Assume that there are three firms, A,B and C, located next to each other. Every unit of output that firm A produces creates a benefit of $7 for B and a cost of $3 to firm C. A's cost function is given by C(x) = 2x^2 + 1, where x denotes firm A's output. This output is sold in a competitive market at a price of $16. Assume that the market price accurately reflects the marginal benefit to the rest of society (i.e. without firms B and C) of consuming each unit.

a) what total amount of output will firm A produce in a competitive market?

b) which output level would be efficient?

c) Suppose the government imposes a tax/subsidy t per unit of firm A's output. What tax/subsidy would implement the efficient allocation?

d) Suppose that firms A and C merge and then choose the output level that is best for them. What would the output be? Does the merger improve efficiency? what would now be the optimal tax/subsidy?