3. Bertrand numerical

Consider the following demand and cost functions for two firms A and B.

[1] Q_A = 10,000 - 1.5P_A + 2.5P_B

[2] TC_A = 5,000 + 20Q_A

[3] Q_B = 15,000 - 2P_B + 1.0P_A

[4] TC_B = 5,000 + 25Q_B

Questions:

(a) Calculate: (a) equilibrium prices; (b) equilibrium quantities; (c) profits.

(b) Given the above functions, how would you introduce a new stricter manufacturing regulation - e.g., the firms need to clean up environmental pollutants? Write the relevant equations to show this. What would be the anticipated effects on prices, quantities, and profits? [If you change any of the above equations, you should be able to solve for the new equilibrium.