Background

Your company has been granted an exclusive license to sell ice cream in Odiorne Point State Park, NH.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.That data is included in 'Elasticity exercise.xlsx' in this module.

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.

Instructions

Use the data in 'Elasticity exercise.xlsx' to perform a multiple regression analysis, with Sales per Hour as your dependent variable and 'Price' and 'Avg Temp' as independent variables.(See the video in this module for tips.) Use the results to answer the following questions.20 points each question.

Q1) You think that quantity demanded is a function of price and the weather, with higher temperatures shifting demand to the right.That would make the general form of the demand function is Q_d= f(P, T) where P is the price of ice cream cones and T is average temperature.Based on your regression analysis, write out your estimate of the specific form of the demand function for ice cream in Odiorne Point State Park.

Q2) Assume the average high temperature will be 70 next year.Use Excel to draw the demand curve. Be careful to put P on the vertical axis and Q on the horizontal axis.Please label thevertical intercept(above what price will 0 units be sold) and thehorizontal intercept(if P=0, how many units are 'sold').

Q3) 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 $3.00 for a cone."Calculate the price elasticity of demand if you charge $3.00 (still assuming an average temperature of 70 degrees).Based on this analysis, do you agree with your employee?

Q4)What price would maximize revenue if your estimate of demand is correct?Explain how your calculation relates to the concept of elasticity.

Q5) The State is considering raising the license fee.Assuming you can operate 7 days a week, 8 hours a day for the 10 week season, and labor is your only direct expense (the contract covers the costs of cones outside of labor).If your company wishes to enter the contract at any positive profit (any profit > $0), what is the maximum amount your company should be willing to pay?

Ice cream sales data
Day	Sales per hour	Price	Avg Temp
1	35.48231044	0.75	77
2	37.51390989	0.75	92
3	27.17147893	0.75	74
4	47.11264394	0.75	91
5	34.18324011	0.75	67
6	37.70236244	0.75	92
7	27.1739321	0.75	73
8	30.71232812	1.50	92
9	35.15889302	1.50	89
10	15.56099398	1.50	79
11	36.90965271	1.50	93
12	23.83763302	1.50	70
13	30.64738823	1.50	75
14	33.28797298	1.50	91
15	33.5143342	1.25	95
16	27.48251282	1.25	71
17	29.12145031	1.25	76
18	28.49203096	1.25	90
19	28.36338801	1.25	91
20	29.83442197	1.25	91
21	29.26281579	1.25	77
22	28.52834129	2.00	87
23	22.27569897	2.00	71
24	24.7841753	2.00	73
25	25.47952897	2.00	67
26	22.9915732	2.00	69
27	27.54980786	2.00	93
28	17.66385393	2.00	77
29	31.15956121	1.00	79
30	32.94684751	1.00	81
31	29.01196861	1.00	74
32	38.76114318	1.00	65
33	30.19883885	1.00	81
34	25.50967689	1.00	80
35	33.74756679	1.00	81
36	27.39747501	2.25	69
37	26.26791575	2.25	90
38	25.48903323	2.25	74
39	27.59115107	2.25	92
40	21.06925579	2.25	67
41	25.15206303	2.25	73
42	19.37086967	2.25	90
43	30.28304833	0.50	82
44	44.30487727	0.50	92
45	24.92568901	0.50	71
46	35.04766009	0.50	94
47	33.78114804	0.50	71
48	38.80032137	0.50	93
49	30.54274749	0.50	72
50	20.28263633	1.75	69
51	22.96570427	1.75	79
52	20.3302452	1.75	72
53	21.60395675	1.75	70
54	25.11430636	1.75	85
55	30.52999717	1.75	94
56	22.65649195	1.75	74
57	28.65130726	1.35	73
58	23.09405291	1.35	67
59	26.39602841	1.35	82
60	23.0192376	1.35	86
61	33.81767969	1.35	84
62	36.50744564	1.35	93
63	23.80027715	1.35	69
64	26.84482461	1.65	81
65	25.21751769	1.65	66
66	25.26372612	1.65	79
67	33.32423068	1.65	91
68	23.37374867	1.65	68
69	21.08156411	1.65	66
70	30.0944907	1.65	91