UNIVERSITY OFUNIVERSITY OF

CRETECRETE

ECONOMICSECONOMICS

DEPARTMENTDEPARTMENT

B.E.NE.TeCB.E.NE.TeC

LABORATORYLABORATORY

FOODIMAFOODIMA

Modeling Food Industry:Modeling Food Industry:Product & Process Product & Process

Innovation, Technology Innovation, Technology Adoption & MergersAdoption & Mergers

Emmanuel Petrakis, Chrysovalantou Milliou & Emmanuel Petrakis, Chrysovalantou Milliou & Igor SloevIgor Sloev

Business Economics and New Technologies Laboratory,Business Economics and New Technologies Laboratory,Department of Economics, University of Crete,Department of Economics, University of Crete,

Department of Economics, Athens University of Department of Economics, Athens University of Economics and Business Economics and Business

&& Department of Economics, Universidad Carlos III de Department of Economics, Universidad Carlos III de

Madrid Madrid

Ι. Ι. Introduction (1)Introduction (1)

Food Industry is characterized Food Industry is characterized mainlymainly by: by:

A large number of Farmers A large number of Farmers →→ perfectly competitive structure in the perfectly competitive structure in the primary sectorprimary sector

A limited number of Food Processing Firms/ Manufacturers A limited number of Food Processing Firms/ Manufacturers →→ oligopolistic structure in food processing with food processors oligopolistic structure in food processing with food processors producing (horizontally and/or vertically) differentiated goods producing (horizontally and/or vertically) differentiated goods

A relatively small number of Supermarkets/Retailers, each selling A relatively small number of Supermarkets/Retailers, each selling most of the food products most of the food products →→ oligopolistic structure in retailing oligopolistic structure in retailing

Intensive Product Creation, Differentiation and Innovation Activities at Intensive Product Creation, Differentiation and Innovation Activities at the Food Processing layer the Food Processing layer →→ Target: enhancement of product variety Target: enhancement of product variety and product quality, increase product differentiationand product quality, increase product differentiation

Frequent Mergers/Acquisitions both in the Retailing and the Frequent Mergers/Acquisitions both in the Retailing and the Manufacturing layer of the tree-tier industryManufacturing layer of the tree-tier industry

Ι. Ι. IntroductionIntroductionMotivation of the research projectMotivation of the research project

To capture (some of) the characteristics of the Food To capture (some of) the characteristics of the Food Industry we build a series of industrial organization Industry we build a series of industrial organization models that properly address the following issues:models that properly address the following issues:

• The food processors strategic incentives to invest in innovative The food processors strategic incentives to invest in innovative activities and in new technology adoption in order to increase activities and in new technology adoption in order to increase product variety, augment differentiation of the goods produced product variety, augment differentiation of the goods produced and enhance product qualities, as well as their market and welfare and enhance product qualities, as well as their market and welfare implications of their strategiesimplications of their strategies

• The food processors and/or the retailers’ incentives to merge The food processors and/or the retailers’ incentives to merge and/or to acquire rivals, as well as the market and welfare and/or to acquire rivals, as well as the market and welfare implications of such mergersimplications of such mergers

FF11 FF22 FF33 FFnn

MM11 MM22 MMnn

RR11 RR22 RRnnSS

1w 1

w1

w

2w 2

w2

wF

nw

Fnw

Fnw

11q

21q 1Fn

q 12q

22q

2Fnq

SnFnq

Snq

1

Snq

2

FinalFinal ConsumersConsumers

Figure 1: Industry StructureFigure 1: Industry Structure

Ι. Ι. IntroductionIntroduction

Purpose of the current researchPurpose of the current research

The main purpose of this research is to develop a tractableThe main purpose of this research is to develop a tractable

model of a tree-tier industry which allows the investigation of:model of a tree-tier industry which allows the investigation of:

The product and process innovation activities of food processing The product and process innovation activities of food processing firms and the effects of such activities on prices, product variety, firms and the effects of such activities on prices, product variety, consumer surplus, firms’ profits and welfare.consumer surplus, firms’ profits and welfare.

