ECON 151 Lecture Notes - Lecture 3: Profit Maximization, Marginal Product, Externality
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Mulberry Realty sells homes in the northeast section of the United States. A frequently asked question by prospective buyers is: If we buy this house, how much can we expect to pay to heat it during the winter? The research division of Mulberry is asked to develop some guidelines for heating costs (Cost) (measured in $) for single family homes. The division decides three variables are related to heating costs: (1) the mean daily outside temperature (Temp) (in degrees Fahrenheit); (2) the number of inches of attic insulation (Insulation); and (3) the age of the furnace in the house (Age) (measured in years). The division collected data during the month of January for a sample of homes. Parentheses contain the variable names (in bold) as listed in the data set.
The data set for this scenario is included in an Excel file.
a. Is the information used in this analysis, cross-sectional data or time series data? (4 pts)
b. State your a priori hypothesis about the sign of the slope for each independent variable. (3 pts each)
c. Write out the estimated regression equation using variable specific names? (5 pts)
d. Interpret the slope coefficient for the variable with the largest slope coefficient. (5 pts)
e. For the slope coefficient with the smallest value (in absolute value), test to see if it has the directional relationship hypothesized in part (b). Alpha = 0.05. (15 pts)
Data Set:
| Cost ($) | Temp (deg) | Insulation (ins.) | Age (yrs) |
| 250 | 35 | 3 | 6 |
| 360 | 29 | 4 | 10 |
| 165 | 36 | 7 | 3 |
| 43 | 60 | 6 | 9 |
| 92 | 65 | 5 | 6 |
| 200 | 30 | 5 | 5 |
| 355 | 10 | 6 | 7 |
| 290 | 7 | 10 | 10 |
| 230 | 21 | 9 | 11 |
| 120 | 55 | 2 | 5 |
| 73 | 54 | 12 | 4 |
| 205 | 48 | 5 | 1 |
| 400 | 20 | 5 | 15 |
| 320 | 39 | 4 | 7 |
| 72 | 60 | 8 | 6 |
| 272 | 20 | 5 | 8 |
| 94 | 58 | 7 | 3 |
| 190 | 40 | 8 | 11 |
| 235 | 27 | 9 | 8 |
| 139 | 30 | 7 | 5 |
Below is data on the weekly quantity demanded of pizza in a small town in South Georgia, prices, and average household incomes. Use the data to perform a linear regression analysis of price and income on quantity demanded. (20 points) a) How well does the regression fit the data?
b) What is the income elasticity of demand for pizza when the income (M) is $40 (thousand) and the price (P) is $30?
|
Quantity (Q) |
Price (P) |
Income (Y) in thousands |
|||
|
1 |
183 |
29.25 |
30.72 |
||
|
2 |
207 |
30.1 |
37.57 |
||
|
3 |
183 |
30.54 |
29.43 |
||
|
4 |
192 |
28.67 |
37.2 |
||
|
5 |
182 |
30.23 |
35.87 |
||
|
6 |
217 |
29.76 |
35.16 |
||
|
7 |
180 |
31.77 |
27.7 |
||
|
8 |
195 |
31.01 |
32.96 |
||
|
9 |
200 |
29.21 |
32.3 |
||
|
10 |
198 |
30.79 |
36.1 |
||
|
11 |
195 |
29.75 |
32.68 |
||
|
12 |
205 |
29.98 |
37.49 |
||
|
13 |
182 |
30.06 |
31.32 |
||
|
14 |
218 |
28.94 |
38.67 |
||
|
15 |
231 |
29.76 |
34.82 |
||
|
16 |
212 |
27.94 |
42.27 |
||
|
17 |
222 |
30.75 |
40.03 |
||
|
18 |
150 |
28.96 |
30.02 |
||
|
19 |
183 |
30.96 |
34.3 |
||
|
20 |
158 |
29.03 |
29.89 |
||
|
21 |
199 |
30.83 |
35.27 |
||
|
22 |
196 |
30.6 |
33.55 |
||
|
23 |
234 |
29.98 |
40.03 |
||
|
24 |
171 |
29.27 |
29.91 |
||
|
25 |
171 |
31.42 |
33.69 |
||
|
26 |
170 |
29.24 |
31.51 |
||
|
27 |
210 |
27.61 |
30.6 |
||
|
28 |
184 |
30.64 |
34.36 |
||
|
29 |
223 |
29.97 |
37.59 |
||
|
30 |
177 |
31.87 |
31.78 |
||
|
31 |
168 |
30.06 |
27.47 |
||
|
32 |
192 |
28.83 |
40.64 |
||
|
33 |
201 |
30.91 |
36.2 |
||
|
34 |
207 |
29.84 |
38.05 |
||
|
35 |
241 |
29.94 |
39.55 |
||
|
36 |
216 |
30.67 |
35.38 |
||
|
37 |
193 |
31.03 |
40.42 |
||
|
38 |
187 |
28.45 |
37.29 |
||
|
39 |
194 |
30.02 |
29.68 |
||
|
40 |
212 |
30.85 |
40.61 |
||
|
41 |
141 |
30.46 |
28.23 |
||
|
42 |
217 |
28.85 |
36.87 |
||
|
43 |
194 |
29.34 |
36.59 |
||
|
44 |
182 |
30.1 |
29.56 |
||
|
45 |
225 |
28.88 |
36.26 |
||
|
46 |
214 |
30.2 |
34.29 |
||
|
47 |
198 |
28.56 |
41.7 |
||
|
48 |
183 |
29.51 |
30.92 |
||
|
49 |
206 |
29.86 |
31.22 |
||
|
50 |
198 |
30.83 |
32.39 |
Using the data below, I need answers to the following questions:
a) Using the data in Table 1, specify a linear functional form for the demand for Combination 1 meals, and run a regression to estimate the demand for Combo 1meals.
