3. Law of one price: In class, we have discussed the law of one price (LOOP), which formalizes the very intuitive "no free lunch" idea that two portfolios that generate the same payoffs should have the same price in a well functioning market. We have also discussed the relation between this rule and the existence of a state price vector. Recall that a state-price vector, ERM, where M is the number of possible outcomes, is such that hs0 = hD for all hЄRN. The relation between the LOOP and the existence of a state price vector is one version of what is known as the fundamental theorem of asset pricing, and has two parts: Part 1: The LOOP holds if and only if there exists a state price vector. Part 2: In a market in which the LOOP holds, the state price vector is unique if and only if the market is complete. A mathematical way of stating that the LOOP holds is that for all h = RN: hD 0hsº = 0. (a) Use your knowledge from linear algebra to prove part 1 of the theorem. (b) Use your knowledge from linear algebra to prove part 2 of the theorem.