Imperfect Competition, Entry and Taxation
in Commodity Markets
Michel Azulai (LSE)
Vinicius Carrasco (PUC-Rio)
João Manoel Pinho de Mello (PUC-Rio)
August 2012
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
• Outright expropriation of assets
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?
3. reduce the producers’ incentives to invest
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
• Total surplus in the producing country is unaffected
The "No" Story for Monopolies: What about Investments?...
• ... prices are such that profitability is large even with higher taxes/royalties
— Current shareholders would still derive a fair return from past investment
— Future investment would remain attractive
However:
In many relevant commodity markets,
1. Neither perfect competition nor monopoly prevails.
Hence:
2 Strategic effects may be of relevance
• effects of taxes/royalties not so clear
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
• There is a fringe of "small" producers
The Argument in a Nutshell:
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
c1
c0 +
q0
T
(1 + ge)
— c0 > maxi∈{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 q i, i ∈ {V, R, B}
— At a cost kiqi∗, the firm can acquire qi∗ in additional capacity.
• Market (inverse) demand
P = a − bQ, Q = qV + qR + qB + q0
Taxes:
P
• Major firms pay τ R
i of taxes on revenues and τ i of taxes on profits (before
investments).
The Model: Timing
1. Major Firms simultaneously decide on quantities/capacity to prevail T periods 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 +
— QG =
X
i∈{V,R,B}
• Letting ce1 ≡ c1 T
(1+ge)
³
q i + qi∗
´
c1
(1 + ge)T
h
Q − QG
a − c0 + ce1QG
Q=
ce1 + b
i
Major Firm’s Demand:
Using the above expression for Q, one has:
³
To be noticed:
´
"
a − c0 + ce1QG
major
G
p
Q
=a−b
ce1 + b
#
1
• Since ce ec+b
< 1, major firm’s demand is more elastic than the market
1
demand
Major Firm’s Demand:
Model nests two interesting possibilities as special cases:
1. Major firm’s demand = Market demand:
ce1 → ∞
2. Major firm’s demand is infinitely elastic
ce1 = 0
Solving the Model: A Major Firm’s Problem:
• Given the competitor’s decision, firm i solves
´
L
h³
´
³
´
i 1 − τ i (q i + qi)
R
major
G
− kiqi
q i + qi + Q−i − ci
max 1 − τ i p
T
−1
q ≥0
(1 + r)
r
i
— where QG
−i =
X
j∈{V,R,B},j6=i
³
q j + qj∗
´
³
Solving the Model: The FOC:
• The first order condition reads
⎧
⎫
Ã
!
G
⎨a
´
Q−i ⎬
b + ce1 ³e
c0
e
max
−
ce1 + ki −
+
; q i = q i + qi∗ (FOC)
⎩ 2b
⎭
2ce1
2bce1
2
We proceed numerically to solve the system induced by FOC
Solving the Model: Numerical Solution
1. For q = (qV , qR, qB ) , define f : R3 → R3 with ith coordinate given by
⎧
⎫
Ã
!
G
⎨a
´
Q−i ⎬
b + ce1 ³e
c0
e
fi (q) = max
−
ce1 + ki −
+
; q i − q i − qi∗
⎩ 2b
⎭
2ce1
2bce1
2
2. For an initial q0, approximate the above at a given region by
f (q) ≈ f (q0) + Df (q0) · (q − q0)
Let q1 be such that the approximation is zero
3. Resume the procedure till convergence of {qn} is obtained.
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 − 1.15Q (world demand for iron ore growing 10%)
| {z }
10% growth
p = 2746,
31 − 1.15Q (world demand for iron ore growing 7%)
| {z }
7% growth
Simulations: Major Firms’ Marginal Cost Parameters
(per Ton)
• V:
cV =
31.5
| {z }
working K
+ |{z}
19 −
F reight
15 −[0.02 ∗ (175 + 15) ∗ 0.92] = 32
|{z}
|
{z
}
premium
Royalties
• R:
cR =
34
+ |{z}
8
− [0.056 ∗ (175) ∗ 0.92] = 33
|{z}
|
{z
}
working K
F reight
Royalties
cB =
36
+ |{z}
8
− [0.056 ∗ (175) ∗ 0.92] = 35
|{z}
|
{z
}
working K
F reight
Royalties
• B:
Simulations: Major Firms’ Cost to Acquire Capacity (1
Ton)
• V:
• R:
• B:
kV∗ = 136
kV∗ = 141
kV∗ = 196
Simulations: Baseline Taxes
•
•
R = 0.02
=
0.18,
τ
τL
V
V
L
R
R
τL
R = τ B = 0.18, τ R = τ B = 0.056
Simulations: Calibrating the Small Firm’s Marginal Cost
Parameters
• c0 = 45, c1 = 0.15 yields the following approximation (as of "today")
Simulations: Exercises
Simulations are centered around the following parameters:
1. Entry/growth of small firms (g)
2. Demand level for iron ore (a)
3. Taxes and Royalties
Simulations: What Does the Model Produce for the
Baseline Case?
Simulations: Results for Increase in Royalties
Simulations: Results for an Increase in Royalties
Simulations: Results for an Increase in Taxes
Simulations: Results for an Increase in Taxes
Results: Interpretation
• Capacity choices are strategic substitutes (much as quantities in a Cournot
model)
— If a firm becomes less aggressive, competitors respond with larger capacity
• An increase in Taxes/Royalties make a local firm less aggressive
— competitors respond with more capacity
• Local firm loses market share
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
• "free-ride" on tax raises implemented by foreign "hungry" governments
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)
• Distortions (and transference of surplus to foreign firms) may be substantial
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?
∗ Effect of renegotiation in booms on "upside" of the option
What Next?
• Incorporate other aspects of regulation in our model
— e.g., binding deadlines for exploration, minimum investment level, etc.
• Simulate (and quantify) joint effects