Consider production process that requires an upstream firm A to make an input, transfer to a downstream firm B, who then sells to the final consumer. One unit of input from A is required for one unit of final output. The marginal cost of production for firm A is 40 per unit. B has zero marginal costs. There are zero fixed costs. The final demand curve for end consumers is P = 200 - q.

1. What is the proft-maximising level of output, the related price and profit, if A and B work together to maximise joint profit.

2. Now assume that each firm acts to maximise its own profit. Firm A sets a price per unit of input to firm B and, likewise, firm B cares a single price to all final consumers (that is, two-part tariffs are not allowed). What is the outcome in this case (prices charged to firm B and final consumers, quantity and profits)? Explain your answer with the help of a diagram.

3. What if the two firms can use a two part tariff and firm B has all of the bargaining power? What is the outcome now?

4. Now assume that the two firms can merge and if they do, the production costs to both units fall to zero (MC = 0 for both A and B). Now assume that the new merged firm is set up so that both A and B are now separate profit centres. Which outcome is better in terms of profit - the merged firm or the outcome outlined in part c?