Question: Addas (Brand A) and Pumba (brand B) are the leading brand names of fitness shoes. The direct demand functions facing each producer are given by

Addas (Brand A) and Pumba (brand B) are the leading brand names of fitness shoes. The direct demand functions facing each producer are given by q_a=180-2p_a+p_b and qb=120-2p_b+p_a. Not that the demand functions are not symmetric. Assume zero production cost (c_a=c_b=0). Solve for the nash-bertrand equilibrium prices (pa,pb). Then, compute the equilibrium output levels (qa,qb), the equilibrium profits and aggregate industry profit.

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