Lecture 1 (2x2)

Lecture 1(2x2) - .CA9 58A=B=GHF5H=J9 [email protected] DCGH98 CB [email protected][email protected] G@=89G K= 69 DCGH98 CB [email protected]?6C5F8 HCC*F;5B=N5H=CB C [email protected] F95 =B H<9

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Unformatted text preview: .CA9 58A=B=GHF5H=J9 GHIR .M@@56IG DCGH98 CB [email protected]?6C5F8 @5GG G@=89G K=@@ 69 DCGH98 CB [email protected]?6C5F8 HCC *F;5B=N5H=CB C: [email protected] F95? =B H<9 [email protected] 2CIF F=;<HG 5B8 8IH=9G .CA9 8IH=9G -958 F958 -  HH9B85B79 HC [email protected] =G <=;<@M F97CAA9B898 [email protected] B979GG5FM '97HIF9 $BHFC8I7H=CB *) [email protected] '5 +5FF5 +TF9N 0( 5B8 GCA9 F=;<HG G? 5G? .& CB79DHI5@ =GGI9G H<=G =G BCH 5B 95GM 7CIFG9 IH [email protected] @=B;I=GH=7 CB9G (M CQ79 <CIFG (CB85M /I9G85M 5B8 198B9G85M 5B8 6M 5DDC=BHA9BH J=5 9 A5=@ @5D5FF5D9F9N 97CB IA8 98I *Q79 /M8=B;G $: H<9F9 =G 5BM [email protected] MCI K=@@ 69 BCH=O98 6M 9 A5=@ 5H @95GH <CIFG =B 58J5B79 [email protected] '5 +5FF5 +TF9N 0( 7CB '97HIF9 %5BI5FM S @J5FC '5 +5FF5 +TF9N 0( 7CB '97HIF9 F=9: CIH@=B9 .CA9 H97<B=75@ BCH9G CB 97CBCA=7 ;FCKH< "FCKH< F5H9G .CA9 H97<B=75@ BCH9G CB 97CBCA=7 ;FCKH< "FCKH< F5H9G +F=79 =B89L9G /<9 [email protected]=CB C: [email protected] K=H< F9GD97H HC H=A9 89F=J5H9 C: H=A9 =G IGI5@@M 9LDF9GG98 5G [email protected] / KFH 9MCB8 97CBCA=7 ;FCKH< 97CBCA=7 [email protected] *F;5B=N5H=CB C: ;CJ9FBA9BH *F;5B=N5H=CBG -9A9A69F H<5H H<9 89F=J5H=J9 K=H< F9GD97H HC H=A9 =G >IGH H<9 [email protected]=CB C: H<9 [email protected] D9F IB=H C: H=A9 ∆ /<9 95G=9GH K5M HC H<=B? 56CIH 5 ;FCKH< F5H9 =G 5G D9F79BH5;9 7<5B;9 ∆ / @=A ∆ [email protected]=CB 5G=7 :F5A9KCF? 5B8 EI9GH=CBG =B CIF 7CIFG9 "FCKH< F5H9 C: & [email protected] '5 +5FF5 +TF9N 0( 7CB '97HIF9 S @J5FC '5 +5FF5 +TF9N 0( 7CB '97HIF9 .CA9 H97<B=75@ BCH9G CB 97CBCA=7 ;FCKH< "FCKH< F5H9G .CA9 H97<B=75@ BCH9G CB 97CBCA=7 ;FCKH< "FCKH< F5H9G DD@=75H=CB C: DF9J=CIG :57HG HC 5 [email protected] .CA9 65G=7 DFCD9FH=9G C: B5HIF5@ @C;5F=H<AG $: $: N $: $: $: H<9B @C; @C; @C; H<9B @C; @C; @C; β H<5H ;FCKG 9LDCB9BH=5@@M )CH9 H<5H H<9 F5H9 C: ;FCKH< C: M K=@@ 69 ;=J9B 6M H<9B @C; β @C; @C; H<9B / @C; H<9B I G=B; [email