Production technology and
risk
Ravello
David Zilberman
OUTLINE
Production
Adoption and the environment
Risk
Policy
Production functions
They relate input use to output
Y=f(X) Y output X vector of input
Varies significantly over spcae and time
Long run production functions- that reflect technology after a
period of adjustment are different than short run
Heterogeneity among producers Yi=AiKiaiLibi
Each element fo the production function may vary by
individuals- better managers may have a larger Ai (neutral shift)
other have better labor or capital productivity. Then there
are differences associated with time change
Heterogeneity of quality
Outputs of different quality demand different input use
Inputs’ quality varies-a good worker can produce more
Land quality and exposure to sun may double yields
It is useful to normalize input units-production functions
are functions of effective input. Distinguish between
applied input (X) and effective input (E) where
E=Xq- where q is an indicator of input use efficiency
Example- X is unit of labor applied by a worker of
productivity q If the production function is Y=f(Z) when
output is measured in unit of effective inputs, it becomes
Y=f(qX)- and you get less output with a bad worker
Capital good vary in quality because of manufacturer,
vintage, past use, etc
Discrete and continuous choices
There may be several alternative technologieseach indexed by i.
Farmers need to make discrete choices- which
technologies to use, and
Continuous choices- Allocation of variable input
The land use – in farms land may be used with
several technologies- or crop
The allocation questionWhether to adopt a technology
How much land to allocate
How much variable input to use wit technology
Risk and credit
If farmers are maximizing profit or expected
utility
Farmers may diversify land among technologies
Because of risk aversion reasons
Credit constraint
Labor constraint ( Seasonality)
We will stat with case of risk neutral farmer and
look at adoption choices
Then move to diversification
How to analyze adoption choices?a multistage process
• Need to choose
–
Whether to adopt a technology
–
How to use it optimally- the decision process
• Quantify each of the technologies- in terms of
productivity, externality and costs
• Assess the best use of each technology and the net
reward it generates
• Select the best technology
• Conduct Sensitivity analysis
–
•
Identify the conditions under which you select each
technology
We use conservation technology as an example
Quantifying a technology
Y=Fi(X1,X2,X3…,Q1,Q2) production function
i= technology 0= traditional, 1,…. N new
Y output Xn quantity of input n
Qm quality indicator m
Z=Gi(X1,X2,X3…,Q1,Q2) Pollution function –relating
output to inputs
P output price
Wn=rice of input n V pollution tax
Ki = fixed cost of technology i
Assessing Optimal use of technology i
VPi=Variable profit of technology I
VPi=Max
PFi(X1,X2,X3…,Q1,Q2) –W1X1- W2X2-W3X3Revenue
Cost
-VGi(X1,X2,X3…,Q1,Q2)
Pollution tax
Optimality conditions
P(dFi/dXn)- Wn - V(dGi/dXn) =0
Marginal -price- Marginal pollution
Revenue
cost
Choices over time
Suppose new technology does not require
investment and the new technology lasts three
years and requires K1. VPit is annual variable
profit of technology i at year t. where t=0,1,2
The new technology is adopted if
VP10-VP00+(VP11-VP01)/(1+r)+(VP12-VP02)/(1+r)2
> K1
The technology with the largest net present value
is adopted
Sensitivity analysis
How changes in parameters affect the optimal
input uses and technology choices
For example if Q1 is an indicator of land quality and
d(VP1-VP0)/dQ1 <0 namely
The difference between the variable profits of
the new technology (i=1) and the old one is
declining
The new technology is more likely be adopted at
low land quality
Conservation technology
Output/acre is a function of effective input ( water)
Y=f(E) E effective water – actually used by crop
Effective water is applied water (X) times input use
efficiency h(q,i) which increases with land quality q and
technology i
h(q,0)=q input use efficiency of technology o is equal to q for
simplicity
h(q,1) >q input use efficiency of modern technology is greater
than q.
