Imperfect competition, entry and taxation of commodity producers

Imperfect Competition, Entry and Taxation

in Commodity Markets

Michel Azulai (LSE)

Vinicius Carrasco (PUC-Rio)

João Manoel Pinho de Mello (PUC-Rio)

Motivation:

Boom in commodity prices is often a trigger for "renegotiation", through:

• Higher tax rates and/or

• More royalty payments

and also (but not considered in this talk) through

Motivation:

But then, ex-post increase in taxes/royalties shouldn’t:

1. be at odds with the standard notion of a renegotiation outcome (all parties weakly better off)?

2. reduce total welfare of the producing country?

The "No" Story for Competitive Markets

• Demand for resource is (infinitely?) inelastic

— Consumers (the Chinese) will not respond to an increase in prices

∗ No (or small) effect on total surplus

• Standard taxation result: inelastic side of the market "pays" (a larger part) for (of the) taxes

— consumers (the Chinese) will pay for the higher taxes/royalties

• "Renegotiation" amounts to a transference from the consumers (in China) to the government

The "No" Story for Monopolies

• Demand for resource is (infinitely?) inelastic

— Consumers (the Chinese) will not respond to an increase in prices

∗ No (or small) effect on total surplus

• Company will sell (roughly) the same quantity at a smaller mark-up

— "Renegotiation" amounts to a transference from the company to the government

The "No" Story for Monopolies: What about

Invest-ments?...

• ... prices are such that profitability is large even with higher taxes/royalties — Current shareholders would still derive a fair return from past

invest-ment

However:

In many relevant commodity markets,

1. Neither perfect competition nor monopoly prevails.

Hence:

2 Strategic effects may be of relevance

This Presentation:

Quantitative evaluation of the effect of higher taxes and royalties on iron ore production in a model where:

• The market demand is inelastic

• There is more than a single global major producer

— Each of which decide on current and future capacity strategically

The Model: Firms and Technology

• Three major firms: V , R and B that produce at marginal costs ci, i ∈

{V, R, B}

• A continuum of firms that can produce q0 at marginal costs

c₀ + c1

(1 + g)e T q0

— c₀ > max_{i∈{V,R,B}{ci}}

— ge is the (average) growth rate of the marginal firms over the next T periods

∗ Capture entry of more efficient small firms and/or efficiency gains for current ones

The Model: Demand, Capacity and Taxes

• Initially, major firms have capacity to produce qi, i ∈ {V, R, B}

— At a cost k_iq_i∗, the firm can acquire q_i∗ in additional capacity.

• Market (inverse) demand

P _{= a − bQ, Q = qV} + q_R + q_B + q₀

Taxes:

• Major firms pay τR_i of taxes on revenues and τP_i of taxes on profits (before investments).

The Model: Timing

1. Major Firms simultaneously decide on quantities/capacity to prevail T pe-riods from now

2. Major and small firms compete by setting prices in T

(a) Kreps and Scheinkman (1983) type of environment

3. Prices are determined and each major firm produce in accordance with capacity

Prices When Small Firms produce:

Whenever they produce, small firm’s marginal cost determine prices. Hence:

• a − bQ = c0 + c₁ (1 + g)e T h Q − QGi — QG = X i∈{V,R,B} ³ q_i + q_i∗´ • Letting ce_{1 ≡} c1 (1+eg)T Q = a − c0 + ce1Q G e c₁ + b

Major Firm’s Demand:

Using the above expression for Q, one has:

pmajor ³QG´ _{= a − b} " a − c0 + ce1QG e c₁ + b # To be noticed: • Since ec1 e

c₁+b < 1, major firm’s demand is more elastic than the market

Major Firm’s Demand:

Model nests two interesting possibilities as special cases:

1. Major firm’s demand = Market demand:

e

c_{1 → ∞}

2. Major firm’s demand is infinitely elastic

e

Solving the Model: A Major Firm’s Problem:

