Let demand for bonds: b and supply is s, in equilibrium, b=s

There are two dates, 1 and 2. There is a market for nominal bonds at date 1 . One unit of bonds pays one dollar without any risk; its date- 1 price is denoted by p (i.e., one unit of bonds is sold for p dollars). The supply of bonds is fixed at 100 (independent of the price p ). In the demand side, there is a unique buyer of bonds. The buyer owns 10 units of goods at date 1. At date 2 the buyer needs to pay a tax to the government at the rate 5% for the interest he earns from his investment on bonds. 1 Independent of his date-2 tax payment and his date-1 investment, at date 2 the buyer faces two states that occur with equal probability: he receives 1 dollar from the government at state 1 and 3 dollars at state 2 . If the buyer consumes c1 at date 1 and 1 If he invests x dollars to buy bonds at date 1 and receives y dollars at date 2 as payments of bonds, then he earns interest yx dollars and his tax burden is 0.1(yx) dollars. 1 c2 at date 2 , his utility U(c1,c2)=lnc1+lnc2. The price of goods at date 1 , denoted P1, is equal to 10 (i.e., one unit of goods is sold for 10 dollars); the price of goods at date 2 , denoted P2, is equal to 10 , too. Derive the equilibrium price p