Find the profit-maximizing price and output for a monopolist producing a computer software package.
The game will be most interesting if you try to imagine you're doing this for real. This is exactly the sort of decision faced by many companies, and they are often playing for hundreds of millions of dollars. A classic example, and the inspiration for this problem, is Microsoft and new versions of Windows. If you were playing for stakes in the hundreds of millions of dollars, you would not be able to afford many mistakes. That means you'd have to get to the right answer a lot faster than trial and error. Believe it or not, this is precisely what economics is good for -- using the appropriate tools from microeconomics (you have to figure out which ones!) it's possible to get exactly the right answer in this game in three turns.
This particular monopolist faces a linear demand curve and has a quadratic total cost function. That is, the demand curve and total cost function have the forms:
Price = a - b*Sales
Cost = c*Output2
In order to solve the problem correctly, you'll need to determine the numerical values of a, b and c (this is exactly what real monopolists have to do).
If you produce more than people are willing to buy at the price you set, the excess will accumulate as inventories. If you produce less than people are willing to buy, the excess demand will be supplied from inventories, if you have any. Inventories play a very important role in this problem -- be sure to think carefully about exactly what you can learn from changes in inventories.
The goal of the game is to find the profit maximizing price and output, and to end up with zero inventories. If you succeed, a suitable message will appear. If you take more than a year or run up too many losses, however, you'll be fired by your CEO and the game will be over. (You can click the restart button to play again.)
Keep in mind that the real point of the game is to think about how to maximize profits, not just to find the right price and quantity. You will be graded on how you solved the problem, not just whether or not you got the right numbers.