Using the Conjectural Variations model, answer the following:
(You must show the step-by-step derivation of all results to get full credit.)
Consider a linear demand curve with quantity intercept a and price intercept b (p = b - b/a q) and 2 firms, each producing a part of the total output (q = q1 + q2) with a marginal cost of c. Firm 1 makes a conjecture (guess) about what firm 2 will do in response to any move firm 1 makes, and decides its move accordingly: q1 = q1(q2).
a) Calculate the two firm's reaction functions with conjectural variations [q1(q2) and q2(q1)].
b) If we assume only that firms behave rationally, what would be the equilibrium set of conjectural variations (dq2/dq1 = dq1/dq2 =?). Is this a Nash Equilibrium? Explain.
c) What do the values of dq2/dq1 and dq1/dq2 found in (a) mean? Which specific model makes this assumption? If firms made this conjecture, what is the total market output?
d) What type of a market structure does this imply? Explain (show) clearly.