The role of the economies of scope in product creation processes.The role of the economies of scope in product creation processes.

The food processors and supermarkets incentive to merge and the The food processors and supermarkets incentive to merge and the effects of mergers on prices, product variety, consumer surplus, firms’ effects of mergers on prices, product variety, consumer surplus, firms’ profits and welfare.profits and welfare.

ΙΙII.. The Model (1) The Model (1)

Farmers:Farmers:A large number of price-taking farmers produce and sell agricultural A large number of price-taking farmers produce and sell agricultural products to the food processors at a price equal to their marginal (and products to the food processors at a price equal to their marginal (and unitary) cost, which is normalized to zero.unitary) cost, which is normalized to zero.

Manufactures:Manufactures:L food processing firms/manufacturers, ℓ=1,2,…,L.L food processing firms/manufacturers, ℓ=1,2,…,L.

Each manufacturer ℓ decides how many differentiated food products to Each manufacturer ℓ decides how many differentiated food products to produce, nproduce, nℓℓ. The total number of goods produced is N= n. The total number of goods produced is N= n11+…+ n+…+ nL.L.

Manufacturers compete in prices: each manufacturer ℓ sets the prices for Manufacturers compete in prices: each manufacturer ℓ sets the prices for all the good he produces, {all the good he produces, {ttℓ1ℓ1, t, tℓ2ℓ2, …,t, …,tℓ nℓℓ nℓ}}. . The vector of all manufacturers’ The vector of all manufacturers’ pricesprices is is ((tt11,…,t,…,tNN)=()=(tt1111,…, t,…, tℓ nℓℓ nℓ,…,,…, ttN1N1,…, t,…, tN nNN nN).).

The vector of quantities sold in the market by retailers is: (QThe vector of quantities sold in the market by retailers is: (Q11,…,Q,…,QNN) ) =(Q=(Q1111,…, Q,…, Q1 nℓ1 nℓ,…, Q,…, QL1L1,…,Q,…,QL nLL nL), where the first ), where the first nn1 1 elements refer to elements refer to manufacturer 1’s goods, the next nmanufacturer 1’s goods, the next n22 elements refer to the manufacturer elements refer to the manufacturer 2’s goods etc.).2’s goods etc.).

ΙΙII.. The Model (2) The Model (2)

Retailers:Retailers:

R R supermarkets/retailers, supermarkets/retailers, r=1,2,…,Rr=1,2,…,R, each (potentially) selling all , each (potentially) selling all manufacturers’ goods. manufacturers’ goods.

Each retailer Each retailer rr chooses the quantity of each good that he buys from each chooses the quantity of each good that he buys from each

manufacturer and resells it to the final consumers, (qmanufacturer and resells it to the final consumers, (qr1r1,…q,…qrNrN), r=1,…,R), r=1,…,R

The total quantity of good The total quantity of good ii sold in the market by all retailers is sold in the market by all retailers is

QQi i = q= q1i1i+…+ q+…+ qRiRi, i=1,…,N, i=1,…,N

Manufactures’ cost structure:Manufactures’ cost structure:

The marginal cost of transformation of any agricultural product to any The marginal cost of transformation of any agricultural product to any food product is normalized to zero.food product is normalized to zero. Each manufacturer faces a cost of creation of a spectrum of goods, Each manufacturer faces a cost of creation of a spectrum of goods, cc((nnℓℓ): ): cc(1)>0, (1)>0, c’c’((nnℓℓ)>0.)>0.

