Consider a perfectly competitive industry in a region with 8 firms.Assume the demand curve in the region is linear and given by P=10-Q^T where P is the price and Q^Tis the total supply in the region.Assume each firm has a marginal cost of 2q.Each firm produces an output level where price equals marginal cost, i.e., P=2q, and aggregate output is simply the sum of all the individual outputs, i.e., Q^T= 8q.

(a)Write it as a system of 3 linear equations in 3 unknowns.What are the unknowns?

(b)Write the linear system in matrix form and find the determinate of the A matrix.Will this system of equations have a unique solution?How can you tell?

(c)Use Cramer's Rule to find the equilibrium price, quantity per firm, and total quantity sold in the market.

Now suppose that a firm from outside the region "dumps" some output of this good into the region.Let _Q be the amount dumped by the outside firm.With this additional source of output, total output in the region becomes Q^T=8q+_Q .

(d)Use Cramer's Rule to solve for the equilibrium price, quantity per firm, and total quantity sold in the market given _Q .

(e)Find the effect of an increase in _Q on (i) equilibrium price, (ii) output per firm, (iii) total output produced by the firms in the region, and (iv) total output sold in the region (including the dumped output).

(f)Based on your answer to (e), do firms in the region reduce their output in response to the dumping?Does aggregate output (including the dumped goods) increase or decrease?Explain/illustrate your results using a simple supply-demand graph.