for Economics and Finance experts only - you must be good in excel and analysis
I think, it will be better, if I awarded marks based on the gestalt, rather than on the marking schema, as you’d be better off. Pl. see the marks at the end.
The following informs you of what was asked. The marks earned by you under each category are provided against it. Kudos are reflected in your marks.
Pl. also see comments inside your Report, if any. Pl. read them in conjunction with this model answer
Issues and Scope: /5
Framing the issues and scope of analysis, incl. the key questions asked on optimal price and advertising dollars. The task list is:
1. Estimate an empirical demand function for TrickKit.
2. Interpret the estimated demand function for TrickKit.
3. Make pertinent recommendations to senior management based on the empirical demand
function.
4. Write a short report summarizing the results of the analysis and any recommendations.
Analysis and Recommendations: /20
1. Assumptions – sample is random and representative
The condition for maximizing total benefit is, MB = MC. Here, MB = MR, and we are given that MC = 0 (i.e., MagnaMed currently has only fixed costs), it is sufficient to set, MR = 0, i.e., maximize Total Revenue
1. Run both the linear and log linear model because we do not know which one will fit better.
1. Linear: Q = a + bP + cM + dN + eA + fPH
1. Log-linear: LN(Q) = LN(a) + b LN(P) + c LN(M) + d LN(N) + e LN(A) + f LN(PH)
1. Notice that our model did not have any cyclical variable because we do not expect Hepatitis B to exhibit any seasonality.
1. Look at the R-square of both the models and decide that both are about the same in explaining the variability.
2. Linear model: R2 = 0.9052, p-value for F-Test = 1.91162 E14
2. Log-linear model: R2 = 0.9091, p-value for F-Test = 1.03278 E14
1. With R2 value between Log-linear and Linear model nearly equal, select the linear model because we can answer the key questions easily. Note that based on p-value, both models are statistically significant
1. State the empirical linear demand function equation.
4. Discuss the regression coefficients and their implications –
0. was the sign expected, what does it mean? I’ll leave this for you.
0. is it significant? What does this imply? Provide all the p-values in a table
|
Regression Coefficient |
p-value |
|
a – intercept |
0.25881 |
|
b – slope for price of QuickKit |
3.81111 E 09 |
|
c – slope for Income |
0.51566 |
|
d- slope for Population |
0.86678 |
|
e- slope for Advertising |
0.00079 |
|
f – slope for HepaTest Price |
0.31911 |
1. Regression Coeff. Advt. is significant. Provide explanation – This is a specialized health product likely used by the specialists probably in hospital setting. So, advertising is addressed to these persons.
1. Regression Coeff. Income is not significant. Provide explanation – This being a specialized health product, if one needs it, there are no two ways about using it. Also, in the Canadian healthcare setting, patient’s income is irrelevant.
1. Regression Coeff. Population < 0, is not significant. Provide explanation – Between January 2013 and December 2015, the increase in population is only 3 percent and Hepatitis B is a special disease. The hepatitis B virus (HBV) is spread by blood/bodily fluid contact with an infected person. (See, http://www.liver.ca/liver-disease/types/viral_hepatitis/Hepatitis_B.aspx ) So, we do not expect the blood/bodily fluid contact to vary significantly with the small population growth. Furthermore, small negative value confirms that disease control may be working.
1. Compute the point elasticity for own price, advertising, income, population, and cross price elasticity with HepaTest. Use the mean of the sample values for the variables, as the typical value, in the formulae.
5. Average Q = 11,258
5. Point Price elasticity at the current price, $30 = b x ($30/11,258) = 1.24
5. You can also compute the own price elasticity, if you so wish, at the average price, $29.19. Either is fine. The point price elasticity at $29.19 = 1.21
5. Income point elasticity = c x (Average Income/Average Q) = 0.83
5. Population point elasticity = d x (Average Population/Average Q) = 4.00
5. Advertising point elasticity = e x (Average Advertising spend /Average Q) = 0.11
5. Cross-price point elasticity = f x (Average price of HepaTest/Average Q) = 0.46
From the above numbers on elasticity, you can alert the reader that,
0. current price ($30) or the price of $29.19 are not optimal , because |E| 1, the condition for maximizing Total Revenue,
0. Advertising has a positive impact on the quantity sold, and hence on total revenue, because, advertising elasticity is positive valued (0.11)
0. Cross-price elasticity is only 0.46; the demand for TrickKit is less sensitive to the competitor’s price. A 10% increase in the price of TrickKit will lead to a reduction of only 4.6% in demand.
