13 Competitive Advantage

13.1 Rethinking Market Size: A Shift Towards Profitability Analysis

The Traditional Approach: Market Size Estimates

In both corporate and entrepreneurial settings, market size estimates are traditionally used to gauge the profit potential of investments in innovation. The idea is simple: a larger market size suggests greater profit opportunities if a product gains a certain market share. This method, however, relies heavily on hypothetical scenarios and often overlooks crucial factors like market share attainability and industry entry barriers.

The Limitations of Market Size as a Profit Proxy

Market size, while indicative, isn’t always a reliable proxy for profitability. For example, a sizable market like the cola industry may seem lucrative, but high entry barriers can drastically limit market share for new entrants. Existing measures like Total Addressable Market (TAM),¹ Serviceable Available Market (SAM),² and Target Market,³ though refined, still fall short because they don’t fully account for the dynamics of market entry, especially for market makers who are creating new segments.

A More Direct Approach: Estimating Profitability Through Customer Demand

A more direct and informative approach involves estimating the demand curve specific to the innovation. This method integrates customer pain points with the effectiveness of the proposed solution. A larger target market, better solution efficacy, and greater differentiation from existing products all contribute to higher expected profitability. This approach, grounded in differentiated Bertrand oligopoly models, allows for the calculation of equilibrium prices, quantities, market shares, and profits, providing a more accurate and actionable profitability estimate.

Understanding Profit as a Truer Measure of Market Potential

Revenue vs. Profit: Shifting the Focus

Traditional market size metrics, like total addressable market, often emphasize total sales value. While this offers a sense of the revenue pool, it doesn’t necessarily reflect a company’s profitability. By using demand and profit functions, we can calculate expected revenue as a market size measure but with a crucial distinction - our primary focus is on profit maximization, not just revenue.

Profit: A More Relevant Indicator for Investment Decisions

Investors typically rely on revenue proxies to gauge profit potential. However, actual profit figures provide a more accurate and meaningful measure for investment decisions. As our earlier calculations showed, understanding the profit per company helps in determining the viability of investment and continued operation.

Profit as a Predictor of Long-Term Success

It’s important to note that these profitability estimates reflect a scenario where the product is well-known, resembling its mature market stage. This perspective aligns well with traditional market size metrics but offers a more realistic and actionable forecast for long-term success.

Profitability in Practice: An Illustrative Case

Understanding Demand Curves and Profit Functions

Consider a scenario in a differentiated Bertrand oligopoly involving two companies. Their demand curves and profit functions can be mathematically expressed, leading to reaction functions that help determine optimized equilibrium prices, quantities, and profits. This mathematical approach, while intricate, offers a tangible way to predict market behavior and profitability.

Let’s apply this to a hypothetical situation where two companies with identical costs and differentiation exist in a market. Using specific parameters, we can calculate equilibrium outcomes, providing insights into potential revenues and profits. The demand curves are

\[ \begin{align} \mathsf{Q_1} &= \mathsf{a_1 - b_1\ P_1 + b_{12}\ P_2} \\[6pt] \mathsf{Q_2} &= \mathsf{a_2 - b_2\ P_2 + b_{21}\ P_1} \end{align} \]

where a_i is the intercept of Company i, b_i is the “own price” slope of Company i, and b_ij is the “competitor price” slope (the substitution effect of the price of Company j) for the product of Company i.

From these demand curves, we get profit functions for both Companies:

\[ \begin{align} \mathsf{\pi_1} &= \mathsf{(P_1 - c_1)\ Q_1 - f_1} \\[5pt] &= \mathsf{(P_1 - c_1)\ (a_1 - b_1\ P_1 + b_{12}\ P_2) - f_1} \\[15pt] \mathsf{\pi_2} &= \mathsf{(P_2 - c_2)\ (a_2 - b_2\ P_2 + b_{21}\ P_1) - f_2} \end{align} \] where c_i is the variable cost per unit of Company i and f_i is the fixed cost of Company i.

Maximizing profit generates reaction functions that we solve either iteratively or as a system of equations to find the differentiated Bertrand equilibrium prices, quantities, and profits. Skipping the math, the formula for the optimized equilibrium prices is

\[\begin{align} \mathsf{P_1^*} &= \mathsf{\frac{-2 a_1 b_2 + 2 b_1 b_2 c_1 + a_2 b_{21} - b_2 b_{21} c_2} {4 b_1 b_2 - b_{12} b_{2}}} \\[16pt] \mathsf{P_2^*} &= \mathsf{\frac{-2 a_2 b_1 + 2 b_2 b_1 c_2 + a_1 b_{12} - b_1 b_{12} c_1} {4 b_2 b_1 - b_{21} b_{12}}} \end{align}\]

