NTNU (N) has just won the award for greatest international potential in the NM for student companies. Their product is very innovative, and N is in the process of obtaining a Norwegian and global patent. At the same time and by chance, the student company Babson (B) in the USA has invented a (almost) identical product, based on a different technology; also B is applying for a global patent. There are no other competitors / competitive products in the market, the products can be considered as perfect substitutes. Both companies will soon be ready to start production and distribution of the two (almost) identical products. World demand for the product is expected to be large and well diversified across many countries and industries. Both companies expect that demand per month is given by:

P = 1,000 - 5Q,

where P = price per product unit, Q = total turnover per month in the global market. N's cost function is given by CN = 2000 + 40QA, B's by CB = 500 + 80QB.

a) Unexpected delays in the construction of B's factory suddenly give N the opportunity to launch its product in the market before B can do so.

How much should the two student companies produce in the first month, and what will be the resulting price for the product? Choose the model that you think best suits the situation and show your calculations.

b) One year later, both companies and products are well established, with global patents in place. The cost functions are unchanged; N and B decide on their production volumes for the next month at the same time (all customers buy electronically once a month, the corresponding market price exists on the same day, and both players know each other and the market well). The managements of the two companies will decide on quantities QN and QB for the next month, provided that they take the other company's profit-maximizing production for granted.

How much should the two student companies produce for next month, and how big will each of the companies' monthly profits be? Also show the dependencies of the decisions mathematically with corresponding equations. Choose the model that you think best suits the situation and show your calculations.

Also show the dependencies of the decisions mathematically with corresponding equations. Choose the model that you think best suits the situation and show your calculations.