Assume that an upstream firm, denoted by U, produces an input at zero cost.
A downstream firm transforms the input into a homogeneous final good on a one-for-one basis at zero marginal cost. Assume, in a first, period, firm U sets the price for the input (w). In a second period, the downstream firm decides how much to produce (Q). Market demand is given by P=1-Q.
What would total profits be if the upstream and downstream firms maximized joint profits?
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