An industry is made up of an upstream sector (U) and a downstream sector (D). Sector U sells its output to sector D which resells it to consumers. The inverse consumer demand curve is given by p = 800 - 2 y. The variable y represents both the output of sector U and the output of sector D. The wholesale price paid by sector D to sector U per unit of output is given by the variable t. Sector U has a marginal cost of production of $ 7. Sector D has a marginal production cost of $ 3 (in addition to paying t per unit). The total profit for each sector is as follows:

D = (p - 3 - t) y

U = (t - 7) y

a) Suppose there is a firm in sector D and a (different) firm in sector U. Find the equilibrium values of t and p.

b) Suppose there is a merger (vertical integration), so that there is only one company that controls both upstream and downstream activities. Find the equilibrium values of t and p.

c) Suppose there is a company in sector D and a (different) company in sector U, but there are royalties (royalties) based on profits. That is, company U chooses the wholesale price (t) and also chooses a royalty (R) (an amount in dollars)) which will be paid by company D to company U. L firm D is free to choose p (or equivalently, y) in order to maximize its own profit. Find the equilibrium values of t, p and R.