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Review Questions 1Yuya Takahashi7=26=20181. Consider an industry where there is only one °rm. Demand is given byQ= 10°p:Assume the °rm±scost function isc(Q) = 2Q:Find a competitive equilibrium.2. Consider a market of homogenous products with two active °rms (the number of °rms is °xed). Demandis given byQ(p) = 40°p:Two °rms are identical and the total cost function is given byTC(q) = 10q:(a) Find a competitive equilibrium (i.e., °ndp°andQ°).(b) Find a Cournot-Nash equilibrium (i.e., °ndpC; qC1;andqC2).(c) Find an equilibrium for a sequential game where °rm 1 moves °rst and °rm 2 moves second. (i.e.,°ndpS; qS1;andqS2).(d) Find a Bertrand-Nash equilibrium (i.e., °ndpB; qB1;andqB2).(e) Compare four di/erent equilibria. Order the price levels and explain why you obtain that result.3. Consider a market with demand given byQ(p) = 100°p:The total cost function is given byTC(q) =50 + 2q2+ 5q:Firms are identical. Letndenote the number of °rms. Note thatPni=1qi=Q:(a) Derive the average cost function,AC(q)and marginal cost function,MC(q).(b) Assume there are now 25 °rms.Consider the short run such that the number of °rms is °xed.Find a competitive equilibrium (i.e., °ndp°; q°; Q°). Are °rms making a positive, zero, or negativepro°t?(c) Find a competitive equilibrium in the long run (i.e., °ndp°; q°; Q°; n°). Hint: °rms enter and exituntil each °rm earns zero pro°t.4. Consider a market with inverse demand functionp= 14°Q. Firms have constant marginal cost 2 and°xed cost 2. Firms compete by simultaneously choosing quantities.(a) Suppose there aren°rms in this market. Derive the Nash equilibrium prices, quantities and pro°ts.