On average land input use efficiently with
traditional technology q=.6 with sprinkler.8 and
drip .9
Production and pollution functions
Y0=f(Xq) Z0=(1-q)X=pollution is residue
Y1=f(Xh(q,1)), Z1=(1-h(q,1))X
Optimal input use technology 0-X0*
Find X=X0* that Max Pf(Xq) –wX-v(1-q)XOptimal input for technology 1
Find X=X1* that Max Pf(Xh(q,1)) –wX-v (1-h(q,1))XK1
First order condition
at X0* Pqdf(Xq)/dE –w-v(1-q)=0
at X1* Ph(q,1)df(E)/dE –wX-v(1-h(q,1))=0
Assessing adoption
The decision making process that leads to
adoption includes several stages
First assessing the optimal input use with each
technologyFor example if there are two technologiestraditional and modern - you first find optimal input
use and profit under each technology
The second stage is choosing the technology
with most profit
Incentives change adoption choices
Example: Irrigation(Hypothetical/California)
Increased yield, reduced water, and reduced drainage
costs more.
Low-cost version (bucket drip, bamboo drip) exists.
Impact greater/adoption higher on lower quality lands—sandy soils
and steep hills.
More adoption with high-value crop, high prices of water drainage, and
output.
Technology
Irrigation
efficiency
Water/
drainage
Yield
(cotton)
Fixed
cost/yr
Traditional
.6
4.0/1.6
1200
500
Sprinkler
.8
3.2/.64
1325
580
Drip
.9
2.7/.27
1400
650
Optimal input use for a technology
P-output price,W=input price,V pollution price
K1 per season cost of modern technology
K0=0 per season cost of Traditional technology
Choice of input use with a given technology
PRi=Max Pf(hX)-WX-V(1-h(q,i))X-Ki
Optimal rule Choose X so that
P
¶f (E )
h - W - V [1 - h(q, i)] = 0
¶E
VMP of applied water=price of applied
water+value of marginal residue
VMP=value of marginal product
Adoption and Policy
Theory yields hypothesis that can be tested
empirically and illustrated with simulations
Prices will affect adoption choices and intensities
Higher output prices will increase input use intensity
Higher input prices and pollution taxes will reduce input
use intensities
Adoption is more likely on lower land quality
Adoption is more likely when
output price is higher
Input price is higher
Pollution tax is higher
Adoption and quality
• PR1=Max Pf(h(q,1) X1)-W X1 -V(1-h(q,I)) X1 -K1
• PR0 =Max Pf(h(q,0) X0)-W X0 -V(1-h(q,0)) X0 -K0
• We know that
–
–
–
h(q,1) > h(q,0)- it increases input use efficiency
At q=1 both technologies input use efficiency is equal to 1
and both technologies have the same output and input use
K1> K0 New technology costs more
• The yield increasing input saving and pollution
reducing effects of the modern technology are higher
at a range of lower technologies
• Adoption occurs at lower qualities
•
Adoption & environmental quality
Profits increase
with quality
$
Below a threshold
level there is no
operation
Profit traditional
technology
0
1 Q-quality
Adoption & environmental quality
$
PR0 =Profit traditional technology
Adoption occurs at
Low qualities between
PR1 =Profit modern technology
qm and qc
PR0
PR1
0
qm
qc
1 Q-quality
Impact of pollution regulation
Without pollution ax traditional technology is
generating less output with more input
After tax the modern technology may be
using more input and output.The gap of
output increases
The Global implication
The growth in population was accompanied by much
less than proportional expansion of cultivated land and
relative increase in variable input and energy use.
There has, however, been increase in input use
efficiency—more output use per unit of critical inputs—
resulting from new technologies
Obvious examples are increased crop yield because
of improved varieties. Traditional methods of breeding
led to crop engineering which attained higher ratios of
fruits to straw.
The high productivity of agriculture slowed expansion
of deforestation.
However, it led to new environmental issues-chemical
residue climate change
The Global implication
Theory is used for both micro level studies and macro
level policy assessment
It gives us a prism to view history
Identify process shaping evolution of ag and society
Technologies and Substitution
At modern era technologies replace
Human effort
Natural resources with
Human capital
Physical capital
Energy
Resource-Saving Innovations
Are Not Limited to Agriculture
The current level of global round wood harvest is
the same as in 1976. It went up during the 1980s,
declined, and has been stable for five years, less
waste materials and use of recycled paper.