Thus the cost function of manufacturer ℓ is TCThus the cost function of manufacturer ℓ is TCℓℓ(n(nℓℓ)=c(n)=c(nℓℓ))

ΙΙII.. The Model (3) The Model (3)

Retailers’ cost structure:Retailers’ cost structure:

There are no reselling costs. Thus the retailing marginal cost for each There are no reselling costs. Thus the retailing marginal cost for each food product is equal to the food processor’s wholesale price, tfood product is equal to the food processor’s wholesale price, tℓ,kℓℓ,kℓ, ℓ=1,2,, ℓ=1,2,…,L; k…,L; kℓℓ=1,…,n=1,…,nℓℓ,, or in another notation (tor in another notation (t11,…,t,…,tNN).).

ΙΙII.. The Model (4) The Model (4)

Utility function of the representative consumer:Utility function of the representative consumer:

VQQQQQQQQ

QQAQQU

NNNN

NN

)2..2..2..(2

1

)....(),..,(

112122

1

11

(1)(1)

• AA: reflects the size of the market.: reflects the size of the market.

• ß: ß: 0<0<ß<1 represents the degreeß<1 represents the degree of product substitutability/ product of product substitutability/ product differentiation .differentiation .

• V: represents the income spent on the rest of the goods.V: represents the income spent on the rest of the goods.

where:where:

Hence, the system of the demand function is:Hence, the system of the demand function is:

NjiQQApN

ijjjii ,...,1,,

,1

(2)(2)

ΙΙII.. The Model (5) The Model (5)

Therefore, the manufacturer Therefore, the manufacturer ℓ’sℓ’s profit functionprofit function is: is:

),( ll

llUl ncQt

l

(3)(3)

and the retailer and the retailer rr’s’s profit functionprofit function is: is:

rn

N

nnn

Dr qtp

1

)( (4)(4)

where:where: ΩΩℓℓ is the set of goods produced by the manufacturer ℓ.is the set of goods produced by the manufacturer ℓ.

ΙΙIIII.. Timing of the Game Timing of the Game

We consider a three-stage gameWe consider a three-stage game::

Stage1Stage1: : Farmers sell their agricultural products to the food Farmers sell their agricultural products to the food

processors at the competitive market prices.processors at the competitive market prices.

Stage 2Stage 2: : Manufacturers decide simultaneously and independently Manufacturers decide simultaneously and independently

how many goods each to producehow many goods each to produce and also set the prices of their and also set the prices of their

goods.goods.

Stage 3Stage 3:: Retailers buy all food processors’ products and resell them Retailers buy all food processors’ products and resell them

to final consumers, setting simultaneously their food product to final consumers, setting simultaneously their food product

quantities (quantities (qqr1r1,…q,…qrNrN), r=1,…,R.), r=1,…,R.

Solving by Solving by Backwards InductionBackwards Induction

IVIV.. Analysis (1) Analysis (1)

EquilibriumEquilibrium Analysis when the number of manufacturers Analysis when the number of manufacturers

(L)(L) and retailers and retailers(R)(R) are given exogenously. are given exogenously.

In theIn the Symmetric SPNESymmetric SPNE (symmetry in prices and in the number of (symmetry in prices and in the number of produced goods) the optimal price and number of goods produced by produced goods) the optimal price and number of goods produced by each manufacturer are (implicitly) determined by the system of each manufacturer are (implicitly) determined by the system of equations:equations:

)('))1(1(

)1(1

)1(

])([

)1()1(2

)1(

*2*

***

**

ncLn

Ln

R

ttAR

nL

At

(5)(5)

IVIV.. Analysis (2) Analysis (2)

In addition, in theIn addition, in the Symmetric SPNESymmetric SPNE::

Manufacturer’s optimal output of each Manufacturer’s optimal output of each single good:single good: )1(11 *

*

Ln

tA

R

RQ

)()1)(1(

)( **

** nc

LnR

tARtnU

R

RtAp

1

*

))1(1()1(

)(*2

2**

LnR

tALnD

Manufacturer’s equilibrium profits:Manufacturer’s equilibrium profits:

Retailer’s prices:Retailer’s prices:

Retailer’s profits:Retailer’s profits:

(6)(6)

(7)(7)

(8)(8)

(9)(9)

IVIV.. Results Results

Proposition Proposition 11:: The manufacturer’s profits are decreasing in The manufacturer’s profits are decreasing in L L and and increasing in increasing in R.R.

