04 Jun Suppose currently PX = $100, PY = $50, and M = $2,000.
Question
ECON 661, Managerial Economics
Homework Assignment 3
Answer all questions and show all your work. Note: You are required to apply the relevant methods learned in this course when answering the questions.
1. Suppose the estimated demand equation of good X looks as follows: (4 pts each)
QX = 10,000 – 2 PX + 3 PY – 4.5M
Where Px is the price of the product itself
PY is the price of another (related) good
M is buyers’ income.
Suppose currently PX = $100, PY = $50, and M = $2,000.
a. What is the price elasticity of demand of good X?
b. What is the cross-price elasticity of good X with respect to the price of good Y?
c. what is the income elasticity of good X?
d. Estimate the demand function (representing the demand curve) of this product.
e. Suppose the local government decides to raise the sales tax on product X, causing the price to rise by 10%. Will sales of the product X rise or fall, and by what percentage amount?
f. If the seller of the product (X) wants to increase her sales quantity by 10% through a price- change, what should she do to price – increase? decrease? By what percentage amount?
2. A manufactures of a well-known brand of toothpaste is considering changing the way he prices his tooth paste. Currently, he is selling it at $5.00 per bottle. He hired a college professor of economics to estimate the demand function for the product. The demand function estimated by the professor is given below: (10 pts)
Qd = 3 – 0.25P
Where P represents the price per bottle.
Is the manufacturer maximizing his sales revenue by charging $5.00 for each bottle? If your answer is no, how much should he charge in order to maximize his sales revenue?
3. For 2006–2011, a company has collected the following data on quarterly sales of its product.
Year
Quarter
t
Sales
(000)
2005
q1
1
2270
q2
2
1800
q3
3
2000
q4
4
2050
2006
q1
5
2440
q2
6
1900
q3
7
1700
q4
8
2200
2007
q1
9
2410
q2
10
2050
q3
11
2100
q4
12
2600
2008
q1
13
2630
q2
14
2100
q3
15
2305
q4
16
2300
2009
q1
17
2309
q2
18
2150
q3
19
2380
q4
20
2632
2010
q1
21
2700
q2
22
2410
q3
23
2560
q4
24
2600
2011
q1
25
2900
q2
26
2500
q3
27
2450
q4
28
2680
a. The manager would like to know if there is an upward trend in sales of the product. Use the data above to estimate the quarterly trend in sales using a linear trend model of the form:
Qt = a + bt.
Where Qt = quarterly sales
(paste your computer printout here)(5pts)
b. Does your statistical analysis indicate a trend? If so, is it an upward or downward trend and how great is it? Is it a statistically significant trend (use the 5 percent level of significance )? (10 pts)
c. Now adjust your statistical model to account for seasonal variation in sales. Estimate the following model of sales:
Qt=a+bt+c1D1+c2D2+c3D3
Where D1, D2 and D3 are respectively dummy variables for quarters I, II, and III (e.g., D1 is equal to 1 in the first quarter of each year and 0 in other quarters).
(paste your computer printout here)(10 pts)
d. Does the data indicate a statistically significant seasonal pattern (use the 5 percent level of significance)? If so, what is the seasonal pattern of sales of the product? (10 pts)
e. Comparing your estimates of the trend in sales in parts a and c, which estimate is likely to be more accurate? Why? (5 pts)
f. Using the estimated forecast equation from part c, forecast sales for quarter 1, 2, 3 and 4 of 2012; quarter 1, 2, 3, and 4 of quarter 13, and quarter 1 of 2014. What possible concerns do you have about these forecasts? (5 pts)
4. Paul’s Plumbing is a small owner operated business. Paul the owner and manager knows the fixed cost of the plant is $780 per day and includes rent for building, tools and equipment. Variable costs included: labor, energy and supplies costs. He collected data on output and total average variable cost over a ten day period.
Day Q AVC
1 10 $50.00
2 20 43.00
3 40 26.00
4 50 25.00
5 70 18.85
6 80 18.37
7 100 15.50
8 120 16.67
9 150 21.00
10 160 28.75
Where Q is total output per day.
a. Use the data to run the appropriate regression to estimate the parameters for the empirical
cost function:
(Paste your computer printout here) (5 pts)
Following the AVC function (given above), you should arrange your data as follows in order to appropriately estimate the AVC function.
AVC
Q
Q2
50.00
10.00
100.00
43.00
20.00
400.00
26.00
40.00
1600.00
25.00
50.00
2500.00
18.85
70.00
4900.00
18.37
80.00
6400.00
15.50
100.00
10000.00
16.67
120.00
14400.00
21.00
150.00
22500.00
28.75
160.00
25600.00
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