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Exam 5: Demand Estimation

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Question 1

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Profit Probability Estimation. Intimate Lighting, Inc., is a rapidly growing lighting accessory outlets that caters to the do-it-yourself home remodeling market. During the past year, 18 stores were operated in small to medium-size metropolitan markets. An in-house study of sales by these outlets revealed the following (standard errors in parentheses): Standard Error of the Estimate = 500. Here, Q is unit sales, P is unit price, P_X is the average unit price at competitor stores, A is advertising expenditures, and I is income per capita. A. Tucson, Arizona was a typical market covered by this analysis. In the Tucson market, "own" price was $60, competitor price was $45, advertising was $13,500, and income was an average $80,000. Calculate and interpret the expected level of unit sales, as well as the 95% and 99% confidence regions for actual sales. B. Calculate the 95% and 99% confidence regions for actual revenues in the Tucson market. C. Estimate the probability that the Tucson store made a profit during this period if total costs were $1,735,200.

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Question 2

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The long-run effect on demand of competitor product-development strategies is:

A) less than the short-run effect.
B) the same as the short-run effect.
C) unrelated to the short-run effect.
D) greater than the short-run effect.

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Question 3

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If P₁ = $5, Q₁ = 10,000, P₂ = $6 and Q₂ = 5,000, then at point P₁ an estimate of the point price elasticity e_P equals:

A. Constant elasticities of demand are observed at different points along a linear demand curve. B. In the linear model approach, the effect on demand of a one-unit change in any independent variable is assumed to be constant. C. In the log-linear model approach, the effect of a one-unit change in any independent variable will tend to vary. D. The elasticities of demand are different at various points along a multiplicative demand curve. E. Log-linear models assume constant elasticities.

Expected Demand Estimation. Snack Foods International, Ltd. has hired you to analyze demand in 25 regional markets for a new Product Y, called Angelica Pickles. A statistical analysis of demand in these markets shows (standard errors in parentheses): Standard Error of the Estimate = 75 Here, Q_Y is market demand for Product Y, P is the price of Y in dollars, A is dollars of advertising expenditures, P_X is the average price in dollars of another (unidentified) product, and I is dollars of household income. In a typical market, the price of Y is $1,500, P_X is $500, advertising expenditures are $50,000, and disposable income per household is $45,000.

If P₁ = $5, Q₁ = 10,000, P₂ = $6 and Q₂ = 5,000, then at point P₂ an estimate of the point price elasticity e_P equals:

Multiple Regression. Kitchen Products, Ltd., is a regional distributor of Regal Bread Making Machine. The company wishes to assess the relative importance of price reductions versus an increase in personal selling efforts as means for enhancing product promotion. To this end, the company recently used a regression analysis approach to study the following monthly unit sales, price, and personal selling expense information for the Bozeman, Montana market: As a first step in the analysis, the company ran simple regressions of unit sales on each of the potentially important independent variables of price and personal selling expenses: The first simple regression equation is: SALES = 371 - 2.59 PRICE The multiple regression equation is: SALES = 195 - 4.33 PRICE + 0.231 SELLEXP

Demand Estimation. The Wallpaper Shop, Inc., is a rapidly growing chain of wallpaper shops that caters to the do-it-yourself home remodeling market. During the past year, 15 stores were operated in small to medium-size metropolitan markets. An in-house study of sales by these outlets revealed the following (standard errors in parentheses): Standard Error of the Estimate = 800. Here, Q is the number of customers served, P is the average price per customer, P_X is the average cost of professionally wallpapering a small room, A is advertising expenditures (in dollars), I is disposable income per capita (in dollars), and GR is the rate of population growth per year (in percent).

A linear model implies:

Demand estimation in a controlled environment is possible with:

Regression Statistics. June Ward, controller for NAFTA, Inc., has asked you to analyze demand in 30 regional markets for Beaver's Cleavers, a new brush cutting device, dubbed Product Y. A statistical analysis of demand in these markets shows (standard errors in parentheses): Standard Error of the Estimate = 40 Here, Q_Y is market demand for Product Y, P is the price of Y in dollars, A is dollars of advertising expenditures, P_X is the average price in dollars of another (unidentified) product, and I is dollars of household income. In a typical market, the price of Y is $100, P_X is $50, and disposable income per family averages $80,000.

The demand for most consumer goods is insensitive to changes in:

When considering effects on the automobile market, a decrease in auto worker health benefits leads to:

A. The standard error of the estimate $\mathrm{a}$ . be bued to determine a range within which the independent $\mathrm{X}$ variables can be predicted with varying degrees of statistical confidence based on the regression coefficients and the value for the $Y$ variable. B. The best estimate of the $t^{\text {th }}$ value for the dependent variable is $\hat{Y}{ }_{t}$ , as predicted by the regression equation C. If the u error terms are normally distributed about the regression equation, there is a $95 \%$ probability that observations of the dependent variable will lie within roughly three standard errors of the estimate. D. If $r=1$ , there is a perfect inverse line ar relation between the dependent $Y$ variable and a single independent $X$ variable. E. If $r=0$ , the dependent and independent variables are autonomous.

A multiplicative model is:

Movement along a demand curve is indicated by the quantity effect of a change in:

Multicollinearity is caused by:

The Identification Problem. Business is booming for Complex Controls, Inc., a leading supplier of analog/digital circuits and systems used for measurement and control. The average price received by CCI for the XKE device, and the number sold (output) over the past six quarters are as follows: Quarterly demand and supply curves for CCI services are: where Q is output (000), P is price, T is a trend factor, and T = 1 during Q-1 and increases by one unit per quarter.

Elasticity Estimation. The Lincoln National Life Insurance Company offers a wide variety of insurance products, including whole-life and term policies. The company has compiled the following data concerning policy sales during recent years: *Price is quoted in terms of cost per $1,000 of coverage.

Suppose Q₁ = 50 when P₁ = $25, and Q₂ = 20 when P₂ = $40. A linear estimate of the demand curve is: