Tyler Kellermann
Markets & Strategic Interactions
Economic Analysis Assignment
Real World Example
Over the weekend of November 9th, I visited Bentonville Arkansas to participate in Walmart’s
“Sell Weekend” for MBA candidates that had received offers to work at the company. Most of
the students in attendance were hired by the merchandising operations division which is the
backbone of Walmart’s business model and is responsible for optimizing Walmart’s product
selection and supply chain - two of the main core competencies of the company. During the
course of our orientation, one of the merchandising VPs spoke to us about how Walmart
approaches pricing decisions with respect to their competition – Amazon in particular.
Walmart is currently investing significant amounts of money into challenging Amazon’s
dominance of e-commerce. Although Walmart is more reluctant to adjust prices in their brickand-mortar stores, and has many rules about how they approach rollback pricing in these
environments, they adjust prices online in real time. In keeping with their emphasis on
“everyday low prices,” Walmart’s IT teams run algorithms that will constantly pull information
on what the price an item is currently selling at on Amazon.com. The merchandising teams will
adjust parameters within a certain range to make sure that Walmart is always selling an item at
a price equal to or slightly below what Amazon is offering. For example, if a certain kind of
television retails on Amazon.com for $199, Walmart’s system will ensure that the price on
Jet.com is equal to or below that number by a few cents or dollars.
Because both companies are so large and have such a massive footprint and brand awareness
in the United States, they set the market for other competitors to follow. Smaller competitor
companies (e.g. Target) sell many of the same goods as Walmart and Amazon but are also
subject to the same market forces that drive pricing and sales decisions. As a consumer, I am
unlikely to pay $225 for a TV that Amazon and Walmart are selling for significantly below that.
Given that I can compare prices almost instantaneously on the internet, I will search to find the
lowest price (or close to the lowest price) that I can buy something for.
This face-off between the two mega-firms gives us an interesting real-world example of
duopolistic competition which we can illustrate mathematically with the Cournot model. To
draw conclusions about Cournot equilibrium, it’s also useful to compare the model results to a
base-case of monopolistic competition where only one firm controls the market. I will illustrate
the outcomes under both models below and show the benefits of having at least two firms
selling the same item. I will also explain several other lessons we can glean from this example.
Monopoly Competition
In order to evaluate the benefits of competition between Walmart and Amazon, we need to
look at what the result would be in the absence of competition. Going back to the example of
television pricing, we will first assume that Amazon is the only company from which we can buy
TV’s. The units blow are illustrative only and reduced for simplicity. They could easily be
multiplied by several orders of magnitude. Under the monopoly model, we will assume that
Amazon’s Q* (quantity produced) is the company’s annual sales volume and they are choosing
how many units to sell and what price to sell them at to maximize their profit.
Assumptions
 Amazon Demand Function: 𝑃 = 50 – 2𝑄
 Amazon Cost Function: 𝐶 = 10 + 2𝑄
 Production until 𝑀𝑅 = 𝑀𝐶
Solution
 = 𝑃𝑄 – 𝐶
= (50 – 2𝑄)𝑄 – (10 + 2𝑄)
= 50𝑄 – 2𝑄 2 – 10 – 2𝑄
= 48𝑄 – 2𝑄 2 – 10
𝜕
𝜕𝑞
= 48 − 4𝑄 = 0
48 = 4𝑄
𝑄 ∗ = 12
𝑃 = 50 – 2𝑄
𝑃 = 50 – 2(12)
𝑃∗ = 26
We see that under these conditions, Amazon “produces” (sells) 12 TVs for which it charges $26
dollars each. Given that this is a monopoly scenario, we also can conclude that Q* and P* are
respectively lower and higher than they would otherwise be under perfect competition.
Cournot Competition
Now that we have seen the most market-inefficient outcome, we can illustrate the benefits of
Walmart entering the ecommerce market to challenge Amazon’s dominance of TV sales. We
will now assume that Walmart has entered the market and is competing in Cournot duopoly
with Amazon. Both Walmart and Amazon decide on their sales volume simultaneously. Also,
because they are such large corporations, we will assume that they face the same cost
functions because their size allows them to optimize in similar ways and gives them the same
leverage with suppliers.
