Question

For questions 10-14 Market demand for widgets is Q = 100-p. Whether there is just one firm selling widgets or many firms selling widgets, the marginal cost and average cost is 10. 50 10 Assume there is one firm selling widgets. What is the equilibrium price (p) p.10 0.90 p=55. Q:45 and quantity sold (Q)? p=60, 0:40 p=650-35 2 Assume there are two firms selling widgets acting as Cournot duopolists (Firm 1 and Firm 2). What is the quantity sold for each firm? Firm 1 sells 22.5. Firm 2 sells 22.5 Firm 1 was 225. Firm sells 45 Firm 1 sells 30 Firm 2 sells 30 Firm 1 selis 45, Firm 2 sells 225 12 2 Assume there are two firms selling widgets acting as Stackelberg Firm 1 sells 45 Fim 2 sells 22.5 Firm 1 cells 30 Fim 2 sl 30 duopolists, with Firm 2 moving first and Firm 1 following. Further assume Firm 1 ses 225 Firm 2 cell 45 that Firm 2's marginal profit function at its maximum is Mr(a) 45-4/2, Tirm 1 sells 225, Firm 2 sells 225 where is the amount of widgets sold by Firm 2. What is the quantity sold for each firm?

Answer 1

100-P 0 P = = 100 - Q P = 100-a P = 100- 45 P = 55 MR = 100-20 MC = AC = 10 100 – 22 =10 100-10 = 20 go = 20 Q=45 P = 100-o Q = QL+Q2 Mis POI - 10Q, TTi = (100-2)21-1001 = 100 Q - R (Qi + 02) - 102, = 9oQ1-Q3 - 2102 or - go-281- Q2 204 put d = 0 201 go - 281-Q2 =o go-d2 = 20 di = 45 - 82 (1) Likewise, T2 = POZ - 2002 (100-Q) &z - 1002 = 100QZ - Q2 (81+0 2) - 10Q2 = 100Qz - Q2Q1-Q2-1002 = 9002 - Q2Q1 - Q3 2112 = 90 - Qi – 202 202 pur put oll2 o 882 90 - QI - 222 = 0 202 = 90 - or

Q2 = 45- Q1 (13) km 2 8 ) Q2 = 45-$14.5 – 22) Q2 = 45 - 45. + 2 302 15 = us =) Q2 = 4 x 4 [Q2=307 Q1 = 45-22 = 45-30 4 5-15 On 3 307 12) now firm 2 leaded and moves firm Girst. i. firma is is follower - Mi = PQI - 1081 1100 - Q) QL -10Q 10001 - Or Colt Q2) - 108 = 90 Q - Q? - QyQz. =

OTI 001 = go - 201 - 02 put o zo ja) 90 - 20, – Q2 = 0 90 - 82 = 20 ar= 45- Q2 [12 = P Q2 - 1002 z (10o-Q) Q2 - 1082 = 10002 - Q2 [Q2 +022 - 2002 = godz - O2 Or - 02 put di = 45-02 in profit fu of firm 2 T2 = goda-Q2 (45-02) - az 2 902 - 4582 + 03 - 23 = = 4522 - 3 45 22 - 912 = 45 - 202 2 d02 2 = put 45-02 allz 20 202 45-02 = 0

Q2 = 45] 01 = 45-45 45 2 Q = 22.5 h 132 curnot solution dl=30, Q2 = 30 : Q= oit Q2 = 30+30 o=60 P = 100-60 =yo 14) Stackelberg soution a = u5, Q2 = 22.5 Q = dit Q2 = 45+22.5 Q = 67.5 P = 100-a = 100 -67.5 - 32.5