Suppose that we have assets A, B and C delivering cash flows one year later. The cash flows will depend on the state of economy as follows:

(a) Suppose that we want to replicate the cash flows of asset C, using asset A and asset B. In other words, we want to construct a portfolio consisting of asset A and B such that the portfolio will have the same cash flows as asset C one year later in both boom and recession. How many asset A and B do we need in the portfolio?

(b) The current prices of asset A and B are given as in the table. What is the price of asset C if there is no arbitrage?

asset A asset B asset C Current price 9 16 ? Payoff in year 1 boom recession 10 10 15 20 30 20