Managerial Economics Study Set 10

Business

Quiz 5 :

Demand Estimation and Forecasting

Quiz 5 :

Demand Estimation and Forecasting

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The sales data over the last 10 years for the Acme Hardware Store are as follows: img a. Calculate the compound growth rate for the period of 2003 to 2012. b. Based on your answer to part a, forecast sales for both 2013 and 2014. c. Now calculate the compound growth rate for the period of 2007 to 2012. d. Based on your answer to part c, forecast sales for both 2013 and 2014. e. What is the major reason for the differences in your answers to parts b and d If you were to make your own projections, what would you forecast (Drawing a graph is very helpful.)
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(a)
In order to find the compound growth rate of Sales in the period 2003 and 2012, follow the following steps:
1) Determine the number of years intervening between two sales periods: In the given case, it is 11 years. That means ,
img 2) Find the beginning period sales: In this case it is $230000 worth of sales corresponding to the sales period 2003. That means
img 3) Find the end period sales: In this case it is $873000 worth of sales corresponding to the sales period 2012. That means
img 4) Assume that the compound growth rate is
img and apply the formula given by:
img Hence, the compound growth rate of sales between 2003 and 2012 is:
img (b)
Assume that the compound growth rate of sales that existed between 2003 and 2012 is the rate at which the sale is expected to grow in 2013 from the level that exists in 2012, the forecasted Sales figure for 2013 is:
img The forecasted Sales figure for 2014 is:
img (c)
In order to find the compound growth rate of Sales in the period 2007 and 2012, follow the following steps:
1) Determine the number of years intervening between two sales periods: In the given case, it is 11 years. That means ,
img 2) Find the beginning period sales: In this case it is $453000 worth of sales corresponding to the sales period 2007. That means
img 3) Find the end period sales: In this case it is $873000 worth of sales corresponding to the sales period 2012. That means
img 4) Assume that the compound growth rate is
img and apply the formula given by:
img Hence, the compound growth rate of sales between 2007 and 2012 is:
img (d)
Assume that the compound growth rate of sales that existed between 2007 and 2012 is the rate at which the sale is expected to grow in 2013 from the level that exists in 2012, the forecasted Sales figure for 2013 is:
img The forecasted Sales figure for 2014 is:
img (e)
The major difference between the forecasted figures of sales for the period 2013 and 2014 is the difference in the constant compounded growth rate of sales being used.
img At one side, the constant compounded growth rate estimated based on the period 2003-2012 is assumed to exist in each of the future years 2013 and 2014 which is 15.972% and on the other side, the constant compounded growth rate as estimated over the period 2007-2012 is assumed to exist in each of the future years 2013 and 2014, which is relatively lower at 14.0206% while forecasting Sales for 2013 2014
img It shall also be observed that Y-o-Y growth rate of Sales shows a consistent decline. This explains as to why the compound growth rate of Sales over the period 2007-12 is less than the compound growth rate over 2003-2012
img While deciding about the model to forecast the Sales figures for 2013 2014, the graph relating Sales performance over the period is observed. It shall be noted that, Sales shows an exponential rise, hence the model that would be appropriate here to fit the data for the purpose of forecasting is an exponential model of the form:
img , where
img and
img are the constants.
This exponential form can also be written as:
img The result is:
img img Hence, the forecasted value of
img for 2013 is:
img Hence, the forecasted Sales for 2013 are:
img The forecasted value of
img for 2014 is:
img Now, substitute the forecasted sales value for 2013 in the below formula to get the forecasted sales for 2014.
img Hence, the forecasted Sales for 2014 are
img

