Relating Product Prices to Long-Run Marginal Cost:
Evidence from Solar Photovoltaic Modules
Stefan Reichelstein
Graduate School of Business, Stanford University
and
Department of Business Administration, University of Mannheim
October 2016
Motivation
Production Costs and Market Prices
Economic theory submits that for a competitive industry in
equilibrium the market price for a product is such that:
Price = Long-Run Marginal Cost = Short-Run Marginal Cost
Fundamental Questions:
Identification and Measurement of Marginal Cost
Which costs are to be included?
When should fixed costs be excluded?
What data sources can we rely on to measure marginal cost?
What role, if any, can firm-level financial accounting information
play?
Motivation
Marginal Cost in the Industrial Organization Literature
The proper measurement of marginal cost has been controversial
in investigations of firm profitability and monopoly pricing.
→ Fisher (1998), Pittman (2009) and Carlton/Perloff (2005)
Quote:
“It is difficult to understand how a firm that sets prices at true marginal
cost is able to survive as a going concern unless that true marginal cost
includes the marginal cost of capital” (Pittman 2009)
Economics textbooks frequently represent capital as a
"consumable" input like materials or labor
But most firms make irreversible investments in capacity.
The long-run marginal cost of one unit of capacity made
available for one period of time is fundamentally ambiguous due to
capacity investments inherently involving a joint cost.
Motivation
Identification of Relevant Costs in Managerial Accounting
Accounting Textbook View (Horngren et al. 2012; Hilton 2015)
Importance of full cost for breaking even in terms of accounting
profit
Short-run decisions: Use of incremental cost (variable cost plus
applicable opportunity costs)
Long-run decisions: discounted future cash flows as the basis
for investment decisions
→ No attempt to identify, or measure, the long-run marginal cost of a
product
Model Framework
Overlapping Capacity Investments
Infinite horizon model of a competitive industry
Aggregate production capacity:
Kt = It−T + It−T +1 + . . . + It−1 ,
where Iτ denotes (aggregate) investment in period τ
To acquire the capacity to deliver one unit of output, firms incur
an investment expenditure of v at the initial date 0.
Technological progress parameter, η, reduces this cost to η t · v in
period t.
Firms anticipate technological progress when making their
investment decisions
Discount rate is given by r. → Discount factor: γ ≡
1
1+r
Model Framework
Cost Structure
Fixed operating costs per unit capacity in period t: ft
Variable cost per unit of output: wt
Corporate income taxes
Tax rate: α
Depreciation schedule allowable for tax purposes: {dτ }Tt=1
Tax factor: ∆ = (1 − α ·
T
P
dt · γ t )/(1 − α)
t=1
Definition: Long-Run Marginal cost
LM Ct ≡ wt + ft +
ηt · v
· ∆ ≡ wt + ft + ct · ∆
T
P
τ
(γ · η)
τ =1
Note: The capacity cost term: ct · ∆ is not a cash cost.
Model Framework
Price Taking Behavior
In a competitive equilibrium, firms break even on their capacity
investments
An individual firm’s supply curve:
Firms are capacity constrained in the short-run. Supply output up to
their capacity limit, provided the market price does not fall below wt
Model Framework
Long-Run Marginal Cost as the Equilibrium Price
Definition {Kt∗ }∞
t=1 is an equilibrium capacity trajectory if, given
competitive supply behavior, capacity investments have a net present
value of zero at each point in time.
Let Pto (Qt ) denote the aggregate willingness-to-pay curve
Finding 1 A capacity trajectory {Kt∗ }∞
t=1 that satisfies the pricing
condition:
Pto (Kt∗ ) = LM Ct
(1)
is an equilibrium capacity trajectory.
Interpretation
Finding 1 identifies LM Ct as the long-run marginal cost in an industry
with declining costs
Inferring Long-Run Marginal Cost
Reliance on Firm-Level Accounting Information
Long-run marginal cost comprises:
(i) operating costs
(ii) capacity related costs
Reliance on Income statements (quarterly) and inventory data.
