Production technology and risk

Ravello

David Zilberman

OUTLINE

Production

Adoption and the environment

Risk

Policy

Production functionsThey relate input use to output Y=f(X) Y output X vector of inputVaries significantly over spcae and time

Long run production functions- that reflect technology after a period of adjustment are different than short runHeterogeneity 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 qualityOutputs of different quality demand different input useInputs’ quality varies-a good worker can produce more Land quality and exposure to sun may double yieldsIt 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 becomesY=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 choicesThere 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 technologyY=Fi(X1,X2,X3…,Q1,Q2) production function

i= technology 0= traditional, 1,…. N newY output Xn quantity of input n Qm quality indicator mZ=Gi(X1,X2,X3…,Q1,Q2) Pollution function –relating output to inputsP output priceWn=rice of input n V pollution tax

Ki = fixed cost of technology i

Assessing Optimal use of technology iVPi=Variable profit of technology I

VPi=Max

PFi(X1,X2,X3…,Q1,Q2) –W1X1- W2X2-W3X3-

Revenue Cost-VGi(X1,X2,X3…,Q1,Q2)

Pollution tax Optimality conditionsP(dFi/dXn)- Wn - V(dGi/dXn) =0Marginal -price- Marginal pollutionRevenue cost

Choices over timeSuppose 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 analysisHow changes in parameters affect the optimal input uses and technology choicesFor 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 technologyOutput/acre is a function of effective input ( water)Y=f(E) E effective water – actually used by cropEffective 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 functionsY0=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)X-

Optimal input for technology 1Find X=X1* that Max Pf(Xh(q,1)) –wX-v (1-h(q,1))X-K1

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 adoptionThe 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 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 technologyP-output price,W=input price,V pollution price K1 per season cost of modern technology K0=0 per season cost of Traditional technologyChoice of input use with a given technologyPRi=Max Pf(hX)-WX-V(1-h(q,i))X-KiOptimal rule Choose X so that

VMP of applied water=price of applied water+value of marginal residueVMP=value of marginal product

Adoption and PolicyTheory yields hypothesis that can be tested empirically and illustrated with simulationsPrices will affect adoption choices and intensities

Higher output prices will increase input use intensityHigher input prices and pollution taxes will reduce input use intensities

Adoption is more likely on lower land qualityAdoption 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

$

Q-quality

0

1

Profit traditional

technology

Profits increase with quality

Below a threshold level there is no operation

Adoption & environmental quality

$

Q-quality

0

1

PR0 =Profit traditional technology

PR1 =Profit modern technology

PR0

PR1

qcqm

Adoption occurs atLow qualities between

qm and qc

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 implicationThe 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 technologiesObvious 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 implicationTheory is used for both micro level studies and macro level policy assessment It gives us a prism to view historyIdentify 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 Impacts

Extra cost

High precision chemical applicators

Aerial sprayer .90 vs .25 Input--pollution--

High

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+L0

2V2-2L1L0Cov)

• The optimal rule i

• L1=(M1-M0)/R(V1+V0-COV)+(V0-COV)/(V1+V0-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

The corellation between crop yields matter

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 economicsNeed 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

references

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Economics: A Dual Approach to Theory and Applications, Elsevier North-Holland, chapter 4, pages , 1978.(1978).

• Mundlak, Yair. "Plowing Through the Data." Annu. Rev. Resour. Econ. 3, no. 1 (2011): 1-19.

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references• Schmidt, Peter. "On the statistical estimation of parametric

frontier production functions." The review of economics and statistics 58.2 (2009): 238-39. Schmidt, Peter. "On the statistical estimation of parametric frontier production functions." The review of economics and statistics 58.2 (2009): 238-39.

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