The Benchmark case:The Benchmark case:

We consider the case where each manufacturer produces one We consider the case where each manufacturer produces one good only. Then its cost function is given by good only. Then its cost function is given by TCTCℓℓ=c(1)=c(1). Let . Let tts s denote denote the equilibrium price in this case for a given number of the equilibrium price in this case for a given number of manufacturers manufacturers NNss (which is equal to the number of goods too). Let (which is equal to the number of goods too). Let L L be such that be such that LnLn** = N = Nss. .

Proposition Proposition 22::

The equilibrium prices of the single good manufacturers The equilibrium prices of the single good manufacturers are are always always lowerlower than the prices of the multi-product than the prices of the multi-product manufacturers, manufacturers, tts s < t< t**..

Let Let c(n) = g nc(n) = g naa, where a ≥ 0. Then a < (>) 1 reflects economies , where a ≥ 0. Then a < (>) 1 reflects economies (diseconomies) of scope.(diseconomies) of scope.

V. Numerical Simulations

Numerical simulation when L and R are given exogenously

Table 1. β=0.6, A=10, g=0.1, a=0.7, L=2

Pr.U : manuf.’s profit, Ln* : total number of goods, TQ : total quantity produced, Pr.D : retailer’s profit, CS: consumers’ surplus, TW : total welfare

R n* Pr.U L n* TQ Pr.D CS TW

2 25.43 0.37 50.87 10.69 17.38 34.75 70.26

3 27.35 0.39 54.69 12.06 9.81 44.18 74.41

4 28.44 0.40 56.90 12.88 6.29 50.38 76.37

5 29.16 0.41 58.37 13.43 4.37 54.74 77.12

6 29.67 0.41 59.35 13.82 3.22 57.97 78.11

50 32.21 0.43 64.42 15.85 0.06 76.15 80.08

∞ 32.6 0.44 65.20 16.17 0 79.27 80.16

V. Numerical SimulationsNumerical simulation when L and R are given exogenously.

Table 2. β=0.6, A=10, g=0.1, L=2, R=4

Pr.U : manuf.’s profit, Ln* : total number of goods, TQ : total quantity produced, Pr.D : retailer’s profit, CS : consumers’ surplus, TW : total welfare

a n* Pr.U L n* TQ Pr.D CS TW

0.5 56.90 -0.004 113.8 13.1 6.47 51.82 77.72

0.6 39.06 0.171 78.1 13.0 6.39 51.15 77.07

0.7 28.45 0.226 56.9 12.88 6.29 50.38 76.37

0.8 21.68 0.675 43.4 12.75 6.19 49.52 75.64

0.9 17.12 0.99 34.2 12.61 6.08 48.60 74.88

1 13.29 1.32 27.84 12.45 5.95 47.63 74.11

1.1 11.59 1.68 23.18 12.29 5.83 46.63 73.32

2 4.19 4.79 8.38 10.86 4.77 38.2 66.89

3 2.50 6.87 5.01 9.72 4.01 32.1 61.95

4 1.9 7.93 3.81 9.01 3.58 28.66 58.86

V. Numerical SimulationsNumerical simulations when L and R are given exogenously.

Table 3. A=10, g=0.1, a=0.7, L=2, R=4

Pr.U : manuf.’s profit, Ln* : total number of goods, TQ : total quantity produced,

