Microeconomics principles and analysis phần 2 ppt

... y=p1. In the right-hand version the person has an endowment of resources R :=(R1; R 2 ), and so his chosen bundle of goods must satisfyp1x1+ p 2 x 2  p1R + p 2 R 2 : (4 .2) The two versions ... CHAPTER 3. THE FIRM AND THE MARKET 2. In a market of a thousand consumers the demand curve for the commodityis given byp = A  bqwhere q is total quantity demanded and A and b are positive ... either sign if n > 2 and j and i in(4 .21 ) represent di¤erent goods (jelly and ice-cream let us say). We say thatcommodities i and j are net substitutes if Hij> 0 and net complements...

... possibilityof combining and dividing production processes.Axiom 6.5 (Additivity) If q0 and q00 2 Q then q0+ q00 2 Q.Axiom 6.6 (Divisibility) If 0 < t < 1 and q 2 Q then tq 2 Q.Let us see ... criterion in (5 .26 ) and (5 .27 ) above.In fact we can prove (see Appendix C)Theorem 5 .2 (Representative Consumer) Average demand in the marketcan be written in the form (5 .26 ) if and only if, for ... (x1) + [1  a] log (x 2  k)where good 1 is rice and good 2 is a “basket” of all other commodities, and 0 < a < 1, k  0.1. Brie‡y interpret the parameters a and k. 2. Assume that the peasant...

... that the person select P1when P 2 is also available and thenalso select P3when P4is available (Bell 19 82, Loomes and Sugden 19 82) . 22 2 CHAPTER 8. UNCERTAINTY AND RISK8.7 An example of the ... been realised. and obtain a set of demand functionsconditional upon !:xi= Di(p; y!) :180 CHAPTER 8. UNCERTAINTY AND RISKFigure 8 .2: The state-space diagram: # = 2 8 .2. 2 State-space ... (8.18) 23 As depicted bonds 1 and 7 are likely to be uninteresting –brie‡y explain what they are. 24 Explain why you get jumps in the demand for bonds in this case. 20 8 CHAPTER 8. UNCERTAINTY AND...

... . . 22 09 Welfare 22 79.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 79 .2 The constitution . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 89.3 Principles ... . . 21 2. 11 Cost and input price . . . . . . . . . . . . . . . . . . . . . . . . . 24 2. 12 Optimal output may be multivalued . . . . . . . . . . . . . . . . 27 2. 13 Convexity and input demands ... . . . . . . . 25 2. 2.4 Assembling the solution . . . . . . . . . . . . . . . . . . . 26 2. 3 The …rm as a “black box” . . . . . . . . . . . . . . . . . . . . . . 27 2. 3.1 Demand and supply functions...

... for …rm 2 we get a relationship  2 giving q 2 as a function of somearbitrary value q1of the output of …rm 1:q 2 =  2 q1: (10.15)Equilibrium and e¢ ciencyTreating 1 and  2 as characterising ... generated by …rm 2. We could measurethis in terms of …rm 2 s output:1 2 2@ 2 @q11(9 .25 )where  2 2is the conventional di¤erential of …rm 2 s production function withrespect to its own output.More ... (10. 12) , we have the FOC:@1q1; q 2 @q1= pqq1+ q 2 q1+ pq1+ q 2  C1qq1 0= 0 if q1> 0: (10.13)We …nd q1as a function of q 2 :q1= 1q 2 (10.14)where...

... (11. 32)  Third, given (11. 32) , we must have:13a (xa1)  Fa> 0:11Sh ow this by usi ng (11 .22 ) and (11 .29 ). 12 Sh ow this by usi ng (11 .22 ) and (11.31).13Sh ow this using (11. 32) and ... actions.sb1sb 2 sb3sa10; 2 3; 1 4; 3sa 2 2; 4 0; 3 3; 2 sa31; 1 2; 0 2; 1Table 10.10: Elimination and equilibrium1. Is there a dominant strategy for either of the two agents? 2. Which ... introduction is provided by Dixit and Skeath (20 04), Gardner (20 03),Osborne (20 04) or Rasmusen (20 01); the older Gibbons (19 92) still p rovidesan excellent and thorough overview of the main...

...  2 x 2 1  2 4. Plot the graph of the bank’s expected pro…ts against y. Show that the bankwill set y = y if 1y >  2 x 2 and y = x 2 otherwise.5. Suppose there are N such …rms and ... v 2 ; :::( 12. 3)De…nition 12. 3 Suppose there are two pro…les [v] and [~v] such that= v1; v 2 ; ::: and, for all h :vh()  vh() ) ~vh()  ~vh() : ( 12. 4) 12. 6. ... problem in social-welfare analysis (it is useful to comparethese with the four axioms on page 22 9).De…nition 12. 2 Suppose there is some such that for all h and all  2  :vh()  vh()....

... variable for …rm 2, and so theoptimisation problem ismaxfq 2 ;gnXi=1piq 2 i   2  2 q 2 ; q11(13.8)The …rst-order conditions are:pi  2  2 iq 2 ; q11= 0 ... positively(deodorant?) and good 2 is just a basket of other goods. Using the basice¢ ciency principles from equation (9.34) and (13 .2) we getUh1Uh 2 =1 2  eh 21 (13.17)where eh 21 is the marginal ... A”Equality A = B x 2 A if and only if x 2 BSubset A  B x 2 B if x 2 AIntersection A \ B A \ B = fx : x 2 A and x 2 BgUnion A [ B A [ B = fx : x 2 A or x 2 BgIn addition the operator “n”is often...

... PrE1jE 2 PrE 2 (A.67)From de…nition A.30 and (A.67) we get Bayes’rule:Pr (E 2 jE1) =Pr (E1jE 2 ) Pr (E 2 )Pr (E1jE 2 ) Pr (E 2 ) + PrE1jE 2 PrE 2 A.8.3 ... q1; q 2 = 0orp 2 qq 2 q 2 + p 2 q 2 = Cqw; q 2 ; q1= 010 Assume that 1<  2 . Su ppose that the …rm ignored the possibilityof splitting the market and just implemented ... p1xa1+ p 2 xa 2  p1Ra1+ p 2 Ra 2 ; the …rst-ordercondition simpli…es to Ua1(xa)=Ua 2 (xa) = p1=p 2 .4. Alf sells some of h is endowment of good 2 to Bill and buys some...

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