Additional data on capacity and sales volume from industry
research group
+
−
Split wit into wit ≡ wit
+ wit
Split fit into fit ≡ fit+ + fit−
where “+" refers to inventoriable costs (→ COGS)
while “-" refers to period costs (→ "Below the Line")
+
Refer to wit
+ fit+ as core manufacturing costs
→ Materials, Labor and Overhead (other than depreciation)
Inferring Long-Run Marginal Cost
Inferring Operating Costs
Figure : Flow Chart: Inferring Operating Costs
Inferring Long-Run Marginal Cost
Inferring Capacity Costs
According to the model framework, the unit of capacity is given:
cit · ∆ = η t ·
vi
T
P
(γ ·
· ∆.
η)τ
τ =1
The technological progress parameter η represents the rate at
which the the cost of equipment declines over time estimate
→ Estimates may be available from industry analysts
The unit cost of new capacity acquisitions vi can be gauged at the
individual firm according to:
CAP Xit = vi · η t · Iit ,
if periodic capacity additions are available at the firm level.
→ Reliance on aggregate capacity additions an alternative route
Application to Solar PV Module Manufacturing
The 80% Learning Curve
Solar modules are the key equipment component of solar PV
systems. Output is measured in Watts (or MegaWatts-MW)
Swanson (2011) documents the following classic "80% learning
curve": With every doubling of the cumulative number of MW
produced, prices fall by 20%
Application to Solar PV Module Manufacturing
Module Price Declines in Recent Years
Since 2010, prices have dropped much faster than the historical trend
line. Observers attribute this price drop to both:
(i) massive additions to solar panel manufacturing capacity
(ii) continued reductions in manufacturing costs
Challenge in disentangling cost reductions from potential excess capacity
Application to Solar PV Module Manufacturing
Sample and Data
Rely on financial statements of ten solar PV manufacturers
Mostly Chinese firms, listed on U.S. exchanges
→ Financial statements prepared according to U.S. GAAP.
Collectively these firms have a market share of about 35% of the
solar PV module industry. Median market share less than 1%.
Firms in our sample are almost "pure play" manufacturers of
photovoltaic modules.
→ Important for informativeness of firm-level income statements in
estimating product costs
Additional data on capacity and product shipments from industry
analysts such as GTM and Lux Research.
Estimating Solar PV Module Costs
Estimation Results
Finding 2 We estimate the technological progress parameter for equipment
capacity costs to be ηeq = 0.76. Our estimated 2013 equipment and facility
capacity costs are ceq =$0.16/W and cf c =$0.01/W, respectively.
Estimating Solar PV Module Costs
LMCs versus ASPs: 2008-2013
Forecasting Solar PV Module Costs
Forecasting LMCs: Assume 50 GW of Annual Output
Interpretation
LMC forecasts as our fundamental trend line → Expect price convergence
Conclusions
Findings
We have estimated the long-run marginal cost for solar PV
modules based on firm-level financial accounting data
Our analysis separates and quantifies two developments that have
shaped this industry in recent years:
i) continued manufacturing cost reductions
ii) overcapacity caused by rapid expansion
Both factors were shown to be significant. Nonetheless, our
estimates suggest that long-run marginal costs are falling faster
than suggested by the traditional 80% learning curve
We interpret the trajectory of extrapolated LMCs as a
fundamental trend line to which ASPs should converge over time.
Conclusions
Implications and Extensions
The DOE knew this all along!
→ The SunShot Goal appears within reach
No indication of predatory pricing or dumping as variable costs
account for only about 65% of total LMCs and consistently:
ASPt ≥ .65 · LM Ct
Policy implications regarding the sustained need for tax subsidies
required to make solar energy cost competitive
→ ITC in the U.S. and Feed-in tariffs in Europe
Future work to examine the link between R&D spending and the
rate of learning at the individual firm level
Applicability of our framework to other industries