Question about Vertical Restraints and Externalities

Suppose that Dunkin' Donuts is the only upstream manufacturer of donuts in Utrecht and that there are two downstream competing retailers that buy at wholesale price w. Market demand for donuts in Utrecht is given by D(p) = 12 − p + e₁ + e₂, where e₁ and e₂ are effort levels that the retailers can put in to make the product look good and increase overall demand. Cost of effort for each retailer are given by ci = 4e_i²  for i ∈ {1, 2}. There is no marginal or fixed costs and the downstream retailers are competing on price only.

a) What will be market prices and effort levels under vertical separation? How does this show the problem of 'free-riding' under horizontal externalises?

b) What will be market prices and effort levels under full vertical integration?

c) What is the consumer and producer surplus in both cases?

d) Discuss what solutions Dunkin' Donuts may have to solve the free riding problem without vertically integrating.