Pr.D : retailer’s profit, CS : consumers’ surplus, TW : total welfare

β n* Pr.U L n* TQ Pr.D CS TW

0.2 155.1 1.13 310.3 38.52 18.79 150.3 228.1

0.3 88.94 0.88 177.9 25.66 12.51 100.1 151.9

0.4 57.95 0.65 115.9 19.26 9.39 75.13 114.0

0.5 40.10 0.50 80.2 15.42 7.53 60.24 91.4

0.6 28.44 0.40 56.9 12.88 6.29 50.38 76.4

0.7 20.11 0.31 40.2 11.08 5.42 43.4o 65.7

0.8 13.6 0.24 27.2 9.73 4.78 38.24 57.8

V. Numerical SimulationsNumerical simulations when L and R are given exogenously.

Table 4. β=0.5, A=10, g=0.1, a=0.9, R=2

Pr.U : manuf.’s profit, Ln* : total number of goods, TQ : total quantity produced, Pr.D :retailer’s profit, CS : consumers’ surplus, TW : total welfare

L n* Pr.U L n* TQ Pr.D CS TW

2 20.9 1.17 41.8 12.5 19.85 39.70 81.75

3 13.8 0.35 41.4 12.6 20.25 40.51 82.09

4 10.2 0.15 40.9 12.6 20.38 40.77 82.15

5 8.1 0.07 40.5 12.6 20.44 40.88 82.16

6 6.7 0.04 40.1 12.6 20.47 40.95 82.15

7 5.7 0.02 39.8 12.6 20.49 40.98 82.13

8 4.9 0.01 39.6 12.6 20.50 41.01 82.10

9 4.3 0.003 39.3 12.7 20.51 41.02 82.08

10 3.9 0 39.0 12.7 20.52 41.03 82.06

V. Numerical Simulations

Numerical simulations when L and R are given exogenously.

Table 5. A=10, β=0.6, a=0.7, L=2, R=4

Pr.U : manuf.’s profit, Ln* : total number of goods, TQ :total quantity produced, Pr.D :retailer’s profit, CS : consumers’ surplus, TW :total welfare

g n* Pr.U L n* TQ Pr.D CS TW

0.1 28.45 0.40 56.90 56.90 6.30 50.38 74.56

0.3 14.36 0.71 28.71 28.71 5.97 47.79 73.11

0.5 10.33 0.91 20.66 20.66 5.74 45.93 71.85

0.7 8.27 1.07 16.54 16.54 5.54 44.40 70.73

0.9 6.97 1.18 13.95 13.95 5.38 43.06 66.97

1.1 6.07 1.28 12.15 12.15 5.23 41.87 65.37

VI. Numerical Simulation Findings• As the number of manufacturers (L) increase we observe an

increase in:

• As the economies of scope become stronger (lower a) we observe an increase in

1. The total number of goods produced (L n*) 2. The total quantity (L n*Q) 3. The retailers’ profits 4. The social welfare

• While the product variety produced by each manufacturer (n*) decreases

1. The total number of goods produced (L n*) 2. The product variety produced by each

manufacturer (n* )

3. The total quantity (L n*Q) 4. The retailers’ profits 5. The consumers’ surplus and social welfare

• While the manufacturers’ profits decrease

VI. Numerical Simulation Findings• As the degree of product substitutability β increases we observe a

decrease in:

• As the number of the retailers R increases we observe an increase in:

1. The product variety produced by each manufacturer (n*)

2. The total number of the goods produced (Ln*)3. The total quantity (Ln*Q)4. The retailers’ and manufacturers’ profits 5. The social welfare

1. The product variety produced by each manufacturer (n*)

2. The total number of the produced goods (Ln*)3. The total quantity (Ln*Q)4. The manufacturers’ profits 5. The consumers surplus.

While the retailers’ profits decrease

VI. Analysis under Free Entry (1)

Equilibrium Analysis under free-entry condition.

In this case we assume that there is free entry in the food processing layer, i.e. the number of manufacturers L* is such that the manufacturers profits are equal to zero.

Proposition 3: The degree of scope economy can take prices 0 < â < ã such that

• If the degree of economies of scope is high enough (0<a≤ ã), then there is only one manufacturer in the market.

• If the degree of economies of scope is low enough (a≥â), or there are diseconomies of scope, then each manufacturer produces a single good.