These optimal price formulas allow us to quickly calculate prices, quantities, and profits. Let’s do that for a particular set of parameters. Make two companies that are equally differentiated and have identical costs:

\[ \begin{align} \mathsf{a_1} &= \mathsf{a_2 = 100} \\ \mathsf{b_1} &= \mathsf{b_2 = 2} \\ \mathsf{b_{12}} &= \mathsf{b_{21} = 1} \\ \mathsf{c_1} &= \mathsf{c_2 = 25} \end{align} \]

With these parameters, we can calculate that the equilibrium outcome is

\[ \begin{align} \mathsf{P_1^*} &= \mathsf{P_2^* = 50} \\[3pt] \mathsf{Q_1^*} &= \mathsf{Q_2^* = 50} \\[3pt] \mathsf{\pi_1^*} &= \mathsf{\pi_2^* = 1250} \end{align} \] ### Revenue as Market Size: Traditional vs. Analytical Perspectives

Traditional View: Total Sales Value as Market Size Indicator

Traditionally, market size metrics like Total Addressable Market focus on the total value of sales in the market. This approach provides an overview of the available revenue pool for companies. It’s a straightforward method to gauge market potential but doesn’t necessarily reflect a company’s true profit potential.

Analytical Shift: Revenue Estimation through Demand and Profit Functions

In contrast, our analytical approach calculates expected revenue using demand and profit functions, offering a more nuanced measure of market size. For instance, at optimal prices, we estimate revenue to be $2500 per company. This method not only quantifies the revenue but also aligns it with strategic pricing and market dynamics.

13.2 Profit as Market Size: A Paradigm Shift

Moving Beyond Revenue to Profit Maximization

While traditional metrics emphasize revenue, our primary goal in entrepreneurial analytics is profit maximization. Investors often rely on revenue figures as rough proxies for profit. However, calculating optimal profit provides a more accurate and actionable measure of a company’s potential. For example, we determined an optimal profit of $1250 per company.

Profit as a Long-term Success Predictor

It’s important to note that these profit estimates are based on a mature market understanding of the product, as if the product is well-established. Early-stage products typically see lower sales, growing as brand awareness and market penetration increase. Thus, profit, in this context, is a projection of the company’s potential as it matures, offering a more strategic perspective compared to traditional revenue-based market size metrics.

Navigating the Growth Path

The transition from initial sales to achieving this profit potential involves significant investment in brand development, production capacity, and market expansion. Balancing pricing strategies with investment in growth is critical. The optimal growth rate should balance these elements, a topic that warrants further exploration to fully understand how competitive advantages impact this trajectory.

13.3 Decoding Competitive Advantages: A Bertrand Model Analysis

Introduction to Competitive Dynamics in Business

In this section, we delve into the intricate world of competitive advantages through the lens of the Bertrand oligopoly model. Our goal is to examine how variations in key parameters—market size, price sensitivity, customer loyalty, and unit variable cost—affect a business’s pricing, market share, and profitability. This analysis will provide entrepreneurs with practical insights into strategic decision-making.

Market Size (a₁)

Prices

When Company 1’s target customer segment expands, indicating an increase in market size, how does it affect its pricing strategy compared to its competitor, Company 2? We use the Bertrand model to map these changes:

Key Insight: As Company 1’s market size increases, its optimal pricing strategy changes, potentially allowing it to either increase market share or improve profit margins.

Quantities

Next, we explore how these market size changes impact the quantities sold by both companies:

Strategic Takeaway: An increase in market size typically leads to higher sales volumes, but entrepreneurs must balance this with pricing strategies to ensure optimal profitability.

Margins

Margins are a direct indicator of profitability. Let’s see how changes in market size influence the margins of both companies:

Business Strategy Insight: Maintaining healthy margins while expanding market size is key to sustainable growth.

Profits

Ultimately, profit is the goal. Here’s how market size affects the profits of Company 1 and Company 2:

Clearly, profits rise much more quickly for Company 1 than for Company 2 when Company 1 has a competitive advantage in market size.

Entrepreneurial Insight: An increased market size can significantly boost profits, but strategic pricing and cost management are essential to capitalize on this advantage.

Real-World Applications and Strategic Implications

In practice, an increase in market size could be due to various factors, such as shifts in customer preferences, regulatory changes, or market expansions. Entrepreneurs should use these insights to hypothesize potential market changes and test these hypotheses with data-driven analytics.

This analysis provides a framework for understanding how different competitive advantages impact a company’s profitability. It underscores the importance of strategic decision-making in leveraging these advantages, with a focus on optimizing profits while maintaining a competitive edge in the market.

Price Sensitivity (b₁)

Understanding Price Sensitivity with a Bertrand Oligopoly Model

In this subsection, we explore the concept of price sensitivity (b₁) in the context of the Bertrand model and its implications for business strategy. Price sensitivity reflects how customers react to price changes—higher sensitivity means customers are more likely to change their buying behavior in response to price fluctuations. Let’s analyze how varying degrees of price sensitivity impact Company 1’s profitability and competitive position.