Consider 3 assets. Asset 1 is a risk-free bond which has normalized price of unity at time t=0. Assume the risk-free rate of interest is 5% per year. The price of Asset 2 is $50 at time t=0. In addition, it is estimated that, if the economy is in an upturn, the price of Asset 2 would be $55, while it would be $45 if the economy is in a "downturn". The price of Asset 3 is unknown at time t=0 and it is $3 if the economy is in an upturn", while it is $2 if the economy is in a "downturn". Use the non-arbitrage theorem to derive the equations that the price of Asset 3 at time t=0 has to satisfy in order to be an arbitrage-free price. (Note: you do not have to solve the equations.)