A school, Yellow Education (YE) has recently won the prize for "biggest international potential" in the domestic championship for student firms. Their product is very innovative, and YE is about to get domestic and global patents. At the same time, by chance, there is also a student firm Green (G) in another country that has invented an almost identical product, based on another technology. G is also seeking a global patent. There are no other competition/ competing products in the market, and the products can be considered to be perfect substitutes. Both firms are ready to start the production and distribution of almost identical products. The world's demand is assumed to be big and well-diversified over a lot of countries and industries. Both firms expect that the demand per month is given by: P = 1000 - 5Q, where P is the price per product unit, Q is the overall turnover per month in the global market.

YE's cost function is given by: C_YE = 2000 + 40Q_A, G's by: C_G = 500 + 80Q_B

a. Unexpected delays with the construction of G's factories gives YE suddenly the possibility to launch its product in the market before G can do it. How much should the student firms produce in the first month, and what does the resulting price for the product? Choose the model that you think best suits the situation and show your calculations.

b. One year late both firms and the products are well-established, with the global patents in place. The cost functions are unchanged: YE and G decide over their production volumes for the next month simultaneously (all of the customers buy electronically once per month, and the equivalent market price exists on the same day, and both actors know each other and the market well). The management in the two firms is going to decide the quantity in QYE and QG for the next month, on the condition that they take the other firms' profit-maximizing production for granted. How much should the two student firms produce for the next month, and how big is each of the firms' monthly profit? Show also the dependencies of the decisions mathematically with equivalent equations. Choose the model that you think suits the situation the best 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.