protected] 9LD5BG=CB $B CH<9F KCF8G H<9 D9F79BH5;9 7<5B;9 =B DF9J=CIG 9EI5H=CB 5B8 H<9 7<5B;9 =B @C; [email protected]@5H=CBG ; 5F9 [email protected] [email protected] S @J5FC '5 +5FF5 +TF9N 0( 7CB '97HIF9 [email protected] '5 +5FF5 +TF9N 0( 7CB '97HIF9 .CA9 H97<B=75@ BCH9G CB 97CBCA=7 ;FCKH< "FCKH< F5H9G .CA9 H97<B=75@ BCH9G CB 97CBCA=7 ;FCKH< "FCKH< F5H9G "F5D<=75@ F9DF9G9BH5H=CB C: 9LDCB9BH=5@ ;FCKH< 5B8 @C; C: 9LDCB9BH=5@ ;FCKH< $B7CA9G 5FCIB8 K9F9 @CK 9BCI;< 9J9FMK<9F9 =B H<9 [email protected] 9J9B =B H<9 F=7<9GH [email protected] /<9 F5H9 C: 97CBCA=7 ;FCKH< <58 HC 69 J9FM [email protected] HC N9FC :CF 5 J9FM @CB; H=A9 @C; @C; IH 1<M 5F9 K9 H5@?=B; 56CIH 9LDCB9BH=5@ F5H9G C: ;FCKH< $G =H D9FH=B9BH HC IB89FGH5B8 97CBCA=7 ;FCKH< $H 89D9B8G CB H<9 ACA9BH 5B8 [email protected] K<9F9 K9 5F9 S @J5FC '5 +5FF5 +TF9N 0( 7CB '97HIF9 $H K5G BCH IBH=@ GCA9H=A9 5:H9F 69;5B 5B8 <5G 7CBH=BI98 M95F [email protected] '5 +5FF5 +TF9N 0( 7CB '97HIF9 H<5H AC89FB 97CBCA=7 ;FCKH< 5H 56CIH D9F .CA9 H97<B=75@ BCH9G CB 97CBCA=7 ;FCKH< "FCKH< F5H9G .CA9 H97<B=75@ BCH9G CB 97CBCA=7 ;FCKH< "FCKH< F5H9G [email protected] /F9B8 @=B9 =B @C; D9F 75D=H5 =B7CA9 69HK99B =B H<9 0. =G 5B8 /F9B8G =B 97CBCA=7 ;FCKH< [email protected] J5F=9G 57FCGG F9;=CBG CF 7CIBHF=9G /<9 89GD9F5H9 G=HI5H=CB C: '95GH [email protected] CIBHF=9G ' S @J5FC '5 +5FF5 +TF9N 0( 7CB '97HIF9 S @J5FC '5 +5FF5 +TF9N 0( 7CB '97HIF9 .CA9 H97<B=75@ BCH9G CB 97CBCA=7 ;FCKH< "FCKH< F5H9G .CA9 H97<B=75@ BCH9G CB 97CBCA=7 ;FCKH< "FCKH< F5H9G [email protected] '5 +5FF5 +TF9N 0( 7CB '97HIF9 [email protected] '5 +5FF5 +TF9N 0( 7CB '97HIF9 .CA9 H97<B=75@ BCH9G CB 97CBCA=7 ;FCKH< "FCKH< F5H9G .CA9 H97<B=75@ BCH9G CB 97CBCA=7 ;FCKH< "FCKH< F5H9G (CF9 7CAA9BHG .CA9 7CAA9BHG K<9B @CC?=B; 5H H<9 DF9J=CIG [email protected] )CH9 H<5H K9 :C7IG =B "+ CF =B7CA9 !CF H<9 ACGH D5FH H<=G 7CIFG9 K9 K=@@ H5@? 