Consider a Bertrand price competition market with differentiated products. Suppose demand for good 1 is Q1=a−bP1+dP2 and demand for good 2 is Q2=a−bP2+dP1. Firm 1 has costs of C1(Q1)=1/2 C1Q1^2 and Firm 2 has costs of C2(Q2)=1/2C2Q2^2
a.Do these demands suggest that Firm 1’s and Firm 2’s products are substitutes from consumers’ perspectives? Explain.
b.Assuming Firm 1 and Firm 2 compete in the prices they charge, derive the reaction functions for each firm in terms of the market parameters, a,b,d,and c.
c.Describe how you would solve for the Bertrand-Nash equilibrium. Show all of your steps, including:
i.Firm profit function
ii.Firm first-order conditions
iii.Firm best-response function
d. Use your results from part (b) to solve for the specific equilibrium when a=18,b=2,d=1,and c1=c2=0. What are the prices, outputs, and firm profits?
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