VI. Analysis under Free Entry (2)

Equilibrium Analysis under free-entry condition.

For any intermediate degree of economies of scope, â ≤a ≤ ã, the equilibrium values of L*, n*, t* are determined by the system of equations:

anana

naaA

R

R

ana

aAt

naL

*2*

*22

**

**

))1)(1((

)1()1(

1

)1)(1(

)1)(1(

1

1

1

(10)

(11)

VI. Free Entry Results (1)

Lemma 1: The number of varieties produced by each manufacturer n* is increasing in A, R, a and is decreasing in g

•Asymptotic Results

Suppose that the parameters [a, β, g, A, R] are such, that n* is big enough. Then the equilibrium values of total output, retailers’ profits, consumers surplus, number of manufacturers and social welfare are approximately:

2

2*

2

22

2

2

)1(2

)2(;

1

1

)1(2,

)1(;

1

R

RMATW

aL

R

RACS

R

A

R

RATQ D

The Benchmark case under free entry condition: We consider the case where each manufacturer produces a single good only. In addition, let ts denote the equilibrium price in this case and let Ns be the number of manufacturers which are determined by the free entry condition (Ns is also equal to the number of goods in this case).

Proposition 4 :

The total number of goods, the total output and the retailers’ profits are higher in the case of multi-product manufacturers than the respective ones in the case of single product manufacturers.

On the contrary, the multi-product manufacturers’ prices are lower than those in the case of single product manufacturers.

VI. Free Entry results (2)

VII. Numerical Simulations

Table 6. β=0.6, A=10, g=0.1, a=0.7

Ns, TWs : number of firms (goods), total welfare in the case of single-product manufacturers

Numerical simulations under free entry conditions.

R n* L L n* Ns TQ Pr. D CS TW TWs

2 14.25 3.28 46.8 26.4 10.7 17.55 35.1 70.2 68.7

3 15.30 3.29 50.3 28.0 12.1 9.91 44.6 74.3 72.8

4 15.90 3.29 52.3 29.0 12.9 6.35 50.8 76.2 74.7

5 16.30 3.29 53.7 29.6 13.5 4.42 55.2 77.3 75.4

6 16.57 3.29 54.6 30.0 13.9 3.24 58.5 77.9 76.4

50 17.97 3.29 59.2 32.2 15.9 0.06 76.8 79.8 78.2

∞ 18.18 3.30 59.9 32.5 16.2 0 79.9 79.9 78.3

VII. Numerical SimulationsNumerical simulation under free entry conditions.

Table 7. ß=0.6, A=10, g=0.1, R=4

Pr.U: manuf.’s profit, Ln*: total number of goods, TQ: total quantity produced, Pr.D: retailer’s profit, CS: consumers’ surplus, TW: total

welfare

a n* L L n* TQ Pr. D CS TW

0.1 3200 1.11 3555 13.30 6.64 53.12 79.7

0.3 268.2 1.42 382.4 13.23 6.58 52.63 78.9

0.5 57.4 1.98 114.0 13.10 6.48 51.81 77.7

0.7 15.9 3.29 52.34 12.93 6.35 50.82 76.2

0.9 3.25 9.79 31.93 12.77 6.24 49.95 74.9

1.1 1 28.97 28.97 12.73 6.22 49.79 74.7

VII. Numerical SimulationsNumerical simulation under free entry conditions.

Table 8: A=10, g=0.1, a=0.7, R=4

Pr.U: manuf.’s profit, Ln* : total number of goods, TQ: total quantity produced, Pr.D: retailer’s profit, CS: consumers’ surplus,