• Given the competitor’s decision, firm i solves

max q_i≥0 h³ 1 − τRi ´ pmajor ³q_i + q_i + QG_−i´ _{− ci}i ³ 1 − τL_i ´(q_i + q_i) (1 + r)T −1 r − kiqi — where QG_−i = X j∈{V,R,B},j6=i ³ q_j + q_j∗´

Solving the Model: The FOC:

• The first order condition reads

max ⎧ ⎨ ⎩ a 2b + c₀ 2ce₁ − Ã b + ce₁ 2bce₁ !_³ ee c₁ + ke_i´ ₋ Q G −i 2 ; qi ⎫ ⎬ ⎭ = qi + qi∗ (FOC)

Solving the Model: Numerical Solution

1. For q = (q_V , q_R, q_B) , _{define f : R}3 _{→ R}3 with ith coordinate given by

f_i (q) = max ⎧ ⎨ ⎩ a 2b + c₀ 2ce₁ − Ã b + ce₁ 2bce₁ ! ³ ee c₁ + ke_i´ ₋ Q G −i 2 ; qi ⎫ ⎬ ⎭ − qi − qi∗

2. For an initial q₀, approximate the above at a given region by f _{(q) ≈ f (q0}) + D_f (q_{0) · (q − q0})

Let q₁ be such that the approximation is zero

Simulations: Demand Parameters

Demand parameters are calibrated so that:

1. Market demand elasticity is 0.1

2. At a price of 161 dollars, China consumes 1400 million tons of iron ore

• (1)+(2) ⇒ b = 1.15 • As for a in T periods:

p = 3298, 43

| {z }

10% growth

− 1.15Q (world demand for iron ore growing 10%) p = 2746, 31

| {z }

7% growth

Simulations: Major Firms’ Marginal Cost Parameters

(per Ton)

• V : c_V = 31.5_{| {z }} working K + _|{z}19 F reight − _|{z}15 premium −[0.02 ∗ (175 + 15) ∗ 0.92]_{| {z }} Royalties = 32 • R : c_R = _|{z}34 working K + _|{z}8 F reight − [0.056 ∗ (175) ∗ 0.92]_{| {z }} Royalties = 33 • B : c_B = _|{z}36 working K + _|{z}8 F reight − [0.056 ∗ (175) ∗ 0.92]_{| {z }} Royalties = 35

Simulations: Major Firms’ Cost to Acquire Capacity (1

Ton)

• V : k_V∗ = 136 • R : k_V∗ = 141 • B : k_V∗ = 196

Simulations: Baseline Taxes

•

τL_V = 0.18, τR_V = 0.02

•

Simulations: Calibrating the Small Firm’s Marginal Cost

Parameters

Simulations: Exercises

Simulations are centered around the following parameters:

1. Entry/growth of small firms (g)

2. Demand level for iron ore (a)

Simulations: What Does the Model Produce for the

Baseline Case?

Results: Interpretation

• Capacity choices are strategic substitutes (much as quantities in a Cournot model)

— If a firm becomes less aggressive, competitors respond with larger ca-pacity

• An increase in Taxes/Royalties make a local firm less aggressive — competitors respond with more capacity

Results: Interpretation

Undesired outcome:

• Transfer of surplus to citizens in, say, Australia... — Effect may be non-negligible!

Simple solutions:

• Taxes on a measure of profits that deducts CAPEX investment

Concluding Remarks:

Our quantitative exercise suggests that:

• Strategic effects of tax and royalty increases may be substantial since: — they imply that firms’ demands are more elastic that the market’s

— They affect capacity decision (and, as a consequence, future market share)

What Next?

• Exploration

— How does taxation affect the pace at which the resource is explored

∗ How distorted becomes exploration when compared to Hotelling Rule?...

• Development activities in the model

— Real options are less valuable the less volatile their payoffs, no?

What Next?

• Incorporate other aspects of regulation in our model

— e.g., binding deadlines for exploration, minimum investment level, etc.