Please do all parts and show work thankyou There are two ide

Please do all parts and show work, thankyou!

There are two identical firms playing in a Bertrand market. In a Bertrand market, firms produce identical products. The firm offering the lower price gets all the customers in the market, and the firm with the higher price receives zero customers. If the firms set the same price, they each get half the customers. Assume the demand curve is given by P-10 - Q, where Q is the total quantity of products sold in the market. 3a) Write the payoff function for a firm assuming the cost of producing one unit is $2 3b) Find the Nash equilibrium of this game (the price each firm sets). Explain your reasoning. Would a firm ever set p-S1? 3c) What is the total quantity sold in the Nash equilibrium outcome? 3d) How much profit does each firm make?

Solution

Answer :

3a) Profit of firm 1= (P-AC)Q1

Thus Profit of firm 1=(P1-2)(10-P1) given 2<P1<P2

payoff=0 if P1>P2

B) Nash equilibrium of a game is when both players/firms charges $2.

No firm would set price=$1 becauae if they set price=$1 then there will be loss of 9.

C)Q=10-P=10-2=8units

D)profit of each firm is zero