Economic Considerations in PAM

Overview

The Plant Agent Model (PAM) makes decisions based on economic signals and constraints that shape investment behavior. This document explains the key economic factors that drive technology transitions, capacity expansions, and closures.

1. Price Signals

Spot Prices (Current Year)

Used for: Furnace group actual balance updates based on production volumes

Source: Derived from current demand intersecting the cost curve

freeze_market_price = extract_price_from_costcurve(current_demand)

Application:

  • Balance sheet calculations: profit = (spot_price - unit_cost) × production

  • NPV calculations for technology switches

  • Closure decisions (if losses exceed CAPEX threshold)

Forecast Prices

Used for:

  • Furnace group strategy evaluation (switches, renovations, closures)

  • Plant group expansion decisions

Method: For each year from construction start through plant lifetime:

  1. Calculate future steel demand (sum across all demand centers)

  2. Calculate future iron demand (virgin iron demand, based on steel demand and scrap availability)

  3. Apply each year’s demand to the existing cost curve to extract price

future_price_series = {"steel": [], "iron": []}  # Years: start_year to (year + construction_time + plant_lifetime)

Rationale: Technology switching and expansions require construction time (3-4 years). Investment decisions use forecasted prices based on projected demand at time of operation, not current prices.

Price Dynamics

  • Prices update annually based on supply/demand balance

  • Higher demand → Higher market price → More expansions

  • Lower demand → Lower prices → More closures

  • Technology shifts change cost curve shape → Affect prices

2. Profitability Checks

NPV-Based Decisions

All major decisions require positive Net Present Value:

Formula:

NPV = Σ [(Revenue_t - OPEX_t - Carbon_Cost_t - Debt_t) / (1 + r)^t] - Initial_Investment

Thresholds:

  • Technology switch: NPV_new - COSA > 0

  • Renovation: NPV_renovation > 0

  • Expansion: NPV_expansion > 0

  • Closure: If historic_balance < -(CAPEX × capacity)

Balance Sheet Constraints

Decisions require sufficient accumulated profits:

Investment Capacity:

equity_needed = capacity × capex × equity_share  # Default: 20% equity
can_afford = plant_group.total_balance >= equity_needed

Example:

  • New furnace: 2.5 Mt capacity × $800/t CAPEX × 20% equity = $400M needed

  • Plant group balance: $550M → Can afford

  • Plant group balance: $300M → Cannot afford, expansion rejected

Profitability vs Affordability

Two separate checks:

  1. Profitable? NPV > 0 (Is the investment economically viable?)

  2. Affordable? Balance ≥ equity_needed (Can we finance it?)

Both must be true for investment to proceed.

3. Capacity Constraints

Annual Addition Limits

Prevents unrealistic industry growth:

Separate Limits by Product:

  • capacity_limit_steel: Max steel capacity additions per year

  • capacity_limit_iron: Max iron capacity additions per year

Enforcement

# Check if expansion would exceed limit
expansion_and_switch_capacity = installed_capacity - new_plant_capacity

if expansion_and_switch_capacity + new_expansion > capacity_limit:
    reject_expansion()  # Too much growth this year

New Plant Allocation

Share of new capacity from greenfield vs brownfield:

new_capacity_share_from_new_plants = 0.5  # 50% from new plants, 50% from expansions/switches

If demand < active capacity → Allow new plants regardless of share (Prevents blocking greenfield when demand is growing)

4. Financing and Debt

Capital Structure

Default financing mix:

equity_share = 0.20  # 20% equity
debt_share = 0.80    # 80% debt

Upfront Cost:

  • Equity portion must be paid from accumulated balance

  • Debt portion financed at cost_of_debt interest rate

Example:

  • Total CAPEX: $1,000M

  • Equity (20%): $200M (deducted from balance)

  • Debt (80%): $800M (repaid over plant lifetime)

Debt Repayment

Uses straight-line amortization (constant principal, declining interest):

annual_principal = total_debt / lifetime
annual_interest = average_debt_balance × cost_of_debt
annual_payment = annual_principal + annual_interest

Impact on Profitability:

  • Debt repayment added to unit production cost

  • Higher debt → Higher per-tonne cost → Lower competitiveness

  • Debt fully repaid after plant_lifetime years (default 20)

Cost of Debt by Country

Interest rates vary by location:

cost_of_debt_dict = {
    "USA": 0.05,  # 5%
    "CHN": 0.04,  # 4%
    "IND": 0.08,  # 8%
    # ...
}

Lower rates → Lower financing costs → More competitive

5. Carbon Pricing

Carbon Cost Integration

Carbon costs added to operating expenses:

unit_carbon_cost = emissions_per_tonne × carbon_price
unit_production_cost = opex + carbon_cost + debt_repayment

Sources of Emissions:

