You are doing an industry analysis of the Bloomington pizza industry.The rate (per year) at which pizza restaurants enter the industry is given by p, where p = price of a pizza in dollars. The price of a pizza is assumed to be max(0, 16 - .5F), where F = number of pizza restaurants in Bloomington. During a given year, the probability that a pizza restaurant fails is 1/(10 + p). Create a birth–death model of this situation.
a. In the steady state, estimate the average number of pizza restaurants in Bloomington.
b. What fraction of the time will there be more than 20 pizza restaurants in Bloomington?