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...

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?