  • Direct (Scope 1): Process emissions, fossil fuel combustion

  • Indirect (Scope 2): Purchased electricity

  • Supply chain (Scope 3): Upstream material production

Carbon Price Trajectory

Time-varying carbon prices affect technology competitiveness:

carbon_cost_series = {
    2025: 50,   # $/tCO2
    2030: 100,
    2040: 200,
    2050: 300,
}

Impact:

  • Rising prices → Favor low-carbon technologies (DRI+ESF, EAF with renewables)

  • Falling prices → Favor cost-optimized technologies (BF with CCS)

Technology-Specific Effects

Different emission intensities create technology tipping points:

Technology

Emissions (tCO2/t steel)

Carbon Cost @ $100/tCO2

BF

2.0

$200/t

BF+CCS

0.4

$40/t

DRI+ESF

0.1

$10/t

EAF (scrap)

0.3

$30/t

Carbon price of $100/tCO2 → $190/t cost advantage for DRI+ESF over BF

6. Stochastic Elements

Probabilistic Adoption

When enabled (probabilistic_agents=True), acceptance is probabilistic:

acceptance_probability = exp(-investment_cost / NPV)
accept = random.random() < acceptance_probability

Rationale:

  • Models real-world hesitation and uncertainty

  • Higher cost/benefit ratio → Lower acceptance

  • Prevents unrealistic instantaneous technology shifts

Example:

  • Investment: $1,000M, NPV: $2,000M → P(accept) = exp(-0.5) = 60.7%

  • Investment: $1,000M, NPV: $500M → P(accept) = exp(-2) = 13.5%

  • Investment: $1,000M, NPV: $5,000M → P(accept) = exp(-0.2) = 81.9%

Technology Selection

When multiple technologies have positive NPV:

Deterministic Mode (probabilistic_agents=False):

  • Always choose highest NPV technology

Probabilistic Mode (probabilistic_agents=True):

  • Weighted random selection: P(tech_i) = NPV_i / Σ(NPV_j)

  • Allows suboptimal but profitable technologies to be chosen

  • Models market diversity and imperfect information

7. Subsidies

Subsidy Types

Three categories, each reducing costs:

  1. CAPEX Subsidies: Reduce upfront investment

    subsidized_capex = base_capex - absolute - (base_capex × relative)

  2. OPEX Subsidies: Reduce operating costs

    subsidized_opex = base_opex - absolute - (base_opex × relative)

  3. Debt Subsidies: Reduce interest rates (absolute points only)

    subsidized_rate = base_rate - absolute_points

Time-Bounded Application

Subsidies active only within specified years:

subsidy.start_year = 2025
subsidy.end_year = 2035

if current_year >= start_year and current_year <= end_year:
    apply_subsidy()

Economic Impact

  • Lower CAPEX → Higher NPV → More likely to switch/expand

  • Lower OPEX → Higher profits → Faster balance sheet recovery

  • Lower debt cost → Lower unit production cost → More competitive

Strategic Use:

  • Target emerging technologies to accelerate adoption

  • Temporary incentives bridge “valley of death” until learning-by-doing reduces costs

  • Geographic targeting supports regional industrial policy

Interaction Effects

Price × Carbon Cost

High carbon prices shift competitive advantage:

  • Low carbon price → Cheapest technology wins (usually BF/BOF)

  • High carbon price → Cleanest technology wins (DRI/EAF)

  • Moderate carbon price → Technology diversity (some switch, some don’t)

Balance Sheet × Investment

Strong balance sheets enable faster technology transition:

  • Profitable plants → Accumulate balance → Can afford switches

  • Unprofitable plants → Negative balance → Cannot switch, eventually close

  • Creates path-dependency: Early adopters compound advantages

Capacity Limits × Demand Growth

Interaction determines industry structure:

  • High growth + tight limits → Favor expansions at existing plants

  • High growth + loose limits → Favor new plant construction

  • Low growth + any limits → Minimal investment, closures dominate

Subsidies × Profitability

Subsidies most effective when:

  • Base NPV slightly negative (subsidy tips to positive)

  • Plant has balance to cover equity share

  • Technology has long-term cost advantage after subsidy expires

Summary

PAM decisions emerge from the interaction of:

  1. Market signals: Spot and forecast prices determine revenues

  2. Profitability: NPV calculations weigh costs vs benefits

  3. Affordability: Balance sheet constrains investment capacity

  4. Capacity limits: Prevent unrealistic industry growth

  5. Financing: Debt structures affect per-unit costs

  6. Carbon pricing: Emission costs shape technology competitiveness

  7. Uncertainty: Probabilistic acceptance models real-world hesitation

  8. Subsidies: Policy interventions accelerate transitions

These factors create emergent industry dynamics:

  • Technology transitions accelerate when prices rise or carbon costs increase

  • Regional differences emerge from varying financing costs and subsidies

  • Path dependency creates winners and losers based on early performance

  • Market dynamics balance growth (expansions) and consolidation (closures)