TW: total welfare

β n* L L n* TQ Pr.D CS TW

0.5 22.44 3.29 73.81 15.49 7.60 60.8 91.2

0.6 15.90 3.29 52.34 12.93 6.35 50.8 76.2

0.7 11.22 3.30 36.97 11.12 5.46 43.8 65.6

0.8 7.57 3.30 25.00 9.76 4.81 38.5 57.7

0.9 4.40 3.30 14.57 8.72 4.31 34.5 51.8

VII. Numerical SimulationsNumerical simulation under free entry conditions.

Table 9: β=0.6, A=10, R=4, a=0.7

Pr.U : manuf.’s profit, Ln* : total number of goods, TQ : total quantity produced, Pr.D : retailer’s profit, CS : consumers’ surplus, TW : total

welfare

g n* L L n* TQ Pr. D CS TW

0.1 15.9 3.29 52.34 12.93 6.35 50.82 76.23

0.3 8.17 3.25 26.57 12.57 6.07 48.57 72.86

0.5 5.96 3.22 19.21 12.29 5.87 46.94 70.41

0.7 4.83 3.20 15.43 12.07 5.69 45.57 68.36

0.9 4.12 3.17 13.07 11.86 5.54 44.37 66.56

1.1 3.62 3.14 11.41 11.67 5.41 43.29 6494

VIII. Numerical Simulation Results

The product variety produced by each manufacturer, n*, the total number of goods, Ln*, the total output, Ln*Q, the retailers’ profits, the consumers’ surplus and the social welfare are decreasing in a, while the number of manufacturers is increasing in a.

As the degree of product substitutability β increases, the product variety produced by each manufacturer, n*, the total number of goods, Ln*, the total output, Ln*Q, the retailers’ and manufacturers’ profits, and the consumers’ surplus and the social welfare decrease.

An increase in the number of retailers, R, leads to an increase in the product variety produced by each manufacturer, n*, the total number of goods, Ln*, the total output, Ln*Q, the manufacturer’s profits, the consumers’ surplus and the total welfare, while it leads to a decrease in the retailers’ profits.

IX. The Case of Upstream Process Innovation Activities

The Process Innovation Activities case: In this scenario, we consider the case where manufacturers have the option to invest in process innovation activities. Thus, in the first stage of the game manufacturers decide both on the number of the goods that they produce and their prices, as well as decide the level of process innovation activity that they will undertake.

Assumptions:The number of the manufacturers (L) is given exogenously. The investment in process innovation activities lead to a reduction of the manufacturers’ production costs. In fact, the manufacturer's cost function is given now by: TC(n,x)=(g-x)na-kx2 where: x represents the level of investment in innovation activities and kx2 is the cost of these activities.

X. Numerical SimulationsNumerical simulations: The case of U process innovation activities.

Table 10: R=2, A=10, g=0.1, a=0.9, β=0.5, k=500

Pr.U : manuf.’s profit, Ln* : total number of goods, TQ : total quantity produced, Pr.D : retailer’s profit, CS :consumers’ surplus, TW : total welfare

L x n* Pr.U L n* TQ Pr.D CS TW

2 .016 23.2 0.93 46.5 12.54 20.06 40.13 82.11

4 .008 10.7 0.11 43.0 12.65 20.47 40.93 82.31

6 .005 6.9 0.02 41.5 12.66 20.53 41.06 82.26

8 .004 5.0 0.001 40.5 12.67 20.54 41.09 82.19

X. Numerical SimulationsNumerical simulations The case of U process innovation activities

Table 11: R=4, A=10, g=0.1,β=0.6, L=2, k=500

Pr.U : manuf.’s profit, Ln* :total number of goods, TQ: total quantity produced, Pr.D: retailer’s profit, CS: consumers’ surplus, TW: total

welfare

a x n* Pr.U L n* TQ Pr.D CS TW

0.6 0.009 41.61 0.11 83.23 13.02 6.40 51.28 77.15

0.8 0.012 23.43 0.55 46.85 12.79 6.22 49.80 75.79

1 0.015 15.20 1.11 30.40 12.52 6.00 48.07 74.34

2 0.021 4.58 4.33 9.16 11.02 4.89 39.14 67.38

3 0.018 2.66 6.53 5.31 9.86 4.11 32.88 62.40

4 0.016 1.98 7.73 3.96 9.12 3.64 29.16 59.20

X. Numerical SimulationsNumerical simulations: The case of U process innovation activities

Table 12: R=2, A=10, g=0.1, a=0.7, L=2,k=500

Pr.U: manuf.’s profit, Ln* : total number of goods, TQ: total quantity produced, Pr.D: retailer’s profit, CS: consumers’ surplus, TW: total welfare

