainless steel, electropolished surfaces - Extensive validation, documentation - Designed for injectable drug production - Cost: **$50–500 per liter** installed capacity **Food-grade** (or "custom") equipment is simpler: - Standard stainless steel (304 or food-grade 316) - Less stringent validation - Similar to brewing or dairy equipment - Target cost: **$10–50 per liter** — comparable to [beer brewing ($5–15/L)](https://www.brewersassociation.org/) The **custom reactor ratio** (0.35–0.85) represents the cost of food-grade equipment relative to pharma-grade. At 0.5, custom equipment costs half as much. | Parameter | Range | Definition | Where it appears | |-----------|-------|------------|------------------| | WACC | 8–20% | Weighted average cost of capital | [CRF equation](#annualized-capital-costs) — the $r$ term | | Asset life | 8–20 years | How long equipment lasts before replacement | [CRF equation](#annualized-capital-costs) — the $n$ term | | Scale exponent | 0.6–0.9 | Economies of scale (see above) | CAPEX scaling | | Pharma-grade CAPEX | $5–25/kg capacity | At 20 kTA reference scale | Baseline capital cost | | Custom reactor ratio | 0.35–0.85 | Food-grade cost ÷ pharma-grade cost | Equipment type mix | #### WACC Justification **WACC (Weighted Average Cost of Capital)** represents the blended cost of debt and equity financing. Our 8–20% range reflects: | Benchmark | Typical WACC | Source | |-----------|--------------|--------| | Established food companies | 6–10% | Industry averages | | Biotech startups (pre-revenue) | 15–25% | VC expected returns | | Cultured meat companies | 12–20% | [Humbird (2021)](https://www.sciencedirect.com/science/article/pii/S2589014X21000026) assumption | The high end (20%) reflects that most cultured meat companies are venture-backed with no revenue. As the industry matures ([higher $m$](#maturity-factor)), WACC should decline toward food-industry norms. --- ## Code Reference {#code-reference} The full model implementation is available in multiple formats: | Format | Location | Notes | |--------|----------|-------| | **JavaScript** (interactive) | Embedded in [dashboard](index.qmd) | Primary implementation | | **Python** (reference) | [dashboard/model.py](https://github.com/unjournal/cm_pq_modeling/blob/main/dashboard/model.py) | Standalone script | | **Squiggle** (reference) | [models/cm_cost_v0.2.squiggle](https://github.com/unjournal/cm_pq_modeling/blob/main/models/cm_cost_v0.2.squiggle) | Synced with dashboard parameters | ### Key Functions The JavaScript implementation includes: - `simulate(n, seed, params)` — Main Monte Carlo loop - `sampleLognormalP5P95(rng, p5, p95, n)` — Sample from lognormal given percentiles - `sampleBetaMeanStdev(rng, mean, sd, n)` — Sample from beta distribution - `crf(wacc, years)` — Capital Recovery Factor calculation - `spearmanCorr(x, y)` — Rank correlation for sensitivity analysis View the [page source](https://github.com/unjournal/cm_pq_modeling/blob/main/dashboard/index.qmd) for the complete implementation. --- ## Limitations {#limitations} ### Known Limitations 1. **Static snapshot model** — Projects costs for a single target year (adjustable 2026-2050). Does not model year-over-year learning curves; instead, the "maturity" parameter serves as a proxy for cumulative industry development. 2. **Downstream is optional** — Scaffolding, texturization, and forming costs can be included via toggle (+$2-15/kg for structured products). 3. **No geography** — Assumes generic global costs, not region-specific labor, energy, or regulatory factors. 4. **Limited contamination modeling** — No batch failure or contamination event distributions. 5. **Some correlations may be underspecified** — While the maturity factor induces correlation between technology adoption, reactor costs, and WACC, other potential correlations (e.g., between cell density and cycle time) are treated as independent. ### Recommendations for Use | Recommendation | What it means | Why | |----------------|---------------|-----| | Use for **relative comparisons** | Compare scenarios: "How much does cheap GF technology reduce costs?" rather than "Costs will be $X/kg" | Parameter uncertainty is wide; the *difference* between scenarios is more robust than absolute values | | Focus on **probability thresholds** | Ask "What's P(cost < $10/kg)?" not "What's the expected cost?" | Probabilities integrate over uncertainty and map to decisions ("Is this worth pursuing?") | | **Validate parameters** with experts | Before publishing, check that ranges match current industry knowledge | Published literature lags industry by 1–3 years; some parameters (GF costs) change rapidly | | **Report uncertainty ranges** | Always show 90% CI, not just median | Wide intervals reflect genuine uncertainty; suppressing them gives false confidence | | **Explore correlated scenarios** | Use the [maturity slider](#maturity-factor) to see "good world" vs "bad world" bundles | Technologies, financing, and supply chains develop together — independent draws miss this | **What "relative comparisons" means in practice:** ✅ **Good use:** "Achieving 150 g/L cell density instead of 50 g/L would reduce costs by 40–60%" ❌ **Risky use:** "Cultured chicken will cost $8.50/kg by 2030" The model is better at estimating *how much* a technology improvement helps than *what the final cost will be*, because relative effects are less sensitive to baseline assumptions. --- ## Sources - [Risner et al. (2021) - UC Davis ACBM Calculator](https://www.mdpi.com/2304-8158/10/1/3) — Original academic cost model - [Humbird (2021) - Scale-Up Economics](https://www.sciencedirect.com/science/article/pii/S2589014X21000026) — Independent TEA analysis - [Good Food Institute - State of the Industry Reports](https://gfi.org) — Annual industry overview - [The Unjournal - Cultured Meat Evaluations](https://unjournal.org) — Independent research evaluations --- ## Changelog | Version | Date | Changes | |---------|------|---------| | v0.3 | 2026-02 | Separated Learn page, consolidated technical docs | | v0.2 | 2026-02 | Explicit scale/uptime, beta distributions, maturity factor | | v0.1 | 2026-01 | Initial Squiggle model based on UC Davis |

Technical Reference

Overview

Model Formulas

1. Total Unit Cost

2. Variable Operating Costs (VOC)

The GF Progress Slider

Why a Binary “Cheap vs. Expensive” Scenario?

3. Annualized Capital Costs

4. Technology Adoption & Maturity

The Maturity Factor (\(m\))

How Maturity Adjusts Adoption Probabilities

What Gets Correlated

5. Monte Carlo Simulation

Parameter Definitions

Basic Parameters

Technology Adoption

Process Intensities

Growth Factor Price Scenarios

Capital Cost Parameters

Reference Scale: Why 20 kTA?

Economies of Scale: The \(K \sim Q^s\) Relationship

Pharma-Grade vs. Food-Grade Equipment

WACC Justification

Code Reference

Key Functions

Limitations

Known Limitations

Recommendations for Use

Sources

Changelog