1. (30 points) Consider a market where two firms compete in the Cournot manner. Each firm has a total cost and they face a joint demand curve of P = 10- - (Q1 + Q2)/2. (a) Find T, as a function of Q and Q2 (b) Find optimal Q as a function of Q2 (c) Find Equilibrium Q1,Q2,71, and #2 2. (40 points) Consider a boss who cannot observe the effort of their employee (denoted r). They only observe whether the project is a success or a failure. A successful project produces a value of 2 for the boss. The boss picks a wage for success and a wage for failure then the employee picks their effort level in response. Neither wage can be less than 0. The employee pays a cost of effort 2. (a) Find the utility function for each player (b) Find r as a function of Ws and Wf (c) Find equilibrium ws, wf, and r (d) What is the total equilibrium utility? (e) What would the efficient effort level be in terms of maximizing total utility? 3. (15 points) Consider an entry game. First the entrant decides whether to enter. Then the incumbant decides whether to undercut. Then the entrant decides whether to undercut in turn. If there is only one firm in the market they get 10. If both firms are in the market with no undercutting they get 5. If one firm undercuts they get 7 and the other firm gets 1. If both firms undercut they both get 2. Draw the extensive form of the game and find the subgame perfect equilibrium. 4. There is an asset available in period 1. In period 2 it can take on values $0,$1,$3, or $4 with equal probability. An option allows the holder to buy the asset in period 2 for $2. What is the value of the option.