56CIH 97CBCA=7 ;FCKH< 5G CDDCG98 HC 9LH9BG=J9 97CBCA=7 ;FCKH< $: 5B 97CBCAM =G ;FCK=B; 5H D9F M95F 5B8 [email protected]=CB =G ;FCK=B; 5H D9F M95F D9F 75D=H5 =B7CA9 =G BCH ;FCK=B; 5H 5@@ /<9F9 =G 9LH9BG=J9 ;FCKH< 6IH H<9F9 =GBPH =BH9BG=J9 ;FCKH< -=7< 7CIBHF=9G 9LD9F=9B79 DCG=H=J9 ;FCKH< =B 5 AI7< <=;<9F G<5F9 C: M95FG H<5B DCCF 7CIBHF=9G C: 5@@ M95FG 5G CDDCG98 HC C: 5@@ M95FG :CF DCCF 7CIBHF=9G 5B8 H<5H H<9 DCCF9F H<9 7CIBHFM =G =B H<9 GA5@@9F H<9 G<5F9 C: DCG=H=J9 ;FCKH< M95FG =B H<9=F <=GHCFM 1<[email protected] 5@@ DCCF 7CIBHF=9G ;FCK 5H FCI;<@M H<9 G5A9 F5H9 K<9B H<9M ;FCK 5 6=H CJ9F D9F M95F H<9 DCCF9F H<9 7CIBHFM H<9 ACF9 B9;5H=J9 H<9 ;FCKH< F5H9 =B H<9 M95FG K<9B H<9M 9LD9F=9B79 B9;5H=J9 ;FCKH< $B [email protected] GH5H=GH=75@ G9BG9 =H =G BCH H<9 8=R9F9BH=5@ D9F:CFA5B79 C: 97CBCA=9G K<9B H<9M 5F9 ;FCK=B; H<5H [email protected]=BG K<M F=7< 7CIBHF=9G 5F9 F=7< 5B8 DCCF 7CIBHF=9G 5F9 DCCF -5H<9F =H =G H<9 8=R9F9BH=5@ 9LD9F=9B79 C: 7CIBHF=9G K<9B H<9M 5F9 G<F=B?=B; H<5H [email protected]=BG K<M 7CIBHF=9G 5F9 F=7< 5B8 DCCF [email protected] '5 +5FF5 +TF9N 0( 7CB '97HIF9 -=7< 7CIBHF=9G ;FCK ACF9 [email protected]@M K<9B H<9M ;FCK H<5B DCCF 7CIBHF=9G :CF BCB C=@ F=7< 7CIBHF=9G 5B8 :CF DCCF 7CIBHF=9G @9GG H<5B 5BBI5@ D9F 75D=H5 =B7CA9 S @J5FC '5 +5FF5 +TF9N 0( 7CB '97HIF9 .CA9 H97<B=75@ BCH9G CB 97CBCA=7 ;FCKH< +F=79 =B89L9G .CA9 H97<B=75@ BCH9G CB 97CBCA=7 ;FCKH< +F=79 =B89L9G B C6J=CIG =GGI9 K<9B IG=B; =B7CA9 85H5 HC A5?9 7CAD5F=GCBG CJ9F H=A9 CF GD579 =G H<5H DF=79G 5F9 7<5B;=B; G K9 <5J9 G99B K<9B K9 H5@? 56CIH 97CBCA=7 ;FCKH< K9 5F9 F95@@M 7CB79FB98 56CIH H<9 5ACIBH C: ;CC8G 5B8 G9FJ=79G D9F D9FGCB ∑ [email protected]@9 =B 5 GC7=9HM /<9 [email protected] K=H< H<9 DF9798=B; 9EI5H=CB =G @=H9F5@@M CB9 C: 588=B; [email protected] 5B8 CF5B;9G #CK 8C K9 K9=;<H H<9 [email protected] 5B8 CF5B;9G 7CBCA=7 H<9CFM GI;;9GHG H<5H =B 7CAD9H=H=J9 A5F?9HG H<5H H<9 DF=79 C: 5 DFC8I7H [email protected] A5F;=B5@ 7CGH HC H<9 7CBGIA9F 5B8 A5F;=B5@ 69B9OH HC H<9 DFC8I79F .=B79 5@@ 7CBGIA9FG ;5=B 5H @95GH 5G AI7< :FCA 7CBGIA=B; [email protected] 5G H<9 D9FGCB K<C =G H<9 A5F;=B5@ 7CBGIA9F C: [email protected] K<C =G >IGH =B8=R9F9BH 56CIH 6IM=B; 5B [email protected] CF BCH H<9 GIA C: DF=79 EI5BH=HM C: [email protected] =G 5 @CK9F 6CIB8 9GH=A5H9 C: H<9 7CBGIA9F K9@:5F9 C: 7CBGIA=B; [email protected] [email protected] '5 +5FF5 +TF9N 0( 7CB '97HIF9 /<9 K9@:5F9 BCH=CB =G 7CAD5F5H=J9 H<9 69B9OHG C: 7CBGIA=B; [email protected] 7CAD5F98 HC CH<9F ;CC8G 5B8 G9FJ=79G H5?