Herrings

This particular fishery is described by a biological growth function of the following form:

Spawn = NatGrow*StartPop*(CarryCap-StartPop)/CarryCap + Shock

where Spawn is the number of new fish, StartPop is the population at the beginning of the period, and NatGrow and CarryCap are parameters representing fish biology. Shock is an annual disturbance drawn from a normal distribution with mean zero and unknown variance. The population at the end of the period will be given by:

EndPop = StartPop + Spawn - Harvest

where Harvest is the number of fish harvested by people (more on that below). This will become the starting population for the next period. (Just to make sure there aren't any ambiguities please note that Spawn, Harvest, EndPop and StartPop may vary with time while NatGrow and CarryCap do not.)

In order to solve the problem you'll need to determine the numerical values of NatGrow and CarryCap. To do this, you will have to go through a few turns collecting data and then run an appropriate regression. The game will be most interesting if you try to imagine you're doing this for real and that collecting data is expensive. Suppose that each turn takes a year in reality. In that case, you wouldn't be able to afford to collect 100 data points before trying to solve the problem -- that would mean doing nothing but data collection for 100 years. Instead, you'd have to collect a few data points and then begin moving toward the optimum. As you did so, of course, you'd collect more information that would allow you to refine your estimates. Watch what happens to the precision of your estimates as you add more data. This situation is typical of real economic problems: with the possible exception of financial markets, there's never as much data as one would like.

The harvest of fish is given by a function of the form:

Harvest = Tech*StartPop*(Effort/100)

where Harvest is the number of fish caught, Tech is a parameter (initially unknown), and Effort is the level of effort. (The factor of 100 appears here for computer convenience rather than economics: it allows a slider on the game to read from 0 to 100 instead of from 0 to 1.) Finally, the fishery is a price-taker in both the fish and labor markets. Its total revenue and total cost are given by:

Revenue = $1*Harvest
Cost = $2000*(Effort/100)

The goal of the game is to find the profit-maximizing level of effort AND to end up with a sustainable population--that is, one for which StartPop equals EndPop at the optimum level of effort.

Herrings