Using Economic Mathematics to Enhance Consumer Insights: Pricing, Promotion, and Market Strategies

The increasingly competitive business environment demands a deep understanding of consumer behavior. Consumers influence the demand for products or services, making the analysis of their behavior essential for effective business strategies. This article discusses the use of economic mathematics to systematically and measurably analyze consumer behavior. Quantitative methods with descriptive and inferential analysis are used, with primary data from consumer surveys and secondary data from industry reports and e-commerce platforms. Data analysis involves linear and non-linear regression models as well as machine learning techniques such as logistic regression and decision trees. The results show that price, promotion, product quality


INTRODUCTION
In today's rapidly evolving business landscape, understanding consumer behavior is not just advantageous but essential.While traditional economic models have long been employed to analyze consumer preferences and purchasing patterns, the integration of advanced mathematical techniques and machine learning has introduced new dimensions to this field.The current state of the art involves using linear and non-linear regression models to predict consumer decisions, as well as leveraging big data and machine learning algorithms like logistic regression and decision trees for more nuanced insights (Mandák & Hančlová, 2019).However, a significant gap exists in the application of these sophisticated tools to systematically combine primary data from consumer surveys with secondary data from digital platforms, creating a more holistic and dynamic understanding of consumer behavior (Popova, 2018).
The novelty of this work lies in its interdisciplinary approach, merging economic mathematics with machine learning techniques to analyze consumer behavior more comprehensively (Morita, 2023).Unlike existing studies that often focus on one aspect of data analysis, this research integrates multiple data sources and analytical methods to uncover the complex interplay of factors such as price, promotion, product quality, and consumer reviews in shaping purchasing decisions (Boud et al., 2016).
The primary aim of this study is to develop and validate a methodological framework that uses economic mathematics and machine learning to systematically analyze consumer behaviour, ultimately providing actionable insights for optimizing business strategies.The principal conclusions drawn from this research indicate that price sensitivity, promotional effectiveness, and the impact of product quality and consumer reviews are critical determinants of purchasing behaviour (Manuere et al., 2022).These findings underscore the importance of data-driven decision-making in crafting targeted marketing strategies that enhance competitiveness in an increasingly digital marketplace (Harjadi & Fatmasari, 2017;Harjadi, et al., 2021;Harjadi & Gunardi, 2022;Harjadi, et al., 2023).

LITERATUR REVIEW
Pricing models, such as the price elasticity of demand, allow businesses to gauge how price changes impact consumer demand.These models are foundational in setting optimal prices (Varian, 2010).For example, Anderson, Fornell, and Lehmann (1994) highlight how understanding price sensitivity can lead to more effective pricing strategies in competitive markets.
Dynamic Pricing: Dynamic pricing, which adjusts prices based on real-time supply and demand, is prevalent in industries like airlines and hospitality.Studies like those by Elmaghraby and Keskinocak (2003) illustrate the benefits of dynamic pricing in maximizing revenue.
Game Theory and Pricing: Game theory is frequently used to model competitive interactions between firms, providing insights into pricing strategies under various market conditions (Dixit & Nalebuff, 1991).It helps businesses anticipate competitor moves and adjust their pricing strategies accordingly.
Promotion Optimization: Economic models help optimize promotional spending by balancing costs with expected returns.Blattberg, Briesch, and Fox (1995) discuss how promotion elasticity models can predict the incremental sales generated by promotions, aiding in budget allocation.
Coupon and Discount Strategies: The use of mathematical models in designing coupon and discount strategies has been widely studied.For instance, Ailawadi, Neslin, and Gedenk (2001) explore the effects of different discount levels on consumer purchase behavior.
Customer Lifetime Value (CLV): CLV models, which incorporate economic mathematics, are crucial for determining the long-term value of customers and guiding promotional investments (Gupta & Lehmann, 2003).

Market Strategies and Economic Mathematics
Market Segmentation: Techniques such as cluster analysis and regression models are used to segment markets based on consumer behavior, allowing for more targeted marketing efforts (Wedel & Kamakura, 2000).Product Positioning: Economic mathematics aids in product positioning by helping businesses identify optimal market positions relative to competitors (Urban & Hauser, 1993).Optimization of Marketing Mix: Linear programming and other optimization techniques are applied to maximize the effectiveness of the marketing mix.Kotler and Keller (2016) discuss how mathematical optimization can improve the allocation of resources across the marketing mix (Maulana et al., 2023).

RESEARCH METHOD
This study employs a quantitative approach, utilizing both descriptive and inferential analysis methods.The research design encompasses several stages, from data collection to the analysis and interpretation of results (Jahidah, 2022).The data used in this study comes from two primary sources: primary data and secondary data.Primary data is obtained through direct surveys of consumers.The questionnaire is designed to gather information on consumer preferences, purchasing habits, factors influencing buying decisions, and responses to changes in prices or promotions.Secondary data is collected from various sources, such as industry reports, academic publications, sales data from ecommerce platforms, and consumer interaction data from social media.
To collect the data, we used both survey questionnaires and digital data collection methods.The questionnaires were distributed to a randomly selected sample of relevant consumer populations.Additionally, consumer behavior data was gathered from ecommerce platforms, social media, and other digital analytics tools.Data analysis was conducted using both descriptive and inferential methods.Descriptive statistics were used to describe the characteristics of the sample data.Linear and non-linear regression models were employed to identify the factors influencing consumer purchasing decisions, with independent variables such as price, promotion, product quality, and consumer reviews (Shaengchart & Kraiwanit, 2022).
Demand models were used to understand how price changes affect the quantity demanded by consumers (Olayiwola, et al., 2024).Machine learning techniques, including logistic regression, decision trees, and artificial neural networks, were applied to analyze consumer behavior patterns and predict future purchasing decisions.The model is then estimated using statistical techniques like Ordinary Least Squares (OLS) or Maximum Likelihood Estimation (MLE) to determine the parameters.Calculating elasticities helps assess how responsive demand is to changes in variables like price.Model validation follows, where the goodness of fit and statistical significance of the coefficients are tested, and cross-validation techniques are used to ensure robustness.After validating the model, it is applied to forecast future demand under various scenarios, such as price changes or promotional strategies, and to optimize pricing and resource planning.Ongoing monitoring is essential to compare actual demand with predictions, refine the model with new data, and adjust strategies as needed.Finally, findings are reported in a clear and actionable format to guide decision-making, helping to inform strategic choices related to pricing, marketing, and resource allocation.
Linear Regression analysis gives Null Hypothesis (H₀): The independent variables (Price, Promotion, Product Quality, and Consumer Reviews) do not have a statistically significant impact on the frequency of purchase per month (Y) (Mandák & Hančlová, 2019).Mathematically, this can be expressed as: H₀: β₁ = 0, β₂ = 0, β₃ = 0, β₄ = 0 Alternative Hypothesis (H₁): At least one of the independent variables (Price, Promotion, Product Quality, or Consumer Reviews) has a statistically significant impact on the frequency of purchase per month (Y).Mathematically, this can be expressed as: H₁: At least one of β₁, β₂, β₃, or β₄ is not equal to 0.
The data analysis process began with data preprocessing to remove anomalies, handle missing data, and transform raw data into a format suitable for analysis.Exploratory analysis was conducted to identify initial patterns and insights from the data.Mathematical models were built and validated using cross-validation techniques to ensure the accuracy and generalizability of the models.The results of the analysis were interpreted to provide insights into consumer behavior and how certain factors influence purchasing decisions.These findings are presented in a report that includes graphs, tables, and narratives explaining the business implications of the research results.
The research methodology is designed to provide a deep understanding of how economic mathematical approaches can be systematically and accurately applied to analyze consumer behavior.By utilizing both primary and secondary data, as well as advanced analysis methods, this study aims to provide valuable insights for business practitioners in formulating effective and efficient strategies.

