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Optimal quality choice under uncertainty on market development
Lota D TaminiCREATE and Laval University
Annual Workshop of the ERCA Research NetworkMarch 8, 2013
Ottawa
Background Competition between firms, (and countries) some of which
are new players in global markets, has intensified.
Firms tend to differentiate their products to relax price competition and seek some form of monopoly rent [Shaked and Sutton, 1982].
E.g.: high-protein hard wheat in the United States (U.S.) and Canada, most of the meat supply chain, and product differentiation and labeling in European countries.
The major Canadian agri-food companies successfully differentiate their products to lower price competition, which explains their solid performance [Deloitte Touche Tohmatsu, 2011].
In most cases, the industrial organization literature has focused on the effects of differentiation strategies on market structure, firms' performances, and welfare effects.
However most of these studies do not take into account the impact of risk and uncertainty aversion on commodity quality.
Risk refers to situations in which the decision maker evaluates the likelihood of each event through a fixed probability.
Under Knightian uncertainty (ambiguity aversion or ambiguity hereafter) the decision maker considers a set of probabilities instead of just one. The lack of information precludes the decision maker from attributing
defined probabilities to events.
In the international trade context, ambiguity aversion can explain persistence in trade and the home consumption bias. Uncertainty-averse economic agents dislike ambiguity. Huang (2007) shows that countries high in ambiguity aversion export disproportionately less to countries with which they are less familiar.
Recent examples of empirical studies of the impact of ambiguity aversion on technology adoption are Engle-Warnick et al. (2011) and Barham et al. (2012).
If a firm is less confident about the future development of a market, investment will be made with caution.
Background
Pennings (2004) examines quality choice and entry timing when future market demand is uncertain and the quality-enhancing investment is irreversible.
Risk increases optimal quality in both the monopoly case and in a Stackelberg-Nash duopoly model with a leader producing a high-quality commodity.
For the monopolist, Nishimura and Ozaki (2007) and Asano and Shibata (2011) assert that the results are drastically different between risk and Knightian uncertainty.
Specifically, an increase in Knightian uncertainty decreases the value of the investment opportunity and the optimal value of quality.
Impact when analyzing emerging markets?
Cairn and Meilke (2012): “… why does Canada face lower Engel elasticities?”
Background
Asano and Shibata (2011): "...introducing a notion of Knightian uncertainty into analyses of product development is appropriate for analyzing situations in which the change of market size in the future cannot be easily forecasted and a lot of scenarios can be assumed."
The purpose of this paper is to analyze The impact of risk and ambiguity aversion on the choice of
i. optimal quality and
ii. the timing of market entry in the agri-food sector.
The impact of vertical integration on the choice of optimal quality.
Background
The model Consumer’s utility [Mussa and Rosen, 1978]
s is the good quality, p the price and the taste parameter.
Market growth [Nishimura and Ozaki, 2007]
, , 1tU s p s p D M p s
t t t t tdM M dt M dB
0,1
: market size
0 : drift parameter
0 : standard deviation
, : density generator of the probability
: standard Brownian motion
tM
B
Producers of differentiated goods
Profit :
Cost of producing a good of quality s :
Revenue function :
Investment in product development of the differenciated good is assumed by the sellers of the differentiated good.
Under vertical integration we assume that buyers purchase the assets of dowstream producers.
p p p pq R q c s q
20c s s
p p iR q E q s
20I s s
The model
We consider a continuous-time model where the decision on when and how much to invest in quality is endogenously determined.
Duopoly with a Stackelberg game for the quality choice: Firms differ in size or technologies.
small asymmetries in cost.
The leader and follower are exogenously assigned at the start of the game.
The timing of the game is as follows: In the first stage,
the leader decides on price it charge until the follower comes into market, on quality and on the critical market size;
the follower set quality and its critical market size.
In the second stage, both firm set price for the duopoly period.
The model
The economic environment mimics the hog supply chain in Québec. Drift parameter : μ=0.05
Standard deviation : σ=0.1 as a base value of volatility of market development.
Marketing cost : c=$25 [Gervais and Lambert (2010) ].
In 2010, hog production in Québec was 7.7 million heads, sales was amounted to $1.2 trillion (MAPAQ, 2010). We assumed that about half of the total demand concerns specialty hogs. The market size of the economy (M) is thus set to 3.5 million heads.
Given these data, the investment parameter ℏ was calibrated to have a value of 1.25⋅10⁶.
Barham et al. (2012) conduct experiments measuring risk and uncertainty aversion of USA farmers. The authors get a mean of 0.79 for the uncertainty aversion with a standard deviation of 0.64.
Structure of the economy
ResultsStackelberg-Nash game with the follower supplying lower-quality good
The follower chooses the lowest quality possible and enters the market as early as possible.
The leader’s choice of quality is a decreasing function of risk [for high level of ambiguity] and ambiguity.
