Cost Basics & LCOE

Finishing sustainable finance: the firm's profit-max problem

The plain-vanilla firm problem

What: Firm maximizes revenue minus costs with inputs capital $K$, labor $L$, and fossil energy $E$. To simplify: normalize the output price to 1 and abstract from labor, so the firm maximizes output minus cost of capital and energy.

Why: Everything in economics reduces to the same answer in disguise — the optimum is where marginal cost equals marginal benefit (MC = MB).

Remember: Restaurant intuition — keep buying pizza ovens until the marginal benefit (extra output from one more oven, holding chefs fixed) equals the marginal cost (the interest rate / cost of capital). The marginal benefit curve slopes down (1st oven essential, 11th oven nearly useless). Same logic for fossil energy: buy natural gas until the extra profit equals its price. (Live example: Strait of Hormuz closed → gas prices up → a fertilizer producer using the Haber-Bosch process buys less gas.)

Sustainable finance changes the problem: cost of capital becomes a function of emissions

What: With sustainable-finance incentives, the interest rate the firm faces is now $r(E)$ — the more fossil energy it uses, the higher its cost of capital.

Why: The MC = MB rule still holds, but what counts as cost has changed. Two effects follow.

• Growth effect. A green firm gets a cheaper cost of capital → $\partial F/\partial K = r$ is satisfied at a higher $K$ → the firm expands its operations and market share. In energy markets you want the solar firms (not coal firms) to expand — this is what sustainable finance could in theory deliver.
• Reform effect. For a fossil-heavy firm, every extra unit of $E$ raises the capital cost — a de facto tax on fossil energy. The effective first-order condition becomes $$\frac{\partial F}{\partial E} = p_E + \frac{\partial r}{\partial E}\cdot K$$ The reform effect is bigger than it looks because $(\partial r/\partial E)\cdot K$ applies to the entire capital stock, not just the marginal unit.

Remember: This is the de-facto-tax intuition: raising the effective price of fossil energy makes firms choose a bit less of it.

Aside — degrowth

Barrage's economist take: the long-run source of sustainable growth (Macro 101) is productivity — doing more with less, which by definition lowers the resource footprint. The problem isn't growth itself but misdirected growth (externalities, wrong prices). Material-input prices have mostly fallen, suggesting scarcity isn't yet a binding constraint — efficiency gains have kept pace with extraction. Fix: get prices right so we use resources more wisely. Growth is not an axiom; it's the natural product of human ingenuity + profit motive when incentives are right.

Does sustainable finance work empirically? (causal-inference caveats)

The identification problem

What: Testing whether a carbon-risk premium causes emission cuts is hard because of OVB (Omitted Variable Bias) and reverse causality.

Remember: A recent 43-country study found that publicly-traded firms in countries with a carbon risk premium (emissions-intensive firms face higher capital costs) subsequently reduced emissions more than firms in countries without it. But: if a government is also signalling stricter future CO$_2$ regulation, the market would penalize exposed firms anyway — so we can't tell whether the price penalty or the regulatory threat drove the cuts.

Bergstresser-type ESG panel study

Remember: Using firms whose ESG (Environmental, Social, Governance) ratings change: an upgrade → sustainably-managed funds more likely to hold the stock; a downgrade → ESG funds shed it (responsive to mandates). BUT they failed to detect a significant effect on environmental management scores; firms instead improved their governance (G) scores — because that's cheaper/easier than real environmental change. Caveat: ESG changes may coincide with new (younger, greener) management — confounder.

Pollution-control bonds (1980s)

Remember: Tax-exempt pollution-control bonds let firms finance pollution-reduction investments. Firms that issued them saw slightly higher subsequent sales growth than comparable non-issuers — evidence of the growth effect. Bottom line across all studies: jury still out, reality still evolving.

The core externality point

The market by itself will not fix sustainability — it needs regulation. The environment has no price; the value society loses from climate damages isn't borne by any individual decision-maker. This is the essence of an externality.

