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?

Bertrand Price Competition Differentiated: Australian and Chilean Chardonnay C Setting Linear demand function for each wine Each wine has a different MC Only two competitors in the relevant market Demand and costs (discuss): verum Qverum = 63.42 - 3.98PVerum + 2.25P Alfasi MCVerum = $4.96/bottle AL/ASI QAlfasi = 49.52 - 5.48P Alfasi + 1.40P Verum CHARD CHHAY MC Alfasi = $3.96/bottle We can construct examples w 2 automobile firms, 2 online shopping firms, etc., and solveBertrand Price Competition Differentiated: Australian and Chilean Chardonnay . Cournot quantity model: we got quantity response-functions . Bertrand price model: we get price response-functions PVerum = 10.44 + 0.2826P Alfasi PAlfasi = 6.49 + 0.1277PVerum If one firm increases price, the other also increases it Solve above 2-equations in 2-unknowns to obtain the equilibrium prices for the two brands Vivek Ghosal. Regulation, Competition, Firm Behavior. Fall 2020.