Deck 2: Demand Analysis and Estimating Demand

Question 1

Consider the following multiplicative demand function where Q_D = quantity demanded, P = selling price, and Y = disposable income:Q_D = 1.6P ^{- 1.5}Y² The coefficient of Y (i.e., .2) indicates that (all other things being held constant):

A) for a one percent increase in disposable income, quantity demanded would increase by .2 percent
B) for a one unit increase in disposable income, quantity demanded would increase by .2 units
C) for a one percent increase in disposable income quantity demanded would increase by .2 units
D) for a one unit increase in disposable income, quantity demanded would increase by .2 percent
E) none of the above

Answer 1

for a one percent increase in disposable income, quantity demanded would increase by .2 percent

Question 2

Phoenix Lumber Company uses the number of construction permits issued to help estimate demand (sales). The firm collected the following data on annual sales and number of construction permits issued in its market area: (a)Which variable is the dependent variable and which is the independent variable?
(b)Determine the estimated regression line.
(c)Test the hypothesis (at the .05 significance level) that there is no relationship between the variables.
(d)Calculate the coefficient of determination. Give an economic interpretation to the value obtained.
(e)Perform an analysis of variance on the regression including an F-test (at the .05 significance level) of the overall significance of the results.
(f)Suppose that 8,000 construction permits are expected to be issued in 2010. What would be the point estimate of Phoenix Lumber Company's sales for 2010?

Answer 2

(a)Dependent variable (Y) -Sales
Independent variable (X) -No. of construction permits issued
(b) (c) (d) (e) (f)X = 8,000
Y = 6.4648 + .5962(8.00) = 11.234 Estimated sales for Phoenix Lumber Company in 2010 would be $11.234 million.

Question 3

Lenny's, a national restaurant chain, conducted a study of the factors affecting demand (sales). The following variables were defined and measured for a random sample of 30 of its restaurants:
Y= Annual restaurant sales ($000)
X₁= Disposable personal income (per capita) of residents within 5 mile radius
X₂= License to sell beer/wine (0 = No, 1 = Yes)
X₃= Location (within one-half mile of interstate highway-0 = No, 1 = Yes)
X₄= Population (within 5 mile radius)
X₅= Number of competing restaurants within 2 mile radius
The data were entered into a computerized regression program and the following results were obtained: Questions:
(a)Give the regression equation for predicting restaurant sales.
(b)Give an interpretation of each of the estimated regression coefficients.
(c)Which of the independent variables (if any) are statistically significant at the .05 level in "explaining"restaurant sales?
(d)What proportion of the variation in restaurant sales is "explained"by the regression equation?
(e)Perform an F-test (at the .05 significance level) of the overall explanatory power of the regression model.

Answer 3

(a)Y = .363 + .00275X₁ + 76.65X₂ + 164.3X₃ + .00331X₄ -46.2X₅
(b)a = .363,Value of dependent variable (Y) when all independent variables (X's) are equal to zero.
b₁ = .00275,For a one dollar increase in per capita disposable income, expected restaurant sales will increase by .00275(* $1000) = $2.7
b₂ = 76.65 ,Expected annual restaurant sales are 76.65(* $1000) = $76,650 higher for a restaurant with a license to sell beer/wine than for one without such a license.
b₃ = 164.3 ,Expected annual restaurant sales are 164.3(* $1000) = $164,300 higher for a restaurant located within one-half mile of an interstate highway.
b₄ = .00331 ,For a one person increase in population, expected restaurant sales will increase by .00331(* $1000) = $3.31.
b₅ = -46.2 ,For a one unit increase in the number of restaurants within a 2-mile radius, expected annual restaurant sales decrease by 46.2(* $1000) = $46,200.
(c)H₀: $\beta$ _i = 0
H₁: $\beta$ _i $\neq$ 0
Reject H₀ if t > t_{.025, 24} = 2.064 or t <-2.064.
The t-values of X₁ and X₄ are greater than +2.064 (and the t-value of X₅ is less than -2.064). Therefore X₁, X₄ , and X₅ are statistically significant at the .05 level in "explaining"restaurant sales.
(d)According to the R-SQUARE statistic, 79 percent of the variation in restaurant sales is "explained"by the regression equation.
(e)H₀: All b_i = 0 (no relationship)
H₁: At least one b_i $\neq$ 0
Reject H₀ if F > F _{.05, 5, 24} = 2.62
The F-STAT is equal to 18.18, which exceeds 2.62. Therefore, one rejects the null hypothesis (at the .05 significance level) and concludes that the five independent variables "explain"a significant proportion of the variation in restaurant sales.

Question 4

The following demand function has been estimated for Fantasy pinball machines: Q_D = 3,500 - 40P + 17.5P_x + 670U + .0090A + 6,500N where
P = monthly rental price of Fantasy pinball machines
P_x = monthly rental price of Old Chicago pinball machines (their largest competitor)
U = current unemployment rate in the 10 largest metropolitan areas
A = advertising expenditures for Fantasy pinball machines
N = fraction of the U.S. population between ages 10 and 30
(a)What is the point price elasticity of demand for Fantasy pinball machines when P = $150, P_x = $100, U = .12, A = $200,000 and N = .35?
(b)What is the point cross elasticity of demand with respect to Old Chicago pinball machines for the values of the independent variables given in part (a)?

Question 5

Given the following demand function:Q = 2.0 P ^{- 1.33} Y^2.0 A^.50where
Q = quantity demanded (thousands of units)
P = price ($/unit)
Y = disposable income per capita ($ thousands)
A = advertising expenditures ($ thousands)
determine the following when P = $2/unit, Y = $8 (i.e., $8000), and A = $25 (i.e., $25,000)
(a)Price elasticity of demand
(b)The approximate percentage increase in demand if disposable income percentage increases by 3%.
(c)The approximate percentage increase in demand if advertising expenditures are increased by 5 percent.

Question 6

In this problem, demonstrate your knowledge of percentage rates of change of an entire demand function (HINT: % $\Delta$ Q = E_P . % $\Delta$ P + E_Y . % $\Delta$ Y). You have found that the price elasticity of motor control devices at Allen-Bradley Corporation is -2, and that the income elasticity is a +1.5. You have been asked to predict sales of these devices for one year into the future. Economists from the Conference Board predict that income will be rising 3% over the next year, and AB's management is planning to raise prices 2%. You expect that the number of AB motor control devices sold in one year will:

A) fall .5%.
B) not change.
C) rise 1%.
D) rise 2%.
E) rise .5%.

Question 7

The manager of the Sell-Rite drug store accidentally mismarked a shipment of 20-pound bags of charcoal at $4.38 instead of the regular price of $5.18. At the end of a week, the store's inventory of 200 bags of charcoal was completely sold out. The store normally sells an average of 150 bags per week.
(a)What is the store's arc elasticity of demand for charcoal?
(b)Give an economic interpretation of the numerical value obtained in part (a)

Question 8

The Future Flight Corporation manufactures a variety of Frisbees selling for $2.98 each. Sales have averaged 10,000 units per month during the last year. Recently Future Flight's closest competitor, Soaring Free Company, cut its prices on similar Frisbees from $3.49 to $2.59. Future Flight noticed that its sales declined to 8,000 units per month after the price cut.
(a)What is the arc cross elasticity of demand between Future Flight's and Soaring Free's Frisbees?
(b)If Future Flight knows the arc price elasticity of demand for its Frisbees is -2.2, what price would they have to charge in order to obtain the same level of sales as before Soaring Free's price cut?