Cost concept 1 — Economic vs. Accounting cost

What: Accounting cost = actual expenses (+ capital depreciation/appreciation per the accounting rules). Economic cost focuses on the cost of utilizing resources and includes opportunity cost.

Why: Even owning an asset isn't free in economic terms — resources can always be put to another use.

Remember:

• Villa Hatt example: ETH owns a building with a lake view. Accounting cost of hosting an event there ≈ yard work, staff, food, energy. The big economic cost omitted is the opportunity cost of not renting it out (Zurich rents are high).
• ETS (Emissions Trading System) policy implication: Governments usually hand out the initial permits for free when an ETS launches. People object that firms then have no incentive to abate — but that's wrong. Even free permits carry an opportunity cost: (1) bankability — saving a permit for future use; (2) market resale — if permits trade at €80/ton and you can abate at €50/ton, you abate and sell the permit for a €30 profit. So the abatement incentive survives because there's an opportunity cost of using the permit, even without an accounting cost of acquiring it.

Cost concept 2 — Marginal vs. Average cost

What: Average cost = total cost ÷ units produced. Marginal cost = cost of the next (additional) unit.

Why: Economics answers "how far do I go?" with MB = MC, so the marginal concept is fundamental.

Remember: Coffee-shop example. Fixed cost (sign + machine) = 4; variable cost (beans, water, energy) = 2/cup. First cup: total cost 6, so average cost = 6/1 = 6; marginal cost = just the variable cost = 2.

Marginal Abatement Cost (MAC) curve

What: List every action to cut CO$_2$, order them cheapest → most expensive. The resulting curve gives the cost of each additional ton abated.

Why: First tons cost almost nothing (or even negative — energy-efficiency measures that pay for themselves); deeper decarbonization (shipping, aviation) gets very expensive → upward-sloping, convex.

Remember: Famous private-sector versions: the McKinsey curve — x-axis abatement potential, y-axis cost, colors = sectors, with some "negative cost" bars at the left. In the DICE model you saw the total abatement-cost curve: abatement cost share $\Lambda_t(\mu_t)=\theta_{1,t}\mu_t^{\theta_2}$ — convex, upward-sloping.

Optimal abatement

What: Abate until MAC = MAB (Marginal Abatement Benefit). For climate, MAB = the SCC (Social Cost of Carbon):

$$\mathrm{MAC}(A^*) = \mathrm{SCC}$$

Why/Remember: Lake Zurich intuition — you could keep abating pollution forever, but past $A^*$ you spend more chasing the last gum wrappers than the benefit is worth → the deadweight / economic cost is the purple triangle area between MAB and MAC over $[A^*, A]$. Empirically on climate we are to the LEFT of $A^*$ (too little abatement): we're forgoing cheap abatement whose benefit exceeds its cost. Stopping short and going past $A^*$ both reduce welfare.

Cost concept 3 — Static vs. Dynamic cost

What: Static cost = the cost of one project in isolation. Dynamic cost = how this project affects the cost of other/future projects (learning-by-doing, knowledge spillovers).

Why: New technologies show rapid learning — the next unit you build is cheaper because you've learned.

Remember:

• Covert & Sweeney (2022) wind turbines: doubling a manufacturer's experience cut own costs by 14–30%; spillovers to other models of the same firm much lower (~2%); cross-firm spillovers detectable but smaller still (~0.1–0.6%). Whether to include the last item depends on whether you take the firm's or society's perspective.
• EV batteries study: residualized EV price (controlling for brand/country/horsepower) falls strongly with battery-supplier experience.
• Causal caveat (OVB / reverse causality): learning curves can be confounded by (1) economies of scale masquerading as learning, and (2) reverse causality — "did experience cut costs, or did cheaper production (figured out some other way) raise sales/output?" A raw experience–cost correlation does not isolate the pure effect of experience.

Cost concept 4 — Partial vs. General Equilibrium cost

What: PE (Partial Equilibrium) = look at one market in isolation, holding everything else constant. GE (General Equilibrium) = trace feedbacks/spillovers to all other markets.

