Let St+1 = St + .1(1 − St/10000)St describe the dynamics of a fish stock; the intrinsic growth rate of this stock is 0.1 and the carrying capacity in tons in 10,000.
(a) Graph the growth function of this fish stock, with the stock on the horizontal axis and growth on the vertical axis. Label your graph.
(b) What is the growth at St = 2000, St = 5000? and St = 7000?
(c) Suppose that in the commercial fishing industry the harvest per boat is ht = St/1000, the price per unit of harvest is p = $100, and the cost of entry is c = $50c. What are the profits per boat when St = 2000?
(d) Is the open access stock is smaller than or larger than S = 2000? Why?
(e) What happens to the open access stock when price (p) increases?