RESEARCH RESULTS
The research results provide a comprehensive analysis of consumer behavior patterns based on the collected data.The findings shed light on how various factors, such as shopping frequency, responsiveness to promotions, and purchasing habits, influence the overall shopping behavior of respondents.Through detailed statistical analysis, the study uncovers key trends and insights that offer a deeper understanding of the factors driving consumer decisions.These results serve as a foundation for further discussion and analysis, helping to inform strategies for enhancing consumer engagement and optimizing marketing efforts.
The data presented in Table 2 provides an overview of the shopping behavior of respondents, highlighting key patterns and preferences.A significant majority, 80% of respondents, shop online at least once a month, indicating a strong inclination towards digital shopping platforms.Additionally, 40% of respondents tend to make purchases during discounts or promotions, suggesting that price reductions and special offers are effective in driving sales.The average number of purchases per month stands at 5, with a median of 4, reflecting the overall purchasing frequency among the sample population.This table offers valuable insights into the shopping habits of the respondents, underscoring the importance of online shopping and promotional activities in consumer behavior.Regression analysis is a powerful statistical tool used to examine the relationships between a dependent variable and one or more independent variables.In this study, regression analysis is employed to explore how factors such as price, promotion, product quality, and consumer reviews influence the frequency of purchases per month.By estimating the coefficients of the regression equation, the analysis provides insights into the direction and strength of these relationships, helping to identify which factors have the most significant impact on consumer purchasing behavior.This method not only allows for the quantification of these effects but also aids in predicting future trends based on the established relationships.Based on the provided regression coefficients, the regression equation that represents the relationship between the frequency of purchase per month (Y) and the independent variables (price, promotion, product quality, and consumer reviews) can be expressed as follows: = β 0 + β 1 () + β 2 (Promotion) + β 3 (Quality) + β 4 (Reviews) Where: • β 0 is the intercept (constant term), • β 1 is the coefficient for the Price, • β 2 is the coefficient for the Promotion, • β 3 is the coefficient for the Quality, • β 4 is the coefficient for the Reviews.Given the coefficients: The regression equation becomes:  = −0,3() + 0,5(Promotion) + 0,2(Quality) + 0,4(Reviews) Here, β 0 represents the base frequency of purchase when all independent variables are zero.
Demand Model: The results show that price elasticity is -1.2, indicating that demand is quite elastic with respect to price changes.A 10% decrease in price can lead to a 12% increase in the quantity demanded (Monardo, 2021).The demand model equation incorporating price elasticity can be expressed as follows: Where: •   = Quantity demanded after the price change Given that a 10% decrease in price leads to a 12% increase in quantity demanded, we can plug in these values: Simplify, So the equation becomes: This indicates that when the price of a product is reduced by 10%, the quantity demanded of that product increases by 12%.In other words, there is a positive relationship between the decrease in price and the increase in the quantity demanded.The elasticity of demand in this scenario is such that a 10% reduction in price leads to a proportionally larger 12% increase in the quantity that consumers are willing to purchase.This demonstrates that consumers are relatively responsive to price changes, and even a modest price decrease can lead to a significant rise in demand.This responsiveness is crucial for businesses as it highlights the potential effectiveness of price reductions as a strategy to boost sales and attract more customers.Machine Learning (Decision Tree Algorithm): There's a table summarizing the findings from the decision tree analysis: Lower prices tend to increase purchase frequency.
Reducing prices can be a strategy to boost sales.
Promotion (Sub-Node) Effective promotions can enhance purchases.
Especially effective when combined with positive reviews.Consumer Reviews (Sub-Node) Positive consumer reviews improve purchase frequency.
Impact is significant but less than promotions or pricing.
Product Quality (Sub-Node) Higher product quality positively affects purchase frequency.
Impact is less significant compared to promotions or pricing.Actor Description Impact on Purchase Frequency Price (Main Node) Lower prices tend to increase purchase frequency.
Reducing prices can be a strategy to boost sales.
Promotion (Sub-Node) Effective promotions can enhance purchases.
Especially effective when combined with positive reviews.Consumer Reviews (Sub-Node) Positive consumer reviews improve purchase frequency.
Impact is significant but less than promotions or pricing.

