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=A i K i a i L i b i Each element fo the production function may vary by individuals- better managers may have a larger A i (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 technologies each 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 question Whether 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(X 1 ,X 2 ,X 3 …,Q 1 ,Q 2 ) production function i= technology 0= traditional, 1,…. N new Y output Xn quantity of input n Qm quality indicator m Z=Gi(X 1 ,X 2 ,X 3 …,Q 1 ,Q 2 ) Pollution function –relating output to inputs P output price W n =rice of input n V pollution tax K i = fixed cost of technology i

Assessing Optimal use of technology i

VP i =Variable profit of technology I VP i =Max PFi(X 1 ,X 2 ,X 3 …,Q 1 ,Q 2 ) –W 1 X 1 - W 2 X 2 -W 3 X 3 Revenue Cost -VGi(X 1 ,X 2 ,X 3 …,Q 1 ,Q 2 ) 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 VP 10 -VP 00 +(VP 11 -VP 01 )/(1+r)+(VP 12 -VP 02 )/(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(VP 1 -VP 0 )/dQ 1 <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

Y 0 =f(X q ) Z 0 =(1-q)X=pollution is residue Y 1 =f(Xh(q,1)), Z 1 =(1-h(q,1))X Optimal input use technology 0-X 0 * Find X=X 0 * that Max Pf(Xq) –wX-v(1-q)X Optimal input for technology 1 Find X=X 1 * that Max Pf(Xh(q,1)) –wX-v (1-h(q,1))X K1 First order condition at X 0 * Pqdf(Xq)/dE –w-v(1-q)=0 at X 1 * 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 technology For example if there are two technologies traditional 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 and steep hills.

on lower quality lands —sandy soils More adoption with high-value crop, high prices of water drainage, and output.

Technology Traditional Irrigation efficiency .6

Water/ drainage 4.0/1.6

Yield (cotton) 1200 Fixed cost/yr 500 Sprinkler Drip .8

.9

3.2/.64

2.7/.27

1325 1400 580 650

Optimal input use for a technology

P-output price,W=input price,V pollution price K 1 per season cost of modern technology K 0 =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

) ¶

E h

-

W

-

V

[ 1 -

h

(

q

,

i

) ] = VMP of applied water=price of applied 0 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

• PR 1 = Max Pf(h(q,1) X 1 )-W X 1 • PR 0 = Max Pf(h(q,0) X 0 )-W X 0 • We know that -V(1-h(q,I)) X 1 -V(1-h(q,0)) X 0 -K 1 -K 0 – – 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 • – K 1 > K 0 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

PR 0 =Profit traditional technology PR 1 =Profit modern technology PR 0 Adoption occurs at Low qualities between q m and q c PR 1 0 q m q c 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

Technology Alternative Input-use efficiency High precision chemical applicators Improved cooking stove Aerial sprayer .90 vs .25

Traditional Wood stove .60 vs .20

Insulation Un-insulated homes .7 vs ,2 Impacts Extra cost Input- pollution- High Wood - Health++ Modest 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 L i . L 1 +L 0 =L-total land Expected profit per acre of technology i is Mi, so that M 1 >M 0 .

Variance per acre is V 1 ,V 1 >V o . 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 L 1 and L O subject to L 1 +L 0 =L Max L 1 M 1 +L 0 M 0 -.5R(L 1 2 V 1 +L 0 2 V 2 -2L 1 L 0 Cov) The optimal rule i L1=(M 1 -M 0 )/R(V 1 +V 0 -COV)+(V 0 -COV)/(V 1 +V 0 COV) 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 L

1 m 1

L

1 +

L

2 m 2 .5

[

r L

2 1 s 1 2

Subject to L

1

L

1 ( m 1 m 2 ) + +

L

2

L

m 2 = [

L

.5

r L

2 1 ( s 1 2 +

L

2 2 s 2 2 + s 2 2 + 2

L

1

L

2 s 12 ] 2 s 12 ) +

L

2 s 2 2 2

L L

1 ( s 2 2 s 12 ) ] +

L

m 2

FOC

m 1 -

L

1 = m 2 -

r

( s 1 2 [

r L

1 ( s 1 2 m 1 m 2 + s 2 2 + s 2 2 2 s 12 ) + 2 s 12 ) -

L

( s 2 2 s 1 2 s 2 2 + s 2 2 s 12 2 s 12 s 12 ) ] =

L

0

L

1 The corellation between crop yields matter s 2 2 s 12 > 0 s 2 2 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 contracts liquidity 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 innovations especially 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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references

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