Nov 19, 2020 in Case Studies

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CASE STUDY 5

Case Study on Estimating the Demand Analysis of Fast Food Meals

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Case Study on Estimating the Demand Analysis of Fast Food Meals

Question a: Using the data in Table 1, specify a linear functional form for the demand for Combination 1 meals and run a regression to estimate the demand for the meals.

Given the data provided in Table 1, a multiple linear regression model for the demand for Combination 1 meals assumes the following form:image2.png. The idealized form consists of both predictors and a predictand. The coefficients in the model form the parameters of the model. The total number of combinations (Q) is the dependent variable y, while the average price (P) and amount spent on promotion (A) constitute independent variables. Hence, the linear functional model for the demand for Combination 1 meals isimage4.png. A regression analysis of the data, which employs multiple regression procedures, yields the following equation parameters: image6.png-16392.7, image8.png1.6, image10.png100626.1 and image12.png19176.3. If to use these parameters in the idealized demand function, the result is the following:image14.png. Using an average weekly price of 3.5 dollars and an average weekly promotion expenditure of 10089 dollars, the estimated demand, in terms of the amount of combinations of meals, is computed asimage16.png, giving the following estimated demand: image18.png.

Question b: Should you use the ordinary least-squares (OLS) method or the two-stage least-square method (2SLS) method for estimating industry demand for rutabagas? Explain briefly.

The nature of the relationship between the demand and price of the rutabagas is complicated since the two variables exhibit a reciprocal influence on each other. In this regard, the residual term generated by the dependent variable is correlated to the one generated by the independent variable; hence, the two-stage least-square technique is admissible. The ordinary least-squares method is applicable in linear models governed by the assumption that the residuals terms generated by the dependent and independent variables are uncorrelated. Since this assumption does not hold for the relationship between the dependent and independent variable, the OLS is disregarded and the SLS is preferred.

Question c: Using statistical software, estimate the parameters of the empirical demand function specified in part a. Write your estimated industry demand equation for rutabagas.

SPSS software was used to estimate the parameters of the model and the two-stage least-square technique implemented in the analysis to obtain them. In the analysis, Q was the dependent variable, P - the predictor, and A - the instrumental variable. Based on the analysis, the coefficients obtained were as followsimage20.png, image22.png1.57,image24.png and image26.png

Using these parameters, the demand equation for the rutabagas is expressed as follows:

image27.png

Question d: Evaluate your regression results by examining signs of parameters, p-values (or t-ratios) and the R2.

The regression results are presented in Table 1

Table 1: Regression Model Summary

Model Summary

Multiple R

0.401456

R Square

0.161167

Adjusted R Square

0.144391

Std. Error of the Estimate

20263.4

t

6.147

On the one hand, the price parameter obtained from the regression has a negative sign, indicating a reciprocal relationship between the price and the amount of rutabagas demanded. On the other hand, the expenditure on promotion parameter has a positive sign, demonstrating that more investments on promotion strategies increase the demand for the rutabagas. Additionally, 14.4% of the changes that occur in the demand for the rutabagas are caused by the combined variations of both the price and investments in promotion. The critical t-value at ? = 0.05 is 2.007; hence, the regression model developed is a relatively good fit for the data set provided.

 
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Question e: Discuss how the estimation of demand might be improved.

Even though the model fits the data to a quantifiable level of accuracy, its sensitivity is debatable. The use of the two-stage linear technique in determining the coefficients factored the reciprocal relationship between the price and the demand. However, the price and the amount invested in promotion may have a similar relationship and, consequently, promotion may act as a confounding factor to the effects of prices on demand. Thus, improvement efforts should aim at discerning this relationship so that hidden influences are also included in the analysis. Moreover, the sample size should be increased so that the data used accurately approximates a normal distribution. Also, the key predictor used in the two-stage regression process should have a residual with a zero value. Hence, during data collection, errors should be minimized to facilitate the narrowing of the error margin. Most importantly, the income of the target customer regardless of being constant needs to be integrated into the model since it is the main determinant of the industrys key consumers.

Question f: Using your estimated demand equation, calculate own-price elasticity and an advertising elasticity. Compute the elasticity values at the sample mean values of the data in Table 1. Discuss, in quantitative terms, the meaning of each of the elasticity.

The elasticity of the price is calculated from the gradient of the price and the averages of the price and quantity demanded. In this case, the price constraint obtained from the regression model is the gradient of the price. Hence, price elasticity is determined as follows:

image28.png

Similarly, promotion elasticity is calculated as follows:

image29.png

The price-elasticity is negative and is approximately -1, indicating a strong law of demand. The price-elasticity asserts that the price and the demand of rutabagas are inversely related and, thus, the demand is dictated by the offered prices. However, the promotion-elasticity is positive, accounting for the contribution of advertisement on boosting the publicity of the rutabagas. Nonetheless, the magnitude of the contribution is limited since the coefficient is less than 0.5.

Question g: If the owner plans to charge a price of $4.15 for a Combination 1 meal and spend $18,000 per week on advertising, how many Combination 1 meals do you predict will be sold each week?

The estimation model is image30.png

Hence, the number of Combination 1 meals per week is

image32.png

Question h: If the owner spends $18,000 per week on advertising, write an equation for the inverse demand function. Then, calculate the demand price for 50,000 Combination 1 meals.

The demand function is image33.png

Hence, the inverse demand function is

image34.png

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Consequently, the demand price is computed as follows:

image35.png

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