San Francisco Bread Company Market Demand Quantity And Price ✓ Solved

Original San Francisco Bread Company Market Demand (Q) Price

Original San Francisco Bread Company Market Demand (Q) Price (P) Competitor Price (Px) Advertising (Ad) Income (I) Data: .62 6 .29 5 .66 5 .01 5 .53 6 .51 7 .20 7 .28 6 .95 5 .42 6 .94 5 .47 7 .99 5 .72 5 .46 6 .31 7 .36 5 .19 6 .95 6 .34 5 .54 7 .89 5 .76 7 .39 5 .42 6 .82 6 .10 5 .77 6 .07 5 .91 5 .17

Paper For Above Instructions

Introduction

This paper analyzes the provided San Francisco Bread Company dataset containing market demand observations and associated variables: quantity demanded (Q), own price (P), competitor price (Px), advertising (Ad), and income (I). The raw data are presented inline in the assignment text. The objective is to describe a rigorous approach to estimating the market demand relationship for the firm, provide model specification, discuss data cleaning and estimation steps, present illustrative estimation results and interpretations, and give managerial recommendations based on demand elasticity concepts and robustness checks (Wooldridge, 2013; Stock & Watson, 2019).

Data Cleaning and Preparation

The raw sequence contains numeric tokens that appear to be paired values (e.g., .62 6). The dataset appears compressed and may only clearly encode Q and P for many observations; competitor price, advertising, and income entries are not clearly delimited. Prior to estimation, the dataset must be parsed into observations with consistent variable columns. Steps:

  • Tokenize by whitespace and punctuation to extract numeric values.
  • Use the header order provided (Q, P, Px, Ad, I) and allocate tokens sequentially; if tokens are missing, mark as NA and document missingness patterns (Little & Rubin, 2019).
  • Perform exploratory data analysis: summary statistics, histograms, and pairwise scatterplots to detect outliers and nonlinearity (Cleveland, 1993).
  • If only Q and P are recoverable for many rows, proceed with a bivariate demand estimation but note omitted-variable bias risk if Px, Ad, or I are important (Wooldridge, 2013).

Model Specification

We propose the following log-linear demand model, commonly used to obtain elasticity estimates directly:

ln(Q_i) = β0 + β1 ln(P_i) + β2 ln(Px_i) + β3 ln(Ad_i) + β4 ln(I_i) + ε_i

This specification yields constant elasticities: β1 is own-price elasticity, β2 cross-price elasticity (competitor price), β3 advertising elasticity, and β4 income elasticity (Stock & Watson, 2019). If the data contain zeros, apply appropriate transformations (e.g., ln(Q+δ) with small δ) or estimate in levels with semilog forms (Gujarati & Porter, 2009).

Estimation Strategy

Estimate parameters using Ordinary Least Squares (OLS) if classical assumptions hold. Check for endogeneity: price P may be endogenous due to simultaneity between price and quantity (Hausman, 1996). If endogeneity is likely, use instrumental variables (IV) where valid instruments are available (e.g., cost shifters, input prices, or lagged variables) and perform Two-Stage Least Squares (2SLS) (Wooldridge, 2013).

Diagnostic tests: heteroskedasticity (Breusch–Pagan), multicollinearity (VIF), specification tests (RESET), and instrument relevance (first-stage F-stat). Robust standard errors or clustered errors should be used if heteroskedasticity is present (Greene, 2018).

Illustrative Estimation Results (Example)

Because the assignment text provides the raw numeric tokens but not a fully parsed dataset in clear columns, the following estimates are illustrative of a log-linear OLS applied to a cleaned set. Suppose OLS on ln-transformed variables yields:

  • β̂0 = 1.20 (SE = 0.15)
  • β̂1 = -1.05 (SE = 0.18) — own-price elasticity
  • β̂2 = 0.45 (SE = 0.12) — competitor-price elasticity
  • β̂3 = 0.10 (SE = 0.04) — advertising elasticity
  • β̂4 = 0.30 (SE = 0.09) — income elasticity
  • Adjusted R2 = 0.62

These illustrative coefficients imply that a 1% increase in the firm's price reduces quantity demanded by about 1.05% (inelastic vs. elastic depends on magnitude >1), while a 1% increase in competitor price raises demand by 0.45%, consistent with substitute behavior (Varian, 2010). Advertising has a positive but small elasticity, and demand increases with consumer income (Deaton & Muellbauer, 1980).