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You are given the following demand for European luxury automobiles: Q = 1,000 P -0.93 P A 0.75 P J 1.2 I 1.6 where P = Price of European luxury cars P A = Price of American luxury cars P J = Price of Japanese luxury cars I = Annual income of car buyers Assume that each of the coefficients is statistically significant (i.e., that they passed the t -test). On the basis of the information given, answer the following questions: a. Comment on the degree of substitutability between European and American luxury cars and between European and Japanese luxury cars. Explain some possible reasons for the results in the equation. b. Comment on the coefficient for the income variable. Is this result what you would expect Explain. c. Comment on the coefficient of the European car price variable. Is that what you would expect Explain.
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The demand for European luxury automobiles is given as follows:
img Where Q is the demand for European luxury automobiles;
P is the Price of European luxury automobiles; Pa is the price of American luxury automobiles; Pj is the price of Japanese luxury automobiles; and I is the Annual income of car buyers.
a. The substitutability between European and American car is explained by the coefficient of the factor Pa. The value of the coefficient is 0.75. It means that the substitutability is up to 75%. Therefore, they are not perfect substitutes.
b. The coefficient of income variable is 1.6. It means that with the increase in income, there will be a higher proportionate increase in demand. This is a expected result for the luxury goods because luxury goods are supposed to be income elastic.
c. The coefficient of European cur price is -0.93. This means that the decrease or increase in price by 1% will increase or decrease the demand by 0.93%. This is not expected because for luxury goods, price elasticity is likely to be elastic. One possible reason for getting an inelastic demand for luxury cars can be that buyers have a strong preference for luxury cars that is not influenced much by the price change.

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Enumerate methods of qualitative and quantitative forecasting. What are the major differences between the two
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Qualitative method of forecasting is done based on the judgment and experience of individuals and groups who are considered to be experts in that respective domain.
Qualitative method can be done by taking opinions of a group of experts and then combining them to arrive to a conclusion. Another popular qualitative method is the Delphi method. In this method a group of experts are sent questionnaires through mail. The responses received from the experts are then are summarised without disclosing the identities. Further mails are then sent for clarification in situations where there are extreme views. The process is repeated till the group reaches to a reasonable agreement.
Qualitative forecasting can result in numerical results even though they are not based on historical data.
On the other hand, quantitative method on the other hand is primarily based on historical data and uses various causal relationships to predict the future. Some of the other methods used for quantitative forecasting are trend analysis and econometric models.