Why: GE is where the fun is — you follow ripple effects from one change through the whole economy.

Remember:

• Firm example (sustainable aviation fuel, SAF): PE cost = just the price differential between kerosene and SAF. GE cost = also the knock-on effects on labor (greener firm recruits more workers — Brazil platform evidence), customers, and capital costs.
• Society example (kerosene/aviation-fuel tax): PE cost = lost surplus in the aviation market. GE adds: reduced airline-sector employment → lower tax revenue; harm to airport-host communities; but also fewer flights → less flight noise → higher housing prices; improved air quality. (Aside: the Chicago Convention actually limits taxing aviation fuel — set aside here.)

Cost concept 5 — Levelized Cost of Electricity (LCOE)

What: A metric to compare very different technologies in a common unit. LCOE is the constant real price of power that would equate the NPV of revenue from a plant's output with the NPV of its production cost:

$$\mathrm{LCOE} = \frac{\mathrm{NPV}(\text{cost})}{\mathrm{NPV}(\text{generation})} = \frac{\sum_t C_t/(1+r)^t}{\sum_t q_t/(1+r)^t}$$

where $C_t$ = total cost in year $t$ (construction + maintenance + fuel), $q_t$ = energy generated in year $t$.

Why: Plants differ in construction time, cost timing, and lifetime — LCOE makes them apples-to-apples. Works beyond electricity (e.g. levelized cost of hydrogen).

Remember (why discount the denominator?): Electricity produced sooner is worth more — money earned tomorrow can be invested to earn interest; a plant that comes online in 20 years is less valuable than one online next year. So discounting generation has both a technical and a real economic rationale.

Worked LCOE example (wind vs coal)

Setup (made-up numbers, $r = 0$ for simplicity → PV = undiscounted sum):

Step 1 — cost sequence each year (numerator):

• Wind: 100, 100 (building), then 5, 5, 5 (operating). Total cost = 215.
• Coal: 20 (building), then 18, 18, 18, 18 (10 maint + 8 fuel). Total cost = 92.

(We ignore social costs / externalities here — air pollution, healthcare, SCC from coal — taking the firm's perspective in an unregulated world.)

Step 2 — generation sequence each year (denominator):

• Wind: 0, 0 (building), then 10, 10, 10. Total = 30 MWh.
• Coal: 0 (building), then 20, 20, 20, 20. Total = 80 MWh.

Step 3 — divide:

• Wind LCOE = 215 / 30 ≈ 7.17 CHF/MWh.
• Coal LCOE = 92 / 80 ≈ 1.15 CHF/MWh.

(If $r \neq 0$, discount every cost and quantity by $(1+r)^t$ for $t = 0,1,2,3,4$.)

Solving for a subsidy to make renewables competitive

Generation subsidy $s$: subtract $s$ from each operating-year cost and solve so wind LCOE = coal LCOE. In this example $s$ ≈ 60 per 10 MWh ≈ 6 CHF/MWh.

Investment subsidy $\tau$: replace construction cost with $C^{\text{cons}}_t(1-\tau)$. Then solve for $\tau$ such that $\mathrm{LCOE}^{\text{renewable}}(\tau) = \mathrm{LCOE}^{\text{fossil}}$.

Exam-style worked version (solar vs gas, $r = 0$): Solar: construction $50/yr in 2022–23, maintenance $5/yr, 10 MWh/yr, 4-yr life. Gas: construction $20 (2022), maintenance $10/yr, fuel $5/yr, 10 MWh/yr, 4-yr life.

• Gas LCOE = $(20 + 4\times15)/(4\times10) = 80/40 = \$2/$MWh.
• Solar LCOE$(\tau) = (50(1-\tau)\times2 + 4\times5)/40 = (100(1-\tau)+20)/40$.
• Set equal to 2: $100(1-\tau)+20 = 80 \Rightarrow (1-\tau)=0.6 \Rightarrow \boldsymbol{\tau = 40\%}$.