β x n* Pr.U L n* TQ Pr.D CS TW

0.2 0.043 220.2 0.00 440.5 38.9 19.1 153.0 229.6

0.3 0.026 107.3 0.39 214.6 25.8 12.6 101.2 152.6

0.4 0.018 65.8 0.40 131.6 19.3 9.4 75.7 114.4

0.5 0.014 44.0 0.36 88.05 15.5 7.6 60.6 91.6

0.6 0.010 30.5 0.31 61.08 12.9 6.3 50.6 76.5

0.7 0.008 21.2 0.26 42.4 11.0 5.4 43.5 65.8

0.8 0.006 14.6 0.21 28.3 9.7 4.8 38.3 57.8

XI. Comparison Results

Comparing the case of Innovation Activities with that with no investment in process innovation, in case that the number of manufacturers (L) is exogenously given, we observe that:

In the case where manufacturers invest in process innovation activities, we observe an increase in:

1. The product variety that each manufacturer produces (n*)

2. The total number of produced goods (Ln* )

3. The Retailers’ profits (slightly)

4. The Consumers’ Surplus

5. The Total Welfare On the contrary, when manufacturers invest in process innovation

activities, we observe a decrease in their profits.

XII. Conclusions In the present research we investigate the product and process innovation activities of the food processing firms, as well as the merger incentives of the food processing firms and their retailers. In particular, the role of the economies of scope at the product creation process is analyzed. Finally, the effects of innovation and mergers on the price levels, the product variety, the number of firms at both the retailing and food processing layer, as well as their welfare effects are analyzed.

Our main findings suggest that: When the number of manufacturers ( L) and the number of the retailers (R) is given exogenously, then the equilibrium product variety n* and the total number of goods (Ln* ), are increasing in the market size (A), while there are decreasing in the degree of product substitutability (ß) and the diseconomies of scope (a).

An increase in the number of manufacturers leads to an increase in the total number of goods. However, the product variety produced by each firm decreases.

The higher is the number of retailers the higher are both the product variety, n*, and total number of goods, Ln*.

XII. Conclusions

Under free entry, the equilibrium number of manufacturers and the product variety produced by each manufacturer crucially depends on the degree of the economies of scope (a):

• If a is “very small” then there is only one manufacturer who produces all goods.

• If a is “very high” then each manufacturer produces only a single product

• For intermediate values of a, the number of manufacturers is increasing in the degree of the diseconomies of scope (a), while the product variety produced by each manufacturer and the total number of the produced goods are decreasing in a.

• The product variety produced by each manufacturer is increasing in the number of the retailers (R ). In addition the number of the manufacturers (slightly) increases in the number of the retailers (R ).

XII. Conclusions

When the manufacturers invest in process innovation activities we observe an increase in: the product variety that each manufacturer produces (n*), the total number of produced goods (Ln* ), the retailers’ profits, the Consumers’ Surplus and the Total Welfare.

In contrast, when the manufacturers invest in process innovation activities, they are locked in a Prisoners’ Dilemma. Thus, we observe lower manufacturers’ profits.

UNIVERSITY OFCRETE

ECONOMICS DEPARTMENT

B.E.NE.TeCLABORATORY

THANK YOUTHANK YOU

Emmanuel Petrakis

Business Economics & New Technologies (B.E.NE.TeC) Laboratory

Economics Dept, University of CreteE-mail: petrakis@econ.soc.uoc.gr