DISCUSSION
In the era of globalization and advancing digitalization, understanding consumer behavior has become a key factor in determining business success.Consumers are the primary determinants of demand for products or services, making their behavior highly influential on business performance (Manalu & Adzimatinur, 2024).Analyzing consumer behavior allows businesses to design more effective and efficient marketing strategies, thereby enhancing their competitiveness in the market.
The approach of economic mathematics employs mathematical models to study and predict consumer behavior.This method aids businesses in identifying consumption patterns, understanding the factors affecting purchasing decisions, and predicting changes in consumer behavior (Anthony & Biggs, 2024).Consequently, business decisions can be made based on measurable data and systematic analysis.The analysis presented highlights several key insights into consumer behavior and the application of economic mathematics to understand and predict it (Mohajan, 2023).
Modeling Consumer Behavior: Utilizing mathematical models to analyze consumer behavior provides a systematic and data-driven framework for making informed decisions.Regression analysis reveals how factors such as price, promotion, product quality, and reviews influence purchase frequency.For example, the negative coefficient associated with price indicates that higher prices tend to decrease purchase frequency, while positive coefficients for promotion and product quality suggest that these factors are effective in increasing purchases (Sunarjo et al., 2021;Manalu et al., 2023).Elasticity of Demand: The price elasticity of demand, calculated at -1.2, indicates that consumer demand is highly sensitive to changes in price.Specifically, a 10% reduction in price results in a 12% increase in the quantity demanded, emphasizing the crucial role of strategic pricing in enhancing sales.
Decision Tree Analysis: The use of machine learning, specifically decision trees, to identify key factors influencing purchase decisions provides a nuanced understanding of consumer behavior.Price is identified as a primary driver, while promotions and consumer reviews also play significant roles.This approach not only confirms the findings from regression analysis but also helps in refining strategies by showing how these factors interact.
Recommendations for Businesses is Pricing Strategy: Offering competitive prices or discounts can be a powerful tool to increase sales, particularly for price-sensitive consumers.Businesses should consider dynamic pricing strategies to respond to market conditions and consumer sensitivity.Promotion and Reviews: Enhancing the quality and frequency of promotions, along with encouraging positive consumer reviews, can substantially impact purchasing behavior.Effective promotions, when combined with favorable reviews, can lead to increased sales.Market Segmentation: Tailoring strategies based on gender-specific preferences can improve marketing effectiveness (Maulana et al., 2023).For instance, high-quality product offerings and strong recommendations may be more effective for female consumers, while price-sensitive promotions may appeal more to male consumers.

CONCLUSIONS
This study underscores the crucial role of understanding consumer behavior in today's highly competitive and digitally-driven market.Through the application of mathematical economics and advanced analytical techniques, including regression modeling and machine learning, we gained valuable insights into factors influencing purchase decisions.The analysis highlighted that pricing, promotions, and consumer reviews significantly impact purchasing frequency, with price elasticity indicating a strong sensitivity to price changes.Key findings reveal distinct consumer preferences based on gender, with differences in the emphasis on product quality versus affordability.The results from regression analysis and decision tree algorithms provide actionable insights for optimizing pricing strategies, enhancing promotional effectiveness, and leveraging positive reviews.
Despite the valuable insights provided, the study is constrained by its sample size and scope.Future research should focus on larger, more diverse samples and consider additional variables such as geographic and temporal factors to enrich understanding.Longitudinal studies and the integration of advanced methodologies could further refine and validate these findings.Overall, this research contributes to a more nuanced understanding of consumer behavior, offering practical recommendations for businesses to tailor their strategies for improved market performance and competitiveness.
Limitations and Future Research: Sample Size: The relatively small sample size of 30 respondents may limit the generalizability of the findings.Future research with larger sample sizes could provide more robust and representative insights.Further Exploration: Additional studies could explore other factors affecting consumer behavior, such as cultural influences or changes in digital trends.Longitudinal studies could also provide insights into how consumer preferences evolve over time (Smith, A, 2019).The study demonstrates the value of integrating economic mathematics and machine learning into consumer behavior analysis.The insights gained from this research provide actionable recommendations for businesses seeking to optimize their marketing strategies.By understanding and leveraging the factors that influence consumer decisions, businesses can better meet the needs of their customers and enhance their competitive position in the market.

Recommendations:
To optimize business performance, it is essential to implement a strategic approach to pricing, promotions, and market segmentation.Competitive pricing or discounts can effectively increase sales, especially among price-sensitive consumers who respond positively to lower prices.In addition, enhancing both the frequency and quality of promotions, coupled with encouraging positive consumer reviews, can significantly drive sales growth.Businesses should also focus on market segments that exhibit responsiveness to these promotional efforts and reviews, as targeting these segments may

Table 1 .
Summary of Sample Characteristics and Consumer Preferences

Table 2 .
Shopping Behavior of Respondents

Table 3 .
Factors Influencing Purchase Frequency Based on Decision Tree Analysis