Interpretation and Policy Implications

An estimated own-price elasticity of roughly -1.05 suggests demand is near unit-elastic; small price increases could lower revenue, while price reductions might raise revenue only marginally. If coefficient magnitude is >1 in absolute value, reducing price could increase revenue but must be weighed against margin impacts (Pindyck & Rubinfeld, 2017). The positive competitor-price elasticity confirms competitors are substitutes: competitor price increases create opportunity for stealing market share.

Advertising elasticity around 0.10 suggests advertising is effective but provides diminishing returns; managers should evaluate marginal cost per advertising dollar versus expected sales lift (Lilien et al., 2013).

Robustness and Validity Checks

Key robustness steps include:

  • Testing for price endogeneity and implementing IV/2SLS if needed (Hausman, 1996).
  • Checking stability across subsamples (seasonality, store location) and adding interaction terms (Wooldridge, 2013).
  • Addressing measurement error in advertising and income variables via validation data or instrumental approaches (Bound, Brown, & Mathiowetz, 2001).

Managerial Recommendations

Based on the illustrative estimates: avoid large price increases as they may reduce quantity disproportionately; consider targeted advertising campaigns where ROI exceeds cost; monitor competitor pricing closely as a source of demand shifts; and collect better data on advertising spend, competitor prices, and consumer incomes to reduce omitted-variable bias in future estimations (McFadden, 2001).

Conclusion

This paper provided a structured plan to estimate the San Francisco Bread Company demand using the provided dataset, emphasizing data cleaning, log-linear modelling for elasticities, and diagnostic testing. The illustrative results underscore how own-price, competitor-price, advertising, and income elasticities inform pricing and marketing decisions. A rigorous empirical implementation requires careful parsing of the raw tokens into full variable columns and checks for endogeneity and measurement error before final managerial decisions are recommended (Wooldridge, 2013; Stock & Watson, 2019).

References

  • Bound, J., Brown, C., & Mathiowetz, N. (2001). Measurement error in survey data. In J. Heckman & E. Leamer (Eds.), Handbook of Econometrics (Vol. 5, pp. 3705–3843). Elsevier.
  • Cleveland, W. S. (1993). Visualizing Data. Hobart Press.
  • Deaton, A., & Muellbauer, J. (1980). Economics and Consumer Behavior. Cambridge University Press.
  • Greene, W. H. (2018). Econometric Analysis (8th ed.). Pearson.
  • Gujarati, D. N., & Porter, D. C. (2009). Basic Econometrics (5th ed.). McGraw-Hill Education.
  • Hausman, J. A. (1996). Valuation of new goods under perfect and imperfect competition. In T. F. Bresnahan & R. J. Gordon (Eds.), The Economics of New Goods. University of Chicago Press.
  • Lilien, G. L., Rangaswamy, A., & DeBruicker, M. (2013). Marketing Engineering: Computer-Assisted Marketing Analysis and Planning. DecisionPro.
  • Little, R. J. A., & Rubin, D. B. (2019). Statistical Analysis with Missing Data (3rd ed.). Wiley.
  • McFadden, D. (2001). Economic choices. American Economic Review, 91(3), 351–378.
  • Pindyck, R. S., & Rubinfeld, D. L. (2017). Microeconomics (9th ed.). Pearson.
  • Stock, J. H., & Watson, M. W. (2019). Introduction to Econometrics (4th ed.). Pearson.
  • Varian, H. R. (2010). Intermediate Microeconomics: A Modern Approach (8th ed.). W. W. Norton & Company.
  • Wooldridge, J. M. (2013). Introductory Econometrics: A Modern Approach (5th ed.). Cengage Learning.

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