Leader’s choice of quality
0 1 2 3 4 5A m b iguity0
5. 0 10 7
1. 0 10 8
1. 5 10 8
2. 0 10 8
2. 5 10 8
3. 0 10 8P r of it
L e a de r pr ov iding hig h qu a lity
F ollow e r pr ov iding low qu a lity
ResultsStackelberg-Nash game with the follower supplying lower-quality good
0. 0 0. 1 0. 2 0. 3 0. 4 0. 5R is k0
5. 0 10 7
1. 0 10 8
1. 5 10 8
2. 0 10 8
2. 5 10 8
3. 0 10 8P r of it
L e a de r pr ov iding hig h qu a lity
F ollow e r pr ov iding low qu a lity
Profits as a function of risk and ambiguity
Vertical integration is more likely when the economic environment is characterized by risk and ambiguity aversion.
An increase in risk (σ↑) and in ambiguity aversion (κ↑) induces an increase in the difference in product differentiation between vertically integrated (VI) and non-integrated buyers (NI).
ResultsStackelberg-Nash game with the follower supplying lower-quality good
0. 1 0. 2 0. 3 0. 4 0. 5R is k
5
0
5
10
15
20Q u ality s
D if f eren c e in Leader 's c h oic e of qu ality s1 2 3 4 5
Am bigu ity
5
0
5
10
15
20
25
30Q u ality s
D if f eren c e in Leader 's c h oic e of qu ality sDifference in the leader’s choice of quality
as a function of the riskDifference in the leader’s choice of quality as a
function of ambiguity
ˆ ˆVI NIL Ls s
ˆ ˆVI NIL Ls s
0. 2 0. 4 0. 6 0. 8 1. 0C os t par am eter L
10
0
10
20
30
40
50
Q u ality s
0. 3
0. 5
0. 9
Vertical integration is more likely when the economic environment is characterized by risk and ambiguity aversion. An increase in risk (σ↑) and in ambiguity aversion (κ↑) induces an increase in
the difference in product differentiation between vertically integrated (VI) and non-integrated buyers (NI).
ResultsStackelberg-Nash game with the follower supplying lower-quality good
ˆ ˆVI NIL Ls s
ambiguity
L
When the follower introduces a higher-quality good, delaying entry can be profitable for the follower. Given the leader's choice of quality, For
Market entry threshold is an increasing (decreasing) function of the value of the risk (σ).
Given the other parameters of the economy,
Market entry threshold is an increasing (decreasing) function of the value of the ambiguity aversion for .
Up to and , market entry threshold is strictly increasing in risk and ambiguity aversion.
ResultsStackelberg-Nash game with the follower supplying higher-quality good
0.77 0.77
0.491 0.491
0.037 1.131
An increase in risk increase the degree of differentiation between the two competing firms.
An increase in ambiguity aversion decreases the degree of differentiation between the two competing firms.
0. 0 0. 5 1. 0 1. 5 2. 0A m b iguity0
5
10
15
20
25
30
35Q ua lity s
L e a de r's c h oic e of qu a lity
F ollow e r 's c h oic e of qu a lity
ResultsStackelberg-Nash game with the follower supplying higher-quality good
An increase in risk increase the degree of differentiation between the two competing firms.
An increase in ambiguity aversion decreases the degree of differentiation between the two competing firms.
The net effect on profit is undetermined a priori. The Stackelberg profit functions are convex, which favor
overinvestment with volatility.
The overall expected gain from the investment depends on the magnitude of the advantages from the investment in quality, which is reduced when the leader provides a high-quality good.
The follower is better off providing low quality when the market appears ambiguous and the quality of the leader's product is high. Waiting to provide a higher-quality good does not compensate for the loss of revenue from not entering the market.
For the highest level of risk and ambiguity aversion, equilibrium outcome converges to the follower's supplying low-quality goods.
ResultsStackelberg-Nash game with the follower supplying higher-quality good
As for the case when the leader supplies a high quality good, vertical integration (VI) increases the quality level of the supplied good.
Both ambiguity aversion and risk increase the length of the difference between the quality supplied by the VI and the non-integrated (NI) buyers.
Vertical integration reduces the waiting time, and the follower enters the market earlier than it would in the absence of vertically integration (function of the parameters of the model).
VI is welfare improving because of reducing waiting time and increasing the quality of the product.
ResultsStackelberg-Nash game with the follower supplying higher-quality good
To conclude The impacts of risk and Knightian uncertainty on the optimal
quality are different.
Contract farming and vertical integration observed in the food industry seems to be an adequate response to the need of innovations under risk and ambiguity aversion.
The level of ambiguity aversion is likely to vary. Further empirical research is needed to disentangle the effect of ambiguity aversion from those of risk.
d d d mF L L L L L
LF L F L
N p c q N p c qM M M MI s
N r N N r N
d d
F F F
FF
N p c qMI s
N r
The model