1. With the linear model, find the optimal price using, either the content of p. 224 (T&M), or the Relation on p. 211, to set MR = 0.
· In the regression equation, Q = a + bP + cM + dN + eA + fPH, substitute the value of the intercept and the average value of M, N, A, and PH. This will yield the demand equation:
Q = 24,487.0962 466.8445 P (1)
1. Finding the Optimal price, by using the MR equation and then setting MR = 0:
· From above equation (1), the inverse demand equation is: P = 53. 3046 - 0.002142 Q
· Use P.224, T&M, and identify, A = 53. 3046, B = 0.002142
· Then, the optimal quantity, Q* = A÷ (2B) = 12, 443.5481
· Substitute the above value of Q* in the inverse demand equation. This will yield, the optimal price, P* = $26.65
OR
1. Finding the Optimal Price, by setting E = -1, (where MR = 0):
·
·
·
· Optimal price = $26.65
1. You can find the corresponding Advertising Spend from the regression equation, for the P* and Q* values, and rest of the variables, except A, at their typical values. Comparison with the current level of advertising spend is interesting.
· Q* = a + bP* + cM + dN + eA + fPH
· 12,443.54808 = 54, 173. 11801 12,443.54808 + 9,344.26465 + 45023.51703 + 0.05193 A +5,203.10292
· This yields, the optimal advertising spend is, $ 22, 916.67
· Current advertising spend is, $30,000, with current price of $30.
Conclusions:
· Current price is high, because the absolute value of own-price elasticity is >1. The optimal price is....
· Advertising elasticity is positive, advertising should be continued. The recommended advertising spend is ….
· Within the price ranges seen in the data, the price of HepaTest does not pose a significant challenge. The possible reason is that the product is used by specialists, but they only prescribe and do not have to pay for it; due to this reason the price of substitute may not be a major consideration.
· Income and population size have a modest influence on the sales, which in light of the Canadian healthcare context and public health education programs in Hepatitis B, is not surprising.
Recommendations
· Own price change from $30 to the optimal price
· Advertising is a good investment. Recommended advertising spend is…
· Continued monitoring and data collection to detect any changes from the current situation.
Writing: /5
1. Table Of Content (TOC)
1. Typo free
1. Presentation of the summaries of various tests.
1. Proper formatting, sentence structure, and English
1. Nice easy to read writing style
· References
Total: 16/30
Table of Contents Table of Contents 1 Introduction 2 Methods 2 Analysis 3 Recommendations 7 References 8 Appendix 9
Introduction
This report has been compiled to analyze the performance of TrickKit, a product from MagnaMed. This report will cover the analysis of the demand for the TrickKit, and come up with the optimal price the product. The report will also include the analysis of the advertising expenses, whether advertising is making any impact on the sales of the product or not. Other relevant recommendations that will help improve the efficient sale of the product will also be covered in this report.
Methods
To analyze the demand for TrickKit product, we shall use a basic linear model and the log-linear models. The linear model will help in attaining a function that will be used in determining the price of the product given the specific quantity demanded. The log-linear model, on the other hand, will be used to attain a model that smoothens out the linear model, and is much accurate in the analysis.
A basic linear model has also been used to determine if the advertising expenses have a positive or a negative relationship with quantity demanded and whether the relationship is significant or not. A linear model will also be used to determine if Hepatest, the alternative to TrickKit, is competitively priced with TrickKit. If it is, then there will be a significant positive relationship in the prices of the two products. That is, when the price of TrickKit goes up, the price of HepaTest is expected to go up, and if the prices go down, then the price of TrickKit should also go down.
