The inverse demand for tacos is given by P = 10 - 0.02Q, where P is the price per taco and Q is the total number of tacos brought to market. There are two taco shops in the local market. Shop 1's cost function is given by C1 = 0.01q12, where q1 is the number of tacos it brings to market. Shop 2's cost function is given by C2 = 0.01q22, where q2 is the number of tacos it brings to market. Given that the two shops compete by setting output (Cournot), answer the following. Let Q = q1 + q2.
a. What is shop 1's profit function?
b. What is shop 2's profit function?
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