Options and spanning. Suppose that there is only one firm with state-contingent profit vector (Y1, Y2) with Y1  Y2 . The spanning requirement is clearly not satisfied by a market in the firm’s shares....

Options and spanning. Suppose that there is only one firm with state-contingent profit vector (Y1, Y2) with Y1  Y2 . The spanning requirement is clearly not satisfied by a market in the firm’s shares. Suppose that a market in call options on the firm’s shares is introduced. The option entitles its holder to purchase one of the N shares in the firm at a fixed specified price once the state of the world is revealed and the firm declares its dividend Ys. If the specified price p0 satisfies Y1 /N  p0 Y2 /N holders of an option to buy 1 share will exercise it if and only if the firm declares a dividend of Y1. (a) Show that the original market in the firm’s shares plus the derivative market in options together satisfy the spanning requirement. (b) Under what circumstances will markets in shares and options satisfy the spanning requirement?