A market is supplied by three price-setting firms. Each produces one variety of the product. Inverse demand equations are:

p1=38-2(q1+(1/2)q2+(1/2)q3)

p2=38-2((1/2)q1+q2+(1/2)q3)

p3=38-2((1/2)q1+(1/2)q2+q3)

The corresponding demand equations

q1=(19/2)-(3/4)p1+(1/4)p2+(1/4)p3

q2=(19/2)+(1/4)p1-(3/4)p2+(1/4)p3

q3=(19/2)+(1/4)p1+(1/4)p2-(3/4)p3

 Average and marginal cost is constant, 2 per unit of output.

(a) Find Bertrand triopoly noncooperative equilibrium prices and profit per firm.

(b) Find Bertrand duopoly profits if firms 1 and 2 merge and the post-merger firm sets the prices of varieties 1 and 2 to maximize post-merger profit.

(c) Find noncooperative equilibrium prices and profits. Compare with the results from (a).

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