Exam tips: the computer exam gives a calculator — beware the classic Flüchtigkeitsfehler (slip) of writing 20 instead of 2 in a division. Read which technology the question asks about before computing. Only the result is graded (write nice round numbers you can do in your head).

LCOE shortcomings (critical-thinking caveats)

1. It collapses time- and location-varying value into one average

Remember: Headlines say "solar is now cheaper than fossil" — often true on LCOE, but electricity is costly to store and transport, and demand varies across space and time. The value of power depends on when and where it's generated. German data: midday solar/wind floods the grid → price (marginal willingness to pay) falls; evening (cars plug in, dinner cooked) → solar drops, demand up → price rises. Extra evening generation is far more valuable than midday. Negative midday spot prices now appear (Australia, Germany, California) — so much solar that prices go negative; the value of adding more solar at that moment is literally negative. LCOE averaging misses all of this.

2. Discount rate / plant lifetime / subsidy treatment materially change rankings

Remember: Assumed construction times here are short for teaching; in practice 20/30/40-year lifetimes (nuclear especially iffy — decommissioning costs). Longer assumed lifetime makes wind look better. Some modeling groups (US EIA, IEA) apply an extra cost-of-capital premium for coal to reflect sustainable-investment incentives; clean vs fossil firms also raise funds differently.

3. Whose perspective? Externalities and subsidies

Remember: From society's perspective: exclude tax incentives/subsidies (taxpayers pay them — you want the real technological cost) but include externalities and knowledge spillovers. From the firm's perspective: subsidies are a benefit to you; externalities you may or may not include. US numbers: on plain private LCOE, combined-cycle natural gas is cheapest (~4.6 ¢/kWh) vs wind/solar (~7.6 ¢/kWh). Add greenhouse-gas external cost → conventional coal becomes most expensive; gas still competitive. Add non-GHG air/particulate pollution cost → coal is by far the most expensive for society, and renewables look much better (fully cheapest if backed by batteries/hydro rather than gas). Externalities aren't a small detail — they can flip which source is "cheapest."

Key formulas & one-line takeaways

Key formulas

• Profit-max FOC (standard): $\partial F/\partial K = r$; $\partial F/\partial E = p_E$.
• Reform-effect FOC (green capital cost): $\partial F/\partial E = p_E + (\partial r/\partial E)\cdot K$.
• Optimal abatement: $\mathrm{MAC}(A^*) = \mathrm{MAB} = \mathrm{SCC}$.
• LCOE: $\displaystyle \mathrm{LCOE} = \frac{\sum_t C_t/(1+r)^t}{\sum_t q_t/(1+r)^t}$.
• With investment subsidy: $C^{\text{cons}}_t \to C^{\text{cons}}_t(1-\tau)$. With generation subsidy: subtract $s\cdot q_t$ from the cost numerator. Then set $\mathrm{LCOE}^{\text{renewable}} = \mathrm{LCOE}^{\text{fossil}}$ and solve for $\tau$ or $s$.

One-line takeaways

• In economics the answer is always MB = MC — only the disguise changes.
• A green cost of capital $r(E)$ creates a growth effect (green firms expand) and a reform effect (implicit fossil tax, scaled by the whole capital stock $K$).
• Free ETS permits still preserve abatement incentives via opportunity cost (resale + bankability).
• Economic cost = accounting cost + opportunity cost (Villa Hatt).
• Optimal abatement: MAC = SCC; climate is empirically left of the optimum (too little abatement).
• Static = one project alone; dynamic = learning/spillovers (Covert & Sweeney: 14–30% own-learning), but watch OVB / reverse causality.
• PE looks at one market; GE traces every ripple (and is far richer).
• LCOE = NPV(cost)/NPV(generation) — an apples-to-apples average price, but it hides intermittency/location value (negative midday prices), and the verdict flips once you add externalities and choose a perspective.
• Always ask: which costs am I not counting?