Question

Question 4 Newly issued stock is being purchased over time by members of a population of 1000 people. Each person acquires at most one and then simply holds it (no resale). In each period 5 percent (.05) of the people who do not yet own a share buy one share ("leaders”). Also in each period some number of followers" who have learned about the stock from contact with the leaders also buy a share. The number of followers who purchase is 0.05 percent (.0005) times the number of "contacts” between all past purchasers and all the remaining people who have not yet purchased. (a) How many leaders are there in period 1? How many leaders in period 2? (b) Given your answer to (a), how many followers end up buying a share in the second period? (c) Given your answers to (a) and (b), how many additional leaders buy in period 3? And then how many additional followers are prompted to buy as a result? (d) Do these calculations for two more periods, and then answer this question: Does it appear that eventually all 1000 people will make a purchase? Why or why not?

Answer 1

Solution:

solution : Given that The total number of shares can be issued will be = 1000. Be cause one can buy max one shares. in one peorfod ch of leaders Nill be 5% of total population which is 50 In 2nd period no. of leaders will be . 950 * 0.5 = 47.5 Total no.of porchasers will be = 97 No. of Contot acts as a no. of dea deos : 47.5. ③ No. of followe as end up baying share in peañod a will be : 47 * 0.0005 = 0.023 so, to tal no. of purchases will be = 47.523

© In peouod 3 Madeas will be In peañod 3 nor of = (1000 - 97.523) *0.05 - 45 123 No. of contacts will be = 45.123. eno. of additional followe as coho will buy will be = 45.123 * 0.0005 = 0.0225 becomes. Total no. of purchasean = 172.1467 0.0225 = 242.168. @ in period 4 no. of leadeas will be : 1000-142.168 * 0.05 = 42.86. Followers purchasors - 142.168+0.0214+ 42.86 5185:049. total no. of peoples are not going to make purchase following these telle because decimal in the calculation reporesents after Certain points some people will be left off to purchase if one strictly following the rate

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