Question

Assume data coming from a price skimming experiment, where the price of a particular product was reduced in an online platform over 17 consecutive days, in steps of $50 from an initial value of $1,000 to a final value of $200. The price was maintained constant during each day, and was changed at the beginning of the following day. The last column represents the total number of purchases observed during the corresponding day.

b) Plot the empirical revenue function, for p in the interval [200, 1000]. What is the optimal price? What are the optimal revenues?

Day	Price	#Purchases
1	1000	1
2	950	2
3	900	1
4	850	5
5	800	6
6	750	6
7	700	13
8	650	11
9	600	12
10	550	19
11	500	17
12	450	20
13	400	22
14	350	25
15	300	29
16	250	28
17	200	30
	Total	247

Answer 1

It shall be noted that data for 17 days has been provided in terms of price and number of purchases made.

Thus, the total revenue earned each day is given by multiplication of price and number of purchases made.

Thus, total revenue earned each of the 17 days is: Price * #Purchases

On plotting Price in primary Y-axis and Total Revenue in the secondary Y-axis with #Purchases along X-axis, the result is:

Thus, as observed, the total revenue is maximum at $ 10450

The optimal price is $550

Thus, optimal revenue is $10450