Question

Your company has been granted an exclusive license to sell ice cream. No one has ever...

Your company has been granted an exclusive license to sell ice cream. No one has ever sold ice cream here before, so you have no idea what the demand will look like. You suspect that people like to buy more ice cream on hotter days, but you are very unsure about what price you should charge to maximize your profit.

Over your first season selling ice cream, you vary your price each week for the 10 weeks your license allows you to operate. You collect data including price you charged that week (giving you 7 data points at each price), the high temperature for that day, and the average number of cones sold per hour each day.

You have paid a fixed fee of \$10,000 to the state which covers materials (both the costs of the cones and the fixed costs associated with the food truck) to supply the ice cream cones that doesn’t vary depending on how many units are sold. A single employee, making \$15/hour can handle up to 40 cones per hour, while a second employee would bring your maximum production up to 100 cones per hour.

Use the data below perform a multiple regression analysis, with Sales per Hour as your dependent variable and ‘Price’ and ‘Avg Temp’ as independent variables.

Your employee from the first season reports the following: “When we charged the higher prices last year, we had some people complaining. I don’t think we should charge any more than \$2.75 for a cone.”

Calculate the price elasticity of demand if you charge \$2.75 (still assuming an average temperature of 80 degrees). Based on this analysis, do you agree with your employee?

Ice cream sales data

Day        Sales per hour Price     Avg Temp

1             30.65    0.75      77

2             30.55    0.75      92

3             25.89    0.75      74

4             31.84    0.75      91

5             24.09    0.75      67

6             27.81    0.75      92

7             25.27    0.75      73

8             28.21    1.50      92

9             28.15    1.50      89

10           23.07    1.50      79

11           31.15    1.50      93

12           19.76    1.50      70

13           26.00    1.50      75

14           29.37    1.50      91

15           28.47    1.25      95

16           23.82    1.25      71

17           24.11    1.25      76

18           29.19    1.25      90

19           28.73    1.25      91

20           24.20    1.25      91

21           24.91    1.25      77

22           21.76    2.00      87

23           21.15    2.00      71

24           20.31    2.00      73

25           16.54    2.00      67

26           20.18    2.00      69

27           23.53    2.00      93

28           21.01    2.00      77

29           26.85    1.00      79

30           27.12    1.00      81

31           28.93    1.00      74

32           22.91    1.00      65

33           27.33    1.00      81

34           24.27    1.00      80

35           26.63    1.00      81

36           17.93    2.25      69

37           20.65    2.25      90

38           15.97    2.25      74

39           23.55    2.25      92

40           20.25    2.25      67

41           19.13    2.25      73

42           19.72    2.25      90

43           30.66    0.50      82

44           28.68    0.50      92

45           24.97    0.50      71

46           34.21    0.50      94

47           25.64    0.50      71

48           31.66    0.50      93

49           26.87    0.50      72

50           18.42    1.75      69

51           25.74    1.75      79

52           20.36    1.75      72

53           22.15    1.75      70

54           28.66    1.75      85

55           26.42    1.75      94

56           24.34    1.75      74

57           21.93    1.35      73

58           23.51    1.35      67

59           26.99    1.35      82

60           32.10    1.35      86

61           25.21    1.35      84

62           27.59    1.35      93

63           19.63    1.35      69

64           23.63    1.65      81

65           20.76    1.65      66

66           24.57    1.65      79

67           29.27    1.65      91

68           24.32    1.65      68

69           19.85    1.65      66

70           25.29    1.65      91

 Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. 95.0% Confidence Interval for B B Std. Error Beta Lower Bound Upper Bound 1 (Constant) 12.348 2.277 5.423 .000 7.804 16.893 Price -4.687 .475 -.602 -9.859 .000 -5.635 -3.738 TEMP .239 .026 .560 9.164 .000 .187 .292 a. Dependent Variable: SalesHour

A general equation : Y= a+ b1X1 + b2X2 ... bnXn

For this

dependent variable(Y) = Sales/hour (S)

Independent Variables - Price (P) , Temperature (T)

From the regression analysis the equation will be as follows :

S = 12.348 + (-4.687)P + (0.239)T

The negative sign for the co-efficient of P signifies an inverse relationship between sales and price. So if price increase the sales will fall and vice-versa.

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