These models will be attained by using Excel’s inbuilt functions.
Analysis
The linear demand function for TrickKit is obtained by regressing the quantity of TrickKits sold on the price of the TrickKits. The linear model for the regression is given by;
Comment by Rajan: This model is incorrect. As was pointed out in 4-AP-13, all five variables (P, M, N, A, and P_h) jointly determine the demand for TrickKit. Regressing only one variable at a time is incorrect. Also, reflection will tell you that were we able to regress one variable at a time in mutilinear models, there would be no need to develop such models. For correct method, pl. peruse the appended Model Solution
The log-linear model provides the following model:
Both the linear and the nonlinear models have a correlation coefficient of -0.8843, and the p-value of the correlation coefficient is less than 0.05. The p-values of the variables in the regression analysis are also less than 0.05.
The linear equation for the advertising expenditure and the quantity demanded is given by:
The variables have a correlation coefficient of -0.1495. The p-value of the regression model is 0.384.
The linear equation for the price of TrickKit and the price of HepaTest is given by:
The variables have a correlation coefficient of -0.4586. The p-value of the regression model is 0.0049.
Explanation
There is a strong negative correlation between the number of TrickKits sold and the price. This means that if the price is increased, the quantity demanded decreases by a particular amount. To be more specific, a unit increase in the price of TrickKits creates a reduction in the quantity demanded by . Based on the data retrieved in December 2015, the quantity demanded stood at 12,903. Thus the price that TrickKits can be sold in January 2016 is:
The price for TrickKit in the month of January should be sold at $24.72 based on the demand for the product from the previous month. Besides this, the data provided, that is price and quantity of the product sold, are statistically significant in the regression model. The correlation coefficient is also statistically significant, meaning that the data can be relied upon to make critical decisions with regards to the pricing of the TrickKit. Furthermore, 78% of the variation in the quantity of TrickKits sold can be explained by the price of the product. The current price of the product should, therefore, be increased by 22 cents so as to make the price optimal.
The results from using the log-linear model are almost similar to the linear model. The approximate price of TrickKits is given by:
Using the log-linear model, the optimal price for TrickKit in the month of January 2016 is $24.98.
The advertising expenditure for the last previous years has no significant correlation with the quantity of TrickKits sold. The weak correlation between the two variables is not statistically significant either since the p-value is greater than 0.05. This implies that we cannot use the amount spent on advertisement to predict the future sales of the TrickKit. The regression model is not statistically significant either, since the p-value is also greater than 0.05, and only 2.23% of the variation in quantity demanded can be explained by the advertisement expenditure. The investment on the advertising hasn’t produced any significant results statistically.
There is also a negative relationship between the prices of TrickKits and HepaTest. The correlation between these two variables is statistically significant since the p-value of the regression model is less than 0.05. The price of HepaTest can also explain 21% of the variation in the price of TrickKit. There are various ways in which we could analyze the price between the two competitive products. When the price of TrickKits go up, the demand for the product goes down, and customers will go for the alternative product, HepaTest. The price for TrickKits will, therefore, go down due to low demands. After some time, when the demand for Hepatest has increased, its price will go up, and customers will seek the alternative product, TrickKit, which by then price would have dropped, thus increasing its demand.
Recommendations
The company should consider using the log-linear model in pricing TrickKits. The results are more accurate. The ceo should also consider setting competitive prices with the alternative product to ensure constant sales.
Based on the analysis of the advertisement expenditure, MagnaMed should invest more capital in advertising their product. By increasing the amount spent on advertising, the company will see a direct increase in the quantity of TrickKits sold. The relationship between advertising and the amount of TrickKits sold is, however, going to be elastic. This implies that any increase of capital spent on adverts will not increase the quantity of TrickKits sold. Advertising could mean giving away goodies, holding promotional stands, sponsoring small community events, etc. and not tied alone to billboards and commercials.
When advertising becomes positively correlated with the quantity of TrickKits sold, the price of the products can be safely brought up, while insignificantly interfering with the demand of the product.
