Guided exercises on demand estimation:
Question 1
Syarikat Bacfree manufactures and sells water filters. The economic forecasting unit of the company has supplied the following demand equation.
QB = 2000 - 5PB + 2.5PC + 0.82Y + 0.6AB
(1200) (1.5) (1.2) (0.5) (0.2)
where , QB = quantity sold
PB = price per unit
PC = average unit price of competitor’s product
Y = income per household
AB = advertising expenditure
R2 = 0.86
S.E.E = 5
Durbin Watson = 10
Sample size = 34
Standard error of coefficients in parentheses
Given, PB = RM50, PC= RM45, AB = RM12,500, Y = RM2,000
a) Does each independent variable have a significant effect on the sales of Bacfree water filters? (95% confidence level)
Clue: since you want to see whether eachindependent variable is significant in influencing the dependent variable, conduct the t-test.
Formula to calculate t-value:
t-computed value= coefficient
standard error of coefficient
| Variables | t-computed value | t-critical value | comment |
| PB | 5/1.5 = 3.33 | > 2.00 | significant |
| PC | 2.5/1.2 = 2.08 | > 2.00 | significant |
| Y | 0.82/0.5 = 1.64 | < 2.00 | insignificant |
| AB | 0.6/0.2 = 3 | > 2.00 | significant |
All independent variables have significantrelationship with dependent variable except for Y.
b) What percentage of demand variation is explained by this model?
Here the question wants you to determine the change in demand that can be explained by your regression equation. Conduct R2 test.
R2 = 0.86
86% of the variation (changes) in demand (QB) can be explained by independent variables (PC, Y & AB). Another 14% cannot influence the changes in QB due to missing independent var’s (factors) that not included in the model.
c) Are all signs of coefficient consistent with economic theory?
| Variables | Estimated Sign | Economic Theory | Comments |
| PB | - | - | There is negative relationship between P and Q. It is consistent because P & Q follows the law of demand |
| PC | + | + | Possible showing that product C is a substitute |
| Y | + | + | Yes, it is consistent. It shows that the good is a normal good |
| AB | + | + | Yes it is consistent because advertising usually has direct relationship with Q. |
Therefore all of the above independent var’s are consistent with the economic theory.
d) Derive an expression for the firm’s demand curve function.
QB = 2000 - 5PB + 2.5PC + 0.82Y + 0.6AB
QB = 2000 - 5PB + 2.5(45) + 0.82(2000) + 0.6(12500)
QB = 11252.50 - 5PB
5PB = 11252.50 - QB
PB = (11252.50 - QB )/ 5
PB = 2250.5 – 0.2Q
e) Using the above data, derive the total revenue (TR), average revenue (AR) and the marginal revenue (MR) functions for Syarikat Bacfree water filters.
TR = P x Q
= (2250.5 – 0.2Q)Q
TR = 2250.5Q – 0.2Q2
AR = 2250.5 – 0.2Q { note: AR = TR/Q }
MR = 2250.5 – 0.4Q { note: MR = dTR/dQ }
f) Based on the information above, estimate current sales for Syarikat Bacfree.
ˆ
Sales volume (QB) = 11252.50 - 5(50)
= 11002.50
g) Compute price elasticity of demand, income elasticity of demand, advertising elasticity of demand and cross elasticity of demand for Syarikat Bacfree.
Price elasticity of demand:
Ep = ∂QB x PB
∂ PB QB
= - 5 x (50/11002.50)
Ep = - 0.023
Income elasticity of demand:
Ey = ∂QB x Y
∂Y QB
= 0.82 x (2000/11002.5)
Ey = 0.15
Cross elasticity of demand:
Ecross = ∂QB x PC
∂ PC QB
= 2.5 x (45/11002.5)
Ecross = 0.01
Advertising elasticity of demand:
EA = ∂QB x AB
∂ AB QB
= 0.6 x (12500/11002.5)
EA = 0.68
h) How concerned should this company be about price discounts by its leading competitor?
It is not a concern because competitor’s product is a weak substitute (cross elasticity = 0.01)
i) Should this company consider discounting its price in order to increase total revenue?
