1) John and Irina compete in the production of herbal Schnaps. The products we produce are identical, so the demand is simply P = 30-QV-QJ. The J and I indicate John's and Irina's output in liters. First both of them have to decide simultaneously and independently whether to invest in a new technology. For each of them the cost of production is Q2k /2 if they don't invest in the new technology and 20+ Q2k /6 if they invest where k stands for J and I. Once their investment decisions are revealed, they both have to make ther production decision (again simultaneous). Thus it is a two stage game with simultaneous play in both stages (and some extra practice for Cournot equilibria)

a) Write out the profit functions for both of them IF THEY BOTH INVEST. Find the equilibrium quantities and profits

b) Write out the profit functions for both of them IF ONLY VOLKER INVESTS. Find the equilibrium quantities and profits

c) Write out the profit functions for both of them IF ONLY JAN INVESTS. Find the equilibrium quantities and profits

d) Write out the profit functions for both of them IF NEITHER OF THEM INVESTS. Find the equilibrium quantities and profits

e) Use the profits of a) to d) to develop the first stage game (the investment decision). Show the payoff table. Do John and/or Irina have a dominant strategy? Is there a Nash Equilibrium and if so, what is it?