b) Using statistical software (Excel), estimate the parameters of the empirical demand function specifiedin part a.Write your estimated industry demand equation.
c) Evaluate your regression results by examining signs of parameters, p-values, and the R2.
d) Discuss how the estimation of demand might beimproved.
e) If the owner plans to charge a price of 4.15 for a Combination 1 meal and spend $18,000 per week on advertising, how many Combination 1 meals do you predict will be sold each week?
f) If the owner spends $18,000 per week on advertising, write the equation for the inverse demand function. Then, calculate the demand price for 50,000 Combination meals.
Estimation and Analysis of Demand for Fast Food Meals
You work for PriceWatermanCoopers as a market analyst. PWC has been hired by the owner of two Burger King restaurants located in a suburban Atlanta market area to study the demand for its basic hamburger meal packageâreferred to as âCombination 1" on its menus. The two restaurants face competition in the Atlanta suburb from five other hamburger restaurants (three MacDonaldâs and two Wendyâs restaurants) and three other restaurants serving âdrive-throughâ fast food (a Taco Bell, a Kentucky Fried Chicken, and a small family-owned Chinese restaurant).
The owner of the two Burger King restaurants provides PWC with the data shown in Table 1. Q is the total number of Combination 1 meals sold at both locations during each week in 1998. P is the average price charged for a Combination 1 meal at the two locations. [Prices are identical at the two Burger King locations.] Every week the Burger King owner advertises special price offers at its two restaurants exclusively in daily newspaper advertisements. A is the dollar amount spent on newspaper ads for each week in 1998. The owner could not provide PWC with data on prices charged by other competing restaurants during 1998. For the one-year time period of the study, household income and population in the suburb did not change enough to warrant inclusion in the demand analysis.
TABLE 1: Weekly Sales Data for Combination 1 Meals (1998)
week Q P A week Q P A
| 1 | 51,345 | 2.78 | 4,280 | 27 | 78,953 | 2.27 | 21,225 |
| 2 | 50,337 | 2.35 | 3,875 | 28 | 52,875 | 3.78 | 7,580 |
| 3 | 86,732 | 3.22 | 12,360 | 29 | 81,263 | 3.95 | 4,175 |
| 4 | 118,117 | 1.85 | 19,250 | 30 | 67,260 | 3.52 | 4,365 |
| 5 | 48,024 | 2.65 | 6,450 | 31 | 83,323 | 3.45 | 12,250 |
| 6 | 97,375 | 2.95 | 8,750 | 32 | 68,322 | 3.92 | 11,850 |
| 7 | 75,751 | 2.86 | 9,600 | 33 | 71,925 | 4.05 | 14,360 |
| 8 | 78,797 | 3.35 | 9,600 | 34 | 29,372 | 4.01 | 9,540 |
| 9 | 59,856 | 3.45 | 9,600 | 35 | 21,710 | 3.68 | 7,250 |
| 10 | 23,696 | 3.25 | 6,250 | 36 | 37,833 | 3.62 | 4,280 |
| 11 | 61,385 | 3.21 | 4,780 | 37 | 41,154 | 3.57 | 13,800 |
| 12 | 63,750 | 3.02 | 6,770 | 38 | 50,925 | 3.65 | 15,300 |
| 13 | 60,996 | 3.16 | 6,325 | 39 | 57,657 | 3.89 | 5,250 |
| 14 | 84,276 | 2.95 | 9,655 | 40 | 52,036 | 3.86 | 7,650 |
| 15 | 54,222 | 2.65 | 10,450 | 41 | 58,677 | 3.95 | 6,650 |
| 16 | 58,131 | 3.24 | 9,750 | 42 | 73,902 | 3.91 | 9,850 |
| 17 | 55,398 | 3.55 | 11,500 | 43 | 55,327 | 3.88 | 8,350 |
| 18 | 69,943 | 3.75 | 8,975 | 44 | 16,262 | 4.12 | 10,250 |
| 19 | 79,785 | 3.85 | 8,975 | 45 | 38,348 | 3.94 | 16,450 |
| 20 | 38,892 | 3.76 | 6,755 | 46 | 29,810 | 4.15 | 13,200 |
| 21 | 43,240 | 3.65 | 5,500 | 47 | 69,613 | 4.12 | 14,600 |
| 22 | 52,078 | 3.58 | 4,365 | 48 | 45,822 | 4.16 | 13,250 |
| 23 | 11,321 | 3.78 | 9,525 | 49 | 43,207 | 4.00 | 18,450 |
| 24 | 73,113 | 3.75 | 18,600 | 50 | 81,998 | 3.93 | 16,500 |
| 25 | 79,988 | 3.22 | 14,450 | 51 | 46,756 | 3.89 | 6,500 |
| 26 | 98,311 | 3.42 | 15,500 | 52 | 34,592 | 3.83 | 5,650 |