Computing power-energy use and per unit
computing cost has declined drastically (“Moore
law” ).
Miniaturization led to the same quality output with
much less material and energy in communication,
computing, radio, and clothing.
Other Examples
Input-use
efficiency
Impacts
Extra
cost
Technology
Alternative
High precision
chemical
applicators
Aerial sprayer .90 vs .25
Input-High
pollution--
Improved
cooking stove
Traditional
Wood stove
.60 vs .20
Wood -Health++
Modest
Insulation
Un-insulated
homes
.7 vs ,2
Energy--
Modest
Risk and adoption
Suppose we have constant return to scale
Land may be allocated among 2
technologies- i=0 less risky, i=1 more risky.
Land to technology i Li. L1+L0=L-total land
Expected profit per acre of technology i is Mi,
so that M1>M0.
Variance per acre is V1,V1>Vo. COV is the
covariance of profits per acre
We assume that farmers have constant
absolute risk a version R and profit are
distributed Normally
Optimal allocation
Determine L1 and LO subject to L1+L0=L
Max L1M1+L0M0-.5R(L12V1+L02V2-2L1L0Cov)
The optimal rule i
L1=(M1-M0)/R(V1+V0-COV)+(V0-COV)/(V1+V0COV)
The Optimal rule suggest share of technology
1 increases with
highest difference in mean profit
Higher variance of technology 0
Negative covariance
The Importance of correlation
MAX
L1m1 + L2m 2 - .5r L21s 12 + L2 2s 2 2 + 2L 1L2s 12
L1
[
]
Subject to L1 + L2 = L
[
]
L1(m1 - m 2 ) + L m 2 - .5r L21 (s 12 + s 2 2 - 2s 12 ) + L2s 2 2 - 2L L1 (s 2 2 - s 12 ) + L m 2
FOC
[
]
m1 - m 2 - r L1(s 12 + s 2 2 - 2s 12 ) - L (s 2 2 - s 12 ) = 0
m1 - m2
s 2 2 - s 12
L1 =
+ 2
L
2
2
2
r(s 1 + s 2 - 2s 12 ) s 1 + s 2 - 2s 12
s 22 - s 12 > 0
L1
The corellation between crop yields
matter
s 22 - s 12 < 0
L
Managing risks- there are many
categories –address by many
institutions-affecting adoption
Risk type
Price
Yield
weather
Revenue
Labor supply
Input price
Solution
Price support
Futures, forward contracts
Crop insurance, disaster
assistance
insurance
Revenue assurance,saving
Mechanization
Futures, forward contract
Future markets
Hedgers – take two positions – use futures to
balance real world risk
Speculators – take one sided positions-better
able to deal with risk
Advantage fo futures over forward contractsliquidity
Key low transaction cost
For farmers- future markets may increase
risks- because of uncertain quantities
Behavioral economics
Need to understand risk behavior
better
Loss aversion-Prospect theory
emphasizes that utility on negative value is
convex and on positive value convex
Adoption is part of a large
innovation system
Innovation is an economic activity
Education industrial complex
Research produce concepts = patent
Private sector develop commercialize market
Farmers and consumers adopt
Design of innovation system is a policy
challenge
Private sector under-develop innovationsespecially for poor-so there is a need for public
sector activities- indirect (policy) or through
investment
Agriculture and agribusiness
Agriculture is changing
Supply change is important
Innovation are developed within supply chains
Contracts replace markets
How technology is developed within supply
chain and agribusiness
How policy is advanced within an evolving
agribusiness system
Expansion of agriculture
Agriculture is expanding to include
environmental services, recreation, fuels
chemicals medicine etc
The extent that it will happened will depend on
productivity and policies
Technology is affected by regulation and policy
IPR
Environmental regulations
The border between agriculture and other
sectors is moving
The end
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