Suppose the inverse demand function is P = a −bQ, where a is the market price when Q=0 and b is the slope of the function. Suppose there are two firms, Firm 1 and Firm 2, where their cost functions are denoted by Ci(Qi) = ciQi for i ∈{1, 2}. a) Write the profit function for each firm with price as a function of Q1, Q2 b) Solve for M Ri for i ∈{1, 2}and solve for the Best Response Functions (where M Ri = M Ci) c) Solve for the Nash Equilibrium. Note that your answer will be in terms of (a, c1, c2, b)
Suppose the inverse
Q=0 and b is the slope of the function. Suppose there are two firms, Firm 1 and Firm 2, where their cost functions are denoted by Ci(Qi) = ciQi for i ∈{1, 2}.
a) Write the profit function for each firm with price as a function of Q1, Q2
b) Solve for M Ri for i ∈{1, 2}and solve for the Best Response Functions (where M Ri = M Ci)
c) Solve for the Nash Equilibrium. Note that your answer will be in terms of (a, c1, c2, b)
d) Solve for the price of the market, P using the inverse demand function and your answers
from part (c). Note that your answer will be in terms of (a, c1, c2, b)
e) Solve for the profit for each firm. Note that your answer will be in terms of (a, c1, c2, b)
f) If c1 = c2, what value of a will profit equal 0 for both firms?
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