Question

City	Q	P	I	A	Psub	Pop
1	32.92	1.89	32.4	4.38	2.08	98.7
2	28.51	1.94	29.9	4.12	2.06	104.5
3	33.94	1.99	29.1	5.06	2.15	105.1
4	33.45	2.04	28.6	5.36	2.18	106.9
5	35.68	2.09	30.2	5.38	2.18	108.9
6	29.01	1.89	31.4	3.47	1.99	115.2
7	30.68	1.94	30.3	4.06	2.05	117.8
8	43.14	1.99	30.4	5.29	2.17	120.2
9	20.84	2.04	28.6	3.39	1.98	120.8
10	31.27	2.09	26.3	5.12	2.16	122.7
11	35.45	1.89	26.5	4.44	2.09	122.9
12	32.14	1.94	29.5	4.18	2.06	124.6
13	43.02	1.99	29.1	5.57	2.2	125.8
14	34.73	2.04	31.2	3.57	2	131.9
15	43.14	2.09	23.8	6.43	2.39	133.1
16	33.17	1.89	28.8	3.95	2.04	135.6
17	41.59	1.94	29.3	4.04	2.05	136.5
18	32.1	1.99	27.4	4.36	2.08	141.8
19	45.74	2.04	27.8	5.81	2.23	144.8
20	35.92	2.09	30.2	4.63	2.11	150.1

I have collected real data on the sale of a microwavable cup of soup across 20 different cities for the same time period (a month). The variables in the dataset are:

Quantity sold in the city for that month: Measured in thousands of units

Price: measured in dollars

Average Income in the city: Measured in thousands of dollars

Ads: Average number of ads run in stores for that city during that month.

Price of a substitute product: measured in dollars

Population of the city: measured in thousands of people

The dataset is on Canvas and, using Excel or any other statistical software, please answer the following questions:

1. Describe the patterns in quantity sold and own and rival prices during this time period using basic descriptive statistics. Graphs are welcome as well.
2. Take the logs of the variables, and estimate the demand function.
   1. Interpret the R-square.
   2. Interpret the coefficients for logP and logPsub
   3. Interpret the p-values associated with each independent variable
3. Are consumers price sensitive? Why or why not? (be as precise as you can – you have estimates!). Does this price sensitivity make sense given the good we are examining?
4. How sensitive are our consumers to changes in the rival good’s price? Explain in detail.
5. Suppose we decide to charge a per ounce price of .07, while at the same time our rival charges a price of .05. All else equal, what would you expect sales to be? How confident are you in your forecast? Explain.
6. Suppose we are charging a price of .065 per ounce and our current marginal cost per ounce is .05. Are we maximizing profits at this price? If not, should we raise or lower price? Why?

Answer 1

The descriptive statistics and the plot of price and substitute's price versus sales is shown below.