No because demand is inelastic. The company should increase the price instead.
j) What type of good is Syarikat Bacfree’s water filters?
It is a normal because income elasticity is between 0 and 1.
k) Assuming the model and data given are relevant for the coming period, calculate the range within which you would expect to find actual sales with 95% confidence level.
Q ± 2 (SEE)
11002.5 ± 2 (5)
10992.5 < Q < 11012.5
l) If the firm’s objective is to maximize total revenue, what price should the firm charge?
To Max TR function:
∂TR = 2250.5 – 0.4Q = 0
∂Q 2250.5 – 0.4Q = 0
– 0.4Q = – 2250.5
Q = – 2250.5/– 0.4
Q = 5626.25 substitute into P function, P = 1125.25
QUESTION 2
Wonderful tiles, Inc. is rapidly growing chain of ceramic tile outlets that caters to the do-it-yourself home remodeling market. In 1992, 30 stores were operated in small to medium-size metropolitan markets. An in-house study of sales by these outlets revealed the following:
Q = 5 – 5P + 1.5A + 0.5Y + 0.2HF
(3) (1.8) (0.7) (0.2) (0.1)
(standard error of coefficients in parentheses)
R2 = 0.93
S.E.E = 6
F-calculated value = 93
F 4,25 α=0.05 = 2.76 (F-tabled value)
Here, Q is tile sales (in thousands of cases)
P is tile price (per case)
A is advertising expenditures (in thousands RM)
Y is disposable income per household (in thousands RM)
HF is household formation (in hundreds)
a) Using a 95% confidence interval, fully evaluate and interpret these empirical results on an overall basis (i.e. R2, F-test, t-test, coefficient, S.E.E).
i) R2 = 0.93. 93% of demand variation is explained by the regression model. The model has a very high explanatory power. (> than 50%)
ii) t-test:
| Variables | t-computed value | t-critical value | comment |
| P | 2.78 | > 2.00 | significant |
| A | 2.14 | > 2.00 | significant |
| Y | 2.50 | > 2.00 | significant |
| HF | 2.00 | > 2.00 | significant |
All independent variables are statistically significant.
iii) F-test
Calculated F-value = 93
Tabled F4, 28, µ = 0.05 = 2.76
F calculated value > F tabled value. Thus, the independent variables as a group explain a significant share of demand variation.
If you are not given the f-tabled value (f-critical value), use this simple rule. If there are 4 – 5 independent variables, the critical F-value is 3. Since F-calculated value, 93 is greater than 3, therefore, the independent variables as a group explain a significant share of demand variation.
iv) Coefficient:
When P changes by RM1, Q changes by 5 thousands case
When A changes by RM1000, Q changes by 1,500 cases
When I changes by RM1000, Q changes by 500 cases
When HF changes by 100, Q changes by 200 cases.
v) SEE (Standart Error of Estimate):
Q ± 2(6)
Q ± 12
b) Selangor was a typical market covered by this analysis. During 1992, in the Selangor market, price was RM5, advertising was RM40,000, income was an average RM20,000 per household per year, and the number of household formation was 5,000.
i) Determine the demand curve function for Wonderful Tiles, Inc.
Q = 5 – 5P + 1.5A + 0.5Y + 0.2HF
Q = 85 – 5P
ii) Should the company increase or reduce price of its product to increase total revenue?
Price elasticity of demand:
Ep = ∂Q x P
∂P Q
= -5 x (5/60)
Ep = -0.42
Interpretat:
Since demand is inelastic, the company should increase price to increase total revenue.
iii) Calculate and interpret the relevant advertising point elasticity.
Advertising elasticity of demand:
EA= ∂Q x P
∂P Q
= 1.5 x (40/60)
EA = 1
Impact:
A 1% increase in advertising budget will cause a 1% increase in quantity demanded.
c) Assume that the preceding model and data are relevant for the coming period, find interval estimation using 95% level of confidence.
Q ± 2(6)
60 ± 12
48 < Q < 72 {Note: Interval or range of Q at 95% confidence
interval}
Tiada ulasan:
Catat Ulasan