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The inverse demand for designer blankets is given by P = 40 - 0.01Q, where P is the price per blanket and Q is the total number of blankets brought to market. Two shops in the local market supply specialty blankets. Shop 1's cost function is given by C1 = 0.02q12, where q1 is the number it brings to market. Shop 2's cost function is given by C2 = 0.02q22, where q2 is the number it brings to market. Given that the two shops compete by setting output (Cournot):
a. write shop 1's profit function. Let Q = q1 + q2.
b. write shop 2's profit function.
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