Assumptions
 Demand Function (Both Firms): 𝑃 = 50 – 2𝑄
 Cost Function (Both Firms): 𝐶 = 10 + 2𝑄
 Production until 𝑀𝑅 = 𝑀𝐶
Solution
1 = 𝑃𝑄1 – 𝐶1
= [50 – 2(𝑄1 + 𝑄2 )]𝑄1 – 10 – 2𝑄1
= 50𝑄1 – 2𝑄12 – 2𝑄1 𝑄2 – 10 – 2𝑄
𝜕1
= 50 – 4𝑄1 – 2𝑄2 – 2
𝜕𝑞
1
𝑄1 = 12 − 0.5𝑄2  Firm 1 Reaction Function
𝑄2 = 12 − 0.5𝑄1  Firm 2 Reaction Function (symmetrical due to same assumptions)
𝑄1 = 12 − 0.5(12 − 0.5𝑄1 )
𝑄1 = 12 − 6 + 0.25𝑄1
0.75𝑄1 = 6
𝑄1∗ = 8
𝑄2∗ = 8
𝑄 ∗ = 𝑄1∗ + 𝑄2∗
𝑄 ∗ = 16
𝑃 = 50 − 2𝑄
𝑃 = 50 – 2(16)
𝑃∗ = 18
Under Cournot competition, quantity sold increases by 4 and price decreases by 6 resulting in a
significant gain of consumer surplus and a reduction of deadweight loss due to monopoly
inefficiency. This model shows that consumers benefit when there are at least two firms in the
market compared to monopoly conditions.
Model Weaknesses
In this case, I have modeled the duopolistic competition between Walmart and Amazon as a
Cournot equilibrium. However, a major flaw with this approach is that the Cournot model
suggests that, like monopolistic competition, the companies involved are making simultaneous
decisions about quantity rather than price. In reality, what we see with Amazon vs. Walmart is
more similar to a Bertrand duopoly. Under the Bertrand model, the firms are making decisions
about price, not quantity. Due to the fact that each firm can constantly undercut the other and
will adjust their reaction functions based on the action of the rival firm, the Bertrand model
usually approaches perfect competition as long as we assume the firms do not collude in setting
prices.
The functions I used to illustrate monopoly and Cournot competition above do not work well
with the Bertrand model because the units will cancel each other in the reaction functions.
However, under Bertrand conditions more units will be sold at lower prices than would happen
under Cournot equilibrium, resulting in a further gain to consumer surplus.
Another weakness of the modeling above is that it assumes the firms sell homogenous,
indistinguishable products and a consumer would be equally happy purchasing from either
supplier. In reality, nearly all consumer products are branded and have different levels of
consumer loyalty attached to them. Walmart and Amazon themselves are brands. This model
does not address the fact that a consumer may be willing to pay $1 more for a TV from Amazon
because they have both a Prime membership, a lot of experience ordering from Amazon, and
comfort with the brand.
Finally, the equations I chose above assume that Walmart and Amazon have equal market
power and therefore face the same demand, cost, and reaction functions. Because the real
world is imperfect, there could be many situations where one company has an advantage over
the other. Even if they face the same conditions with regard to televisions, Walmart may have
an edge in produce because it has more experience selling fresh fruits and vegetables and
negotiating with farm suppliers. Conversely, Amazon has significantly more revenue streams
than Walmart (e.g. AWS, Kindle, etc.) and likely has more leverage over B2C shipping
companies like UPS because it ships more packages through online sales than Walmart. These
differences are not reflected in the models above.
Model Predictions
As we have seen mathematically, we would expect that consumers benefit when at least two
large competitors are present in the marketplace. I would expect that due to price
undercutting, the two firms would squeeze each other’s profit margins as well as put significant
downward price pressure on smaller players. In the past, Walmart has been barraged with
criticism about how its business model has put smaller retailers out of business. Small
companies cannot match Walmart’s aggressive cost-cutting and economies of scale.
I would expect that increased competition with Amazon will result in even more centralization
in the retail industry and will make it very difficult for other companies to compete on price
alone. We should expect that Target will continue to embrace its strategy of differentiation and
double-down on producing and selling items with higher design aesthetics. Small businesses
will have to compete on service quality if they wish to remain afloat.
In the longer term, especially if growth trends of both behemoths continue at the same pace,
we may see anti-trust regulators in the U.S. take an interest in the retail industry. Walmart saw
nearly a 45% growth in its ecommerce business in the last quarter. Amazon continues to post
strong revenue growth. These trends indicate more consolidation in the retail industry for both
brick and mortar and ecommerce sales. The Hamilton Project, part of the Brookings Institution,
has tracked the growth in the Herfindahl-Hirschman Index for a variety of industries and
reported a large growth in the HHI index for the retail sector over the last several decades –
several times above the DOJ horizontal merger threshold:1
1
“Firm concentration is rising, particularly in retail and finance,” The Hamilton Project, June 13, 2018, accessed November 19,
2018, http://www.hamiltonproject.org/charts/firm_concentration_is_rising_particularly_in_retail_and_finance
Another broad concern is the effect that this dynamic will have on wages. Apple, Google and a
handful of other technology companies were fined over $400 million in 2014 for colluding in
the hiring market. The firms agreed not to hire employees of each other which kept wages
down and reduced competition for talent in the technology industry. I see a risk that Walmart
and Amazon could do the same, especially as their business models evolve to become more
similar to each other. As Walmart expands its ecommerce footprint, Amazon is buying or
building more brick and mortar stores through its acquisition of Whole Foods and rollout of
automated convenience stores. It would be unsurprising if the two firms were tempted to rig
the labor market to protect to their profits, especially given the fact that margins are so small in
retail to begin with.