# Micro_Steve

 Rational preference completetransitive Utility fn. x preferred y <=> u(x)>=u(y) If U. fn. exists, then preference is rational WARP Weak Axim of Revealed Preference = Consistency among choices Rational choice structure satisfies WARP Converse may not be true Walasian demand X is convexCompetitive budget => Price takers denoted x(p,w) Properties of Walasian Demands 1. homogeneous of degree 0: x(p,w)=x(ap,aw)2. Walas' law: px=w Walasian demand: wealth effects Wealth expansion path=Engel path={x(p,w):w>0}Normal good: income increases, then consumption inc. Walasian demand: price effects =price expansion path={x(p_k,p_l,w0): p_k>>0}price higher, consume lower=> cf. Giffen good: price higher, consume highersubstitution matrix=D_px(p,w)diagoal=own-price effectsoff-diagoal=cross-price effects Walasian demand 3 characteristics Homogeneity condition (home. degree of 0)Cournot Aggregation (Walas' law)Engel Aggregation (Walas' law) cf. WART, rationality assumption not needed x(p,w) satisfies WARP if px(p',w')<=w & x(p,w) is not same with x(p',w') implies p'x(p,w)>w' Slutzky compensated law of demand (p'-p)[x(p',w')-x(p,w)]<=0 total effects = wealth effects + substitute effects Slutzky equation dx=D_px(p,w)dp+D_wx(p,w)dw=D_p x(p,w)dp + D_w x(p,w)[dp*x(p,w)]=[D_p x(p,w)+D_w x(p,w)x(p,w)']dp=S_s(p,w)dp If WARP=> Law of Demand => dp*S_s(p,w)*dp <=0 ==> S_s = substitute matrix is negative semidefinite Substitute matrix is negative semidefinite 1. diagonal<=0: own-price effect2. |own-price effect| > cross-price effect S_s * P=0 because of Homo. degree of 0 Indifference properties monotonicitylocal non-satiation (rule out thick I.C.) Utilily Maximization max U(x)s.t. xp<=w Indirect utility fn. Utility max. => x*(p,w) => U(x*(p,w))=V(p,w) Properties of indirect u. fn. h.d. 0inc. in wnon-inc. in pquasi-convex (lower contour set is convex)preferent strictly convex & u(.) conti => V(.) conti. Expenditure minimization min pxs.t. u(x)>=u0=> x*=h(p,u): Hicksian demand Expenditure fn. h(p,u)=> p*h(p,u) = e(p,u) Properties of e(p,u) h.d. 1 in pstrictly inc in unon-dec. in pconvex in p Duality b/w UMP & EMP 1. If x* is opt. in UMP s.t. px=w, then x* is optimal in the EMP s.t. u>=U(x*)2. If x* is opt. in EMP s.t. u>=u0, then x* is opt. in the UMP s.t. px*=w 3. x(p,w)=h(p,V(p,w))4. h(p,u)=x(p,e(p,u)) 5. e(p,u) is inverse of v(p,w) Sheperd's lemma d e(p,u)/ d p = h(p,u) Roy's lemma x=-[dV(p,w)/dp]/[dV(p,w)/dw] Slutzky thm. dh/dp = dx/dp + dx/dw*x CV vs. EV CV => u0 baseEV => u1 base Netput vector y={q1,..,qn; -z1,...,zm} Input requirement set Y(q0)={z: f(z)>=q0} Output producible set Y(z0)= {y: y<=f(z0) or (z0,y) included in Y} where Y is a production set Possible Properties of production set 1. nonempty2. closedness3. no free lunch (no input=> no output)4. possibility of inaction5. (strong) Free disposability (y included Y, and y'<=y, then y' included Y)6. irreversibility: y included Y, -y cannot be included Y7. Additivity8. convexity Returns to scale increasing return to scaleconstant "dec. Non jointness & seperability Profit fn. >> Hotelling's lemma Cost fn. >> Shepherd's lemma Authorlucia831124 ID80289 Card SetMicro_Steve DescriptionMicro_Steve Updated2011-04-18T06:36:59Z Show Answers