Download Problem set 1 | ECON 3620 - Industrial Organization and more Quizzes Economics in PDF only on Docsity! TERM 1 MR=P+(P/Q)Q DEFINITION 1 n=l(Q/P)(P/Q)l MR=P(P/Q)Q(P/P) = P+P (P/Q)(Q/P) MR=P(1+ (P/Q)(Q/P) = (P/Q)(Q/P)= -(1/n) MR=P{1-(1/n)} ()profit-max implies MR=MCMR>0 P {1-(1/n)>01>(1/n)(n>1) TERM 2 Inverse demand function and the marginal revenue function DEFINITION 2 a) Q(P)=100-2P MR=100=4Q b) Q(P)=50-(1/2)Q MR=50-Q c) Q(P)=60-3Q MR=60-6Q TERM 3 total fixed cost, total sunk cost,total avoidable fixed cost DEFINITION 3 12000 annual lease 20000 loan and purchase 1000 to get out of lease 2000 can sell purchase x2 total Fix cost= 12000+20000= 32000 sunk cost= 1000+(20000- 4000)1000+1600017000 avoidable cost= (12000- 1000)+400015000 TERM 4 Continue to operate? What if they cannot get out of the lease? DEFINITION 4 profit-max are 20000 and total VC are 5500. operate if Rev avoidable cost Rev VC + avoidable FC Rev 15000+5500 Rev 20500 20000 20500 so should shut down avoidable cost = 4000+5500= 9500 20000 9500 should operate TERM 5 Lerner Index (LI) DEFINITION 5 LI= {(P-MC)/P} MR=MCP+(P/Q)Q=MC P+P(P/Q)(Q/P)=MCP- (1/n)=MC P(1/n)=P-MC(1/n)=(P-MC)/P (1/n)=LI recall MR=P[1-(1/n)] use MC=MR MC=P[1-(1/n)] MC=P-(P/n) MC-P= (P/n) (P-MC)/P=(1/n) TERM 6 Q^D=(6000-50P)/9 part1of3 DEFINITION 6 a) derive the inverse demand function 9Q=6000- 50P=50P=6000-9Q P=120-(9/50)Q b) firm max profit by producing q=(P-10)/2 P=MCP=2q+10 q*=(P-10)/2 c)Derive market supply curve Q^s=nq^s=50q^s Q^s=(50/2)(P-10) Q^s=25P250 TERM 7 Q^D=(6000-50P)/9 part2of3 DEFINITION 7 d) market-clearing price and aggregate quantity trading set Q^s=Q^d 25P-250=(6000-50P)/9 225P-2250=6000-50P 275P-2250=6000 275P=8250 P=30 Q^s(P)=25(30)-250 Q^s=500 TERM 8 Q^D=(6000-50P)/9 part3of3 DEFINITION 8 e) how much of each firm produce? confirm that each firm earns zero profit in equilibrium q^s=Q^s/50 q^s=500/50 =10 q^s=10 =Pq-c 30(10)-100(10)^2-10(10) =300-100-100- 100 =300-300 =0 TERM 9 single plant $10000.q cars, q trucks. same plant 1000+70q+80q DEFINITION 9 MC of producing cars? MC of producing trucks? economies of scope exist? 100 cars and 200 trucks. MC=70 MC=80 C(q,q) TERM 10 lawn-mower owner (1)200 per year, spend $1 every acre cut (2)40 per year, spend $5 part1of2 DEFINITION 10 a) total cost function for both methods, letting q represent the # of acres of grass cut C=200+q C=40+5q b) find avg. cost function and marginal cost for each method AC= (200/q)+1 AC=(40/q)+5 MC=1 MC=2