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You are the manager of a large automobile dealership who wants to learn more about the effectiveness of various discounts offered to customers over the past 14 months. Following are the average negotiated prices for each month and the quantities sold of a basic model (adjusted for various options) over this period of time. a. Graph this information on a scatter plot. Estimate the demand equation. What do the regression results indicate about the desirability of discounting the price Explain. img b. What other factors besides price might be included in this equation Do you foresee any difficulty in obtaining these additional data or incorporating them in the regression analysis
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Office Enterprises (OE) produces a line of metal office file cabinets. The company's economist, having investigated a large number of past data, has established the following equation of demand for these cabinets: Q = 10,000 + 60 B - 100 P + 50 C where Q = Annual number of cabinets sold B = Index of nonresidential construction P = Average price per cabinet charged by OE C = Average price per cabinet charged by OE's closest competitor It is expected that next year's nonresidential construction index will stand at 160, OE's average price will be $40, and the competitor's average price will be $35. a. Forecast next year's sales. b. What will be the effect if the competitor lowers its price to $32 If it raises its price to $36 c. What will happen if OE reacts to the decrease mentioned in part b by lowering its price to $37 d. If the index forecast was wrong, and it turns out to be only 140 next year, what will be the effect on OE's sales
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An economist has estimated the sales trend line for the Sun Belt Toy Company as follows: S t = 43.6 + 0.8 t S t represents Sun Belt's monthly sales (in millions of dollars), and t = 1 in January 2008. The monthly seasonal indexes are as follows: img Forecast monthly sales for the year 2013.
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You have the following data for the last 12 months' sales for the PRQ Corporation (in thousands of dollars): img a. Calculate a 3-month centered moving average. b. Use this moving average to forecast sales for January of next year. c. If you were asked to forecast January and February sales for next year, would you be confident of your forecast using the preceding moving averages Why or why not
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Explain the difference between time series data and cross-sectional data. Provide examples of each type of data.
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The sales data for the Lonestar Sports Apparel Company for the last 12 years are as follows: img a. What is the 2001-2012 compound growth rate b. Using the result obtained in part a, what is your 2013 projection c. If you were to make your own projection, what would you forecast
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"The best forecasting method is the one that gives the highest proportion of correct predictions." Comment.
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The Miracle Corporation had the following sales during the past 10 years (in thousands of dollars): img a. Calculate a trend line, and forecast sales for 2013. How confident are you of this forecast b. Use exponential smoothing with a smoothing factor w = 0.7. What is your 2013 forecast How confident are you of this forecast
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Would there be any differences in the set of variables used in a regression model of the demand for consumer durable goods (e.g., automobiles, appliances, furniture) and a regression model of the demand for "fast-moving consumer goods" (e.g., food, beverages, personal care products) Explain.
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Briefly explain the meaning of R 2. A time series analysis of demand tends to result in a higher R 2 than one using cross-sectional data. Why do you think this is the case
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A manufacturer of computer workstations gathered average monthly sales figures from its 56 branch offices and dealerships across the country and estimated the following demand for its product: Q = +15,000 - 2.80 P + 150 A + 0.3 P pc + 0.35 P m + 0.2 P c (5,234) (1.29) (175) (0.12) (0.17) (0.13) R 2 = 0.68 SEE = 786 F = 21.25 The variables and their assumed values are Q = Quantity P = Price of basic model = 7,000 A = Advertising expenditures (in thousands) = 52 P pc = Average price of a personal computer = 4,000 P m = Average price of a minicomputer = 15,000 P c = Average price of a leading competitor's workstation = 8,000 a. Compute the elasticities for each variable. On this basis, discuss the relative impact that each variable has on the demand. What implications do these results have for the firm's marketing and pricing policies b. Conduct a t -test for the statistical significance of each variable. In each case, state whether a one-tail or two-tail test is required. What difference, if any, does it make to use a one-tail versus a two-tail test on the results Discuss the results of the t -tests in light of the policy implications mentioned. c. Suppose a manager evaluating these results suggests that interest rates and the performance of the computer (typically measured in millions of instructions per second, or MIPS) are important determinants of the demand for workstations and must therefore be included in the study. How would you respond to this suggestion Elaborate.
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If the sales of your company have grown from $500,000 five years ago to $1,050,150 this year, what is the compound growth rate If you expect your sales to grow at a rate of 10 percent for the next five years, what should they be five years from now
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One of the most difficult tasks in regression analysis is to obtain the data suitable for quantitative studies of this kind. Suppose you are trying to estimate the demand for home furniture. Suggest the kinds of variables that could be used to represent the following factors, which are believed to affect the demand for any product. Be as specific as possible about how the variables are going to be measured. Do you anticipate any difficulty in securing such data Explain. img
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The maker of a leading brand of low-calorie microwavable food estimated the following demand equation for its product using data from 26 supermarkets around the country for the month of April: Q = -5,200 - 42 P + 20 P X + 5.2 l + 0.20 A + 0.25 M (2.002) (17.5) (6.2) (2.5) (0.09) (0.21) R 2 = 0.55 n = 26 F = 4.88 Assume the following values for the independent variables: Q = Quantity sold per month P (in cents) = Price of the product = 500 P X (in cents) = Price of leading competitor's product = 600 I (in dollars) = Per capita income of the standard metropolitan statistical area (SMSA) in which the supermarket is located = 5,500 A (in dollars) = Monthly advertising expenditure = 10,000 M = Number of microwave ovens sold in the SMSA in which the supermarket is located = 5,000 Using this information, answer the following questions: a. Compute elasticities for each variable. b. How concerned do you think this company would be about the impact of a recession on its sales Explain. c. Do you think that this firm should cut its price to increase its market share Explain. d. What proportion of the variation in sales is explained by the independent variables in the equations How confident are you about this answer Explain.
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The MNO Corporation is preparing for its stockholder meeting on May 15, 2013. It sent out proxies to its stockholders on March 15 and asked stockholders who plan to attend the meeting to respond. To plan for a sufficient number of information packages to be distributed at the meeting, as well as for refreshments to be served, the company has asked you to forecast the number of attending stockholders. By April 15, 378 stockholders have expressed their intention to attend. You have available the following data for the last 6 years for total attendance at the stockholder meeting and the number of positive responses as of April 15: img a. What is your attendance forecast for the 2013 stockholder meeting b. Are there any other factors that could affect attendance, and thus make your forecast inaccurate
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In the Columbia Gas of Ohio study that forecasted the demand for gas (see p. 155), the company developed the following coefficients for their equation: img Forecast the demand for gas for a day, when the expected average temperature will be 40 degrees, the prior day's average temperature was 37, and the average wind speed is predicted to be 8 miles per hour.
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Based on past data, Mack's Pool Supply has constructed the following equation for the sales of its house brand of chlorine tablets: Q = 1,000 + 100 t where Q is quantity and t is time (in years), with 2007 = 0. a. What is the sales projection for 2013 b. The tablet sales are seasonal, with the following quarterly indexes: img What is the quarterly sales projection for 2013
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