References
Applied Problems Assignment 14
Maurice, S. C., & Thomas, C. R. (2013). Managerial Economic - Foundations for Business Analysis and Strategy. New York: McGraw-Hill Irwin.
Appendix
Linear demand function
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SUMMARY OUTPUT |
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Regression Statistics |
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Multiple R |
0.883214 |
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R Square |
0.780067 |
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Adjusted R Square |
0.773598 |
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Standard Error |
616.8871 |
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Observations |
36 |
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ANOVA |
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df |
SS |
MS |
F |
Significance F |
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Regression |
1 |
45891396 |
45891396.03 |
120.5924 |
1.01E-12 |
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Residual |
34 |
12938689 |
380549.6711 |
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Total |
35 |
58830085 |
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Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
Lower 95.0% |
Upper 95.0% |
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Intercept |
21993.11 |
982.9621 |
22.37431724 |
6.38E-22 |
19995.49 |
23990.73 |
19995.49 |
23990.72553 |
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P |
-367.747 |
33.48799 |
-10.98145684 |
1.01E-12 |
-435.803 |
-299.691 |
-435.803 |
-299.6911513 |
Non-linear demand function
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SUMMARY OUTPUT |
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Regression Statistics |
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Multiple R |
0.884329523 |
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R Square |
0.782038705 |
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Adjusted R Square |
0.775628079 |
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Standard Error |
0.05471856 |
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Observations |
36 |
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ANOVA |
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df |
SS |
MS |
F |
Significance F |
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Regression |
1 |
0.365255781 |
0.365255781 |
121.9909984 |
8.62064E-13 |
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Residual |
34 |
0.101800106 |
0.002994121 |
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Total |
35 |
0.467055886 |
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Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
Lower 95.0% |
Upper 95.0% |
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Intercept |
12.53023453 |
0.29058082 |
43.12134061 |
2.87441E-31 |
11.93970325 |
13.1207658 |
11.93970325 |
13.1207658 |
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ln(P) |
-0.952366654 |
0.086226407 |
-11.04495353 |
8.62064E-13 |
-1.127599796 |
-0.777133513 |
-1.127599796 |
-0.77713351 |
Advertisement expenditure
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SUMMARY OUTPUT |
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Regression Statistics |
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Multiple R |
0.149545385 |
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R Square |
0.022363822 |
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Adjusted R Square |
-0.006390183 |
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Standard Error |
1300.615457 |
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Observations |
36 |
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ANOVA |
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df |
SS |
MS |
F |
Significance F |
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Regression |
1 |
1315665.562 |
1315666 |
0.777764 |
0.384018484 |
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Residual |
34 |
57514419.29 |
1691601 |
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Total |
35 |
58830084.85 |
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Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
Lower 95.0% |
Upper 95.0% |
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Intercept |
11995.9258 |
864.4032772 |
13.8777 |
1.45E-15 |
10239.24698 |
13752.60461 |
10239.24698 |
13752.60461 |
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A |
-0.032202139 |
0.036514124 |
-0.88191 |
0.384018 |
-0.106407767 |
0.042003488 |
-0.106407767 |
0.042003488 |
Prices between TrickKits and HepaTest
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SUMMARY OUTPUT |
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Regression Statistics |
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Multiple R |
0.458608262 |
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R Square |
0.210321538 |
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Adjusted R Square |
0.1870957 |
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Standard Error |
2.807386816 |
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Observations |
36 |
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ANOVA |
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df |
SS |
MS |
F |
Significance F |
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Regression |
1 |
71.37019509 |
71.37019509 |
9.055498686 |
0.004906625 |
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Residual |
34 |
267.9683049 |
7.881420733 |
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Total |
35 |
339.3385 |
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Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
Lower 95.0% |
Upper 95.0% |
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Intercept |
101.5740786 |
24.0579721 |
4.222054882 |
0.000170592 |
52.68239686 |
150.4657603 |
52.68239686 |
150.4657603 |
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P_h |
-6.108936417 |
2.030062548 |
-3.009235565 |
0.004906625 |
-10.23451988 |
-1.983352952 |
-10.23451988 |
-1.983352952 |