=B; H<9 DF=79G C: CH<9F ;CC8G 5B8 G9FJ=79G 5G ;=J9B .C K<5H =: H<9 DF=79 C: [email protected] 5B8 CF5B;9G ;C9G ID 6M 5B8 H<9 DFC8I7H=CB 5B8 7CBGIADH=CB C: [email protected] 5B8 CF5B;9G GH5MG H<9 G5A9 19 8C BCH K5BH HC 7CIBH H<9 DF=79 =B7F95G9 5G 97CBCA=7 ;FCKH< G=B79 H<9 F95@ CIHDIH =B7CA9 C: H<9 97CBCAM <5G BCH 7<5B;98 $: H<9B =B7F95G98 9J9B =: K9 GH=@@ DFC8I79 H<9 [email protected] C: CIHDIH <5G 1<5H =G IGI5@@M 8CB9 =G HC 7CBGHFI7H 5 DF=79 =B89L [email protected] '5 +5FF5 +TF9N 0( 7CB '97HIF9 .CA9 H97<B=75@ BCH9G CB 97CBCA=7 ;FCKH< +F=79 =B89L9G 9MCB8 97CBCA=7 ;FCKH< 97CBCA=7 [email protected] 5G F9:9F9B79 H<9 19 K=@@ [email protected] H5@? 56CIH 97CBCA=7 ;FCKH< =B H<=G [email protected] 5G 5B =B7F95G9 =B D9F 75D=H5 =B7CA9 3IGI5@@M A95GIF98 6M "+ D9F 75D=H54 7CBCA=7 [email protected] =B 7CBHF5GH =G 56CIH H<9 GHFI7HIF9 69<5J=CF 5B8 B5HIF9 C: H<9 97CBCAM =B 5 GC7=9HM /<=G BCH=CB F9EI=F9G HC H5?9 =BHC 577CIBH H<9 [email protected]=CBG<=DG 69HK99B DC@=H=7G 5B8 97CBCA=7G HC IB89FGH5B8 H<9 DFC79GG C: GC7=5@ 7<5B;9 1<=7< 8=R9F9B79G 69G=89G H<9 CB9G <=;<@=;<H98 K<9B @CC?=B; 5H 97CBCA=7 ;FCKH< F5H9G 75B 69 :CIB8 69HK99B [email protected] 5B8 [email protected]=B; 5F95G *F;5B=N5H=CB C: ;CJ9FBA9BH F95H=CB C: CF;5B=N5H=CBG 0G=B; DF=79G =B M95F H DF=79 =B89L =B =G $B89L 5B8 M95F 65G9 $: DF=79G K9F9 =B M95F 5B8 =B M95F $B89L $: DF=79G <5J9BPH 7<5B;98 5H 5@@ H<9 [email protected] N9FC 5B8 H<9 DF=79 =B89L /C 7CBJ9FH + DF=79G =BHC + [email protected] =: M95F -95@+ + =G H<9 65G9 / )[email protected] HC G5M H<=B;G 5F9 ACF9 7CAD@=75H98 =B H<9 F95@ [email protected] *J9F H=A9 H<9 ?=B8 C: H<=B;G H<5H [email protected] 7CBGIA9 7<5B;9G GC H<5H H<9 7CBGIADH=CB [email protected] =G 7<5B;=B; H<FCI;< H=A9 7FCGG 7CIBHF=9G H<9 ?=B8G C: H<=B;G [email protected] 7CBGIA9 =G 8=R9F9BH F=79 =B <=B5 5B8 H<9 0. ,I5@=HM 5B8 7<5F57H9F=GH=7G C: 89J=79G 7<5B;9 H<=B? 56CIH @5DHCDG S @J5FC '5 +5FF5 +TF9N 0( 7CB '97HIF9 [email protected] '5 +5FF5 +TF9N 0( 7CB '97HIF9 9MCB8 97CBCA=7 ;FCKH< 97CBCA=7 [email protected] *F;5B=N5H=CB C: ;CJ9FBA9BH 9MCB8 97CBCA=7 ;FCKH< 97CBCA=7 [email protected] *F;5B=N5H=CB C: ;CJ9FBA9BH [email protected] '5 +5FF5 +TF9N 0( 7CB '97HIF9 [email protected] '5 +5FF5 +TF9N 0( 7CB '97HIF9 9MCB8 97CBCA=7 ;FCKH< 97CBCA=7 [email protected] *F;5B=N5H=CBG 9MCB8 97CBCA=7 ;FCKH< 97CBCA=7 [email protected] *F;5B=N5H=CBG GCA9 7CAA9BHG 1=H< H<9 9L79DH=CB C: H<9 :CIF C=@ 7CIBHF=9G K<=7< 5F9 [email protected] F=7< CF DCCF 89D9B8=B; CB H<9 DF=79 C: C=@ 5@@ C: H<9 CH<9F F=7< 7CIBHF=9G F5B? OFGH CF G97CB8 =B H<9=F DC@=HM G7CF9G /<9 DC@=HM G7CF9 3K<=7< =G 7C@@97H98 6M 5 ;FCID C: F9G95F7<9FG CF=;=B5@@M 65G98 =B H<9 DC@=H=75@ G7=9B79 89D5FHA9BH <9F9 5H ([email protected] =G 5 7CADCG=H9 =B89L F5B?=B; J5F=CIG :95HIF9G C: DC@=H=75@ GMGH9AG =B J5F=CIG 7CIBHF=9G /<9 DC@=HM G7CF9 F5B;9G :FCA HC 5B8 =B H<9 [email protected] H<9 7CIBHF=9G 5F9 @=GH98 6M F5B? (CF9 =B:C <HHD KKK GMGH9A=7D9579 CF; DC@=HM DC@=HM <HA /<9 G=N9 C: H<9 79BHF5@ ;CJ9FBA9BH 8C9G BCH J5FM GMGH9A5H=75@@M 57FCGG =B7CA9 6IH #=;< =B7CA9 7CIBHF=9G <5J9 G=;[email protected] @5F;9F ;CJ9FBA9BHG 5G K9@@ 5G ACF9 ;CJ9FBA9BHG '5F;9F ;CJ9FBA9BHG =B <=;< =B7CA9 7CIBHF=9G [email protected] :FCA 5 AI7< @5F;9F G9H C: GI6 B5H=CB5@ ;CJ9FBA9BHG H<5H =B DCCF 7CIBHF=9G [email protected] '5 +5FF5 +TF9N 0( 7CB '97HIF9 [email protected] '5 +5FF5 +TF9N 0( 7CB '97HIF9 5G=7 :F5A9KCF? 5B8 EI9GH=CBG =B H<=G 7CIFG9 /<F99 GC7=5@ CF89FG HC DIH GCA9 GHFI7HIF9 5B8 [email protected]=B H<9 DF9J=CIG 8=R9F9B79G =B 97CBCA=7 ;FCKH< CF;5B=N5H=CB C: ;CJ9FBA9BH 5B8 BIA69F C: CF;5B=N5H=CBG !CF5;=B; CF89F <IBH9F 5B8 ;5H<9F9F GC7=9H=9G )5HIF5@ GH5H9 '=A=H98 779GG *F89FG 3' *4 *D9B 779GG *F89FG * * 19 K=@@ :C7IG CB H<9 @5GH HKC /<9 65G=7 =895 H<5H K=@@ 69 [email protected] =G H<5H HF5BG=H=CB :FCA ' *G HC * *G =G 5GGC7=5H98 K=H< GIGH5=B98 97CBCA=7 ;FCKH< ACF9 89AC7F5H=7 ;CJ9FBA9BHG 5B8 ;F95H9F BIA69F C: CF;5B=N5H=CBG 5G=7 EI9GH=CBG HC 69 5BGK9F98 1<=7< 5F9 H<9 7<5F57H9F=GH=7G 5B8 H<9 @C;=7 C: 957< GC7=5@ CF89F #CK 8C K9 D5GG :FCA ' * HC * * 1<=7< [email protected] C: H<9G9 CF89FG 75B K9 OB8 6CH< =B <=GHCFM 5B8 HC85MPG [email protected] [email protected] '5 +5FF5 +TF9N 0( 7CB '97HIF9 ...
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This note was uploaded on 03/08/2011 for the course ECON 602 taught by Professor Chugh during the Spring '11 term at Johns Hopkins.

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