Market Price Calculation and Proxy Profit

Overview

The Plant Agent Model (PAM) relies on market prices to calculate plant profitability and balance sheets. However, the Trade Module doesn’t simulate a true market price - it optimizes global allocation based on production costs. This document explains how “proxy profit” approximates realistic market dynamics.

The Challenge

Trade Module Optimization:

  • Uses levelized cost of steel/iron (LCOS) as the bid price for suppliers

  • Minimizes global cost of allocation to meet demand

  • Naturally captures competitive advantage based on production costs

  • Does NOT reflect: Profit maximization or true market price/value of commodities

Problem: Without market prices, we can’t calculate realistic profits or balance sheets for plant agents.

Solution: Proxy Profit Method

Step 1: Derive Cost Curve

Aggregate all plants’ production costs to create a supply curve:

Cost ($/t)  ↑
           │     ╱──────
           │    ╱
           │   ╱
           │  ╱
           │ ╱
           │╱___________→ Cumulative Capacity (t)

  • X-axis: Cumulative production capacity (sorted by cost, lowest to highest)

  • Y-axis: Levelized cost of steel/iron (LCOS) for each plant

  • Result: Upward-sloping supply curve

Step 2: Find Market-Clearing Price

Identify where the supply curve intersects demand:

Cost ($/t)  ↑
Market price│-----╱──────
            │    ╱  │
            │   ╱   │ 
            │  ╱    │
            │ ╱     │
            │╱______│_____→ Cumulative Capacity (t)
```               Demand

- Vertical line at demand quantity
- Intersection with cost curve and y-axis = **market price**

### Step 3: Calculate Proxy Profit

For each plant:

```python
profit_i = (market_price - lcos_i) × sales_i

Where:

  • market_price: Derived from cost curve intersection (Step 2)

  • lcos_i: Plant i’s levelized cost of steel/iron

  • sales_i: Plant i’s allocated production volume (from Trade Module)

Example

Scenario

  • Demand: 100 Mt steel

  • Plants:

    • Plant A: LCOS = $400/t, Capacity = 50 Mt

    • Plant B: LCOS = $500/t, Capacity = 40 Mt

    • Plant C: LCOS = $600/t, Capacity = 30 Mt

Cost Curve

0-50 Mt:  $400/t (Plant A)
50-90 Mt: $500/t (Plant B)
90-120 Mt: $600/t (Plant C)

Market Price Calculation

  • Demand = 100 Mt

  • Falls in Plant C’s range (90-120 Mt)

  • Market Price = $600/t (marginal plant’s cost)

Profit Calculation

Plant A: profit = (600 - 400) × 50 = $10,000M
Plant B: profit = (600 - 500) × 40 = $4,000M
Plant C: profit = (600 - 600) × 10 = $0M  (marginal plant breaks even)

Implementation in PAM

Where It’s Used

  1. Balance Sheet Updates (Plant.update_furnace_and_plant_balance()):

    • Uses market price to calculate: balance = (market_price - unit_cost) × production

    • Aggregates to plant and plant group balances

  2. NPV Calculations (FurnaceGroup.optimal_technology_name()):

    • Uses forecasted market prices for each year, by extracting future demands from current cost curves

    • Projects future revenues based on future demand and predicted prices

  3. Expansion Decisions (PlantGroup.evaluate_expansion()):

    • Uses forecasted market prices for each year, by extracting future demands from current cost curves

    • Determines if new capacity will be profitable at projected prices

Price Updates

Market prices are recalculated after every Trade Module run:

# In simulation.py or handlers
market_price = extract_price_from_costcurve(
    demand=current_demand,
    cost_curve=sorted_plants_by_cost
)

Limitations

  1. Assumes Perfect Competition: All plants receive the same market price

    • Reality: Regional price differences, contracts, quality premiums

  2. No Price Dynamics: Prices update annually based on current supply/demand

    • Reality: Intra-year volatility, speculation, inventory effects

  3. Marginal Cost Pricing: Market price = marginal plant’s cost

    • Reality: Market power, cartels, trade barriers affect pricing

  4. No Demand Elasticity: Demand is fixed, doesn’t respond to price

    • Reality: High prices → demand destruction, substitution

Why This Approach Works

Despite limitations, proxy profit provides:

  1. Competitive Differentiation: Low-cost plants earn higher profits

  2. Realistic Losses: High-cost plants may operate at losses

  3. Investment Signals: Profitable plants can finance expansions

  4. Technology Transition Incentives: Cleaner/cheaper tech improves profitability

This approximation is sufficient for modeling long-term industry transformation where:

  • Annual time steps smooth out short-term volatility

  • Strategic decisions (technology switches, expansions) depend on multi-year trends

  • Relative competitiveness matters more than absolute price levels