Don makes a one time investment. He purchases a 30 year bond with semiannual coupons and face value $800, and with a semiannual coupon rate r^(2) and a semiannual yield rate i^(2) = 6%. Immediately after receiving his coupons, he deposits his coupons into an account earning a nominal semiannual interest rate of i^(2) = 3%. At the end of the 30 years, the accumulated value of these deposits + his face value $2, 300. Find r^(2). Also, find the bond price.

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Question 1 [5 pt.] MORAL HAZARD. Consider a principal agent model with unobservable actions and the following specifications: two actions, E = {e₁,e₂} - cost of actions: g(e₁) = 5/3, g(e₂) = 1 -v(w) = √w, u = 0 - TH = 10, TL = 1 - f(THе₁) = 2/3, f(TH|e₂) = 1/2 (a) [3pt.] Describe the participation constraint and the incentive constraint when the prin- cipal wishes to implement e₁. Derive wages that can implement e₁. (b) [2pt.] Represent geometrically the wage pairs (WL, WH) which satisfy the constraints. In the same figure, represent the firm's cost minimization problem. Question 1 [5 pt.] MORAL HAZARD. Consider a principal agent model with unobservable actions and the following specifications: two actions, E = {e₁,e₂} - cost of actions: g(e₁) = 5/3, g(e₂) = 1 -v(w) = √w, u = 0 - TH = 10, TL = 1 - f(THе₁) = 2/3, f(TH|e₂) = 1/2 (a) [3pt.] Describe the participation constraint and the incentive constraint when the prin- cipal wishes to implement e₁. Derive wages that can implement e₁. (b) [2pt.] Represent geometrically the wage pairs (WL, WH) which satisfy the constraints. In the same figure, represent the firm's cost minimization problem.

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