4. Spreadsheet simulation (more advanced): Suppose that stock growth is given by F(X) = aX – bX2, where (a = r, b = r/k). Note that steady-state harvest H = E[a/b – E/b]. If for simplicity we assume that P = 1 and total costs are given by TC = cE, then the open-access equilibrium occurs where TR = TC, implying that E[a/b – E/b]= cE, or E0 = a – bc. The group optimum equilibrium occurs where MR = MC. With P = 1, then MR = a/b – 2E/b. Thus the group-optimum equilibrium occurs where a/b – 2E/b =

c, or E* = a – bc

/2. Assuming that a = 1000, b = 1, p = $1, c = $100:

a. Solve for the “group-optimum” and “open-access” equilibrium values for E, X, and H.

b. Create a table that shows F(X) values for 50-unit increments of X (starting at X = 0 up to X = 1000). Plot the F(X) values from the table in a fully labeled diagram and show the “group optimum” and “open access” equilibrium values for X on the horizontal axis, and for H on the vertical axis.