1、Chapter Six,Demand,Properties of Demand Functions,Comparative statics analysis of ordinary demand functions - the study of how ordinary demands x1*(p1,p2,y) and x2*(p1,p2,y) change as prices p1, p2 and income y change.,Own-Price Changes,How does x1*(p1,p2,y) change as p1 changes, holding p2 and y co
2、nstant?Suppose only p1 increases, from p1 to p1 and then to p1.,x1,x2,p1 = p1,Fixed p2 and y.,p1x1 + p2x2 = y,Own-Price Changes,Own-Price Changes,x1,x2,p1= p1,p1 = p1,Fixed p2 and y.,p1x1 + p2x2 = y,Own-Price Changes,x1,x2,p1= p1,p1=p1,Fixed p2 and y.,p1 = p1,p1x1 + p2x2 = y,p1 = p1,Own-Price Change
3、s,Fixed p2 and y.,x1*(p1),Own-Price Changes,p1 = p1,Fixed p2 and y.,x1*(p1),p1,x1*(p1),p1,x1*,Own-Price Changes,Fixed p2 and y.,p1 = p1,x1*(p1),p1,x1*(p1),p1,p1 = p1,x1*,Own-Price Changes,Fixed p2 and y.,x1*(p1),x1*(p1),p1,x1*(p1),p1,p1 = p1,x1*,Own-Price Changes,Fixed p2 and y.,x1*(p1),x1*(p1),p1,x
4、1*(p1),x1*(p1),p1,p1,x1*,Own-Price Changes,Fixed p2 and y.,x1*(p1),x1*(p1),p1,x1*(p1),x1*(p1),p1,p1,p1 = p1,x1*,Own-Price Changes,Fixed p2 and y.,x1*(p1),x1*(p1),x1*(p1),p1,x1*(p1),x1*(p1),p1,p1,p1 = p1,x1*,Own-Price Changes,Fixed p2 and y.,x1*(p1),x1*(p1),x1*(p1),p1,x1*(p1),x1*(p1),x1*(p1),p1,p1,p1
5、,x1*,Own-Price Changes,Fixed p2 and y.,x1*(p1),x1*(p1),x1*(p1),p1,x1*(p1),x1*(p1),x1*(p1),p1,p1,p1,x1*,Own-Price Changes,Ordinarydemand curvefor commodity 1,Fixed p2 and y.,x1*(p1),x1*(p1),x1*(p1),p1,x1*(p1),x1*(p1),x1*(p1),p1,p1,p1,x1*,Own-Price Changes,Ordinarydemand curvefor commodity 1,Fixed p2
6、and y.,x1*(p1),x1*(p1),x1*(p1),p1,x1*(p1),x1*(p1),x1*(p1),p1,p1,p1,x1*,Own-Price Changes,Ordinarydemand curvefor commodity 1,p1 price offer curve,Fixed p2 and y.,Own-Price Changes,The curve containing all the utility-maximizing bundles traced out as p1 changes, with p2 and y constant, is the p1- pri
7、ce offer curve.The plot of the x1-coordinate of the p1- price offer curve against p1 is the ordinary demand curve for commodity 1.,Own-Price Changes,What does a p1 price-offer curve look like for Cobb-Douglas preferences?,Own-Price Changes,What does a p1 price-offer curve look like for Cobb-Douglas
8、preferences?TakeThen the ordinary demand functions for commodities 1 and 2 are,Own-Price Changes,and,Notice that x2* does not vary with p1 so thep1 price offer curve is,Own-Price Changes,and,Notice that x2* does not vary with p1 so thep1 price offer curve is flat,Own-Price Changes,and,Notice that x2
9、* does not vary with p1 so thep1 price offer curve is flat and the ordinarydemand curve for commodity 1 is a,Own-Price Changes,and,Notice that x2* does not vary with p1 so thep1 price offer curve is flat and the ordinarydemand curve for commodity 1 is a rectangular hyperbola.,x1*(p1),x1*(p1),x1*(p1)
10、,Own-Price Changes,Fixed p2 and y.,x1*(p1),x1*(p1),x1*(p1),p1,x1*,Own-Price Changes,Ordinarydemand curvefor commodity 1 is,Fixed p2 and y.,Own-Price Changes,What does a p1 price-offer curve look like for a perfect-complements utility function?,Own-Price Changes,What does a p1 price-offer curve look
11、like for a perfect-complements utility function?,Then the ordinary demand functionsfor commodities 1 and 2 are,Own-Price Changes,Own-Price Changes,With p2 and y fixed, higher p1 causessmaller x1* and x2*.,Own-Price Changes,With p2 and y fixed, higher p1 causessmaller x1* and x2*.,As,Own-Price Change
12、s,With p2 and y fixed, higher p1 causessmaller x1* and x2*.,As,As,Fixed p2 and y.,Own-Price Changes,x1,x2,p1,x1*,Fixed p2 and y.,Own-Price Changes,x1,x2,p1,p1 = p1,y/p2,p1,x1*,Fixed p2 and y.,Own-Price Changes,x1,x2,p1,p1,p1 = p1,y/p2,p1,x1*,Fixed p2 and y.,Own-Price Changes,x1,x2,p1,p1,p1,p1 = p1,y
13、/p2,p1,x1*,Ordinarydemand curvefor commodity 1 is,Fixed p2 and y.,Own-Price Changes,x1,x2,p1,p1,p1,y/p2,Own-Price Changes,What does a p1 price-offer curve look like for a perfect-substitutes utility function?,Then the ordinary demand functionsfor commodities 1 and 2 are,Own-Price Changes,and,Fixed p
14、2 and y.,Own-Price Changes,x2,x1,Fixed p2 and y.,p1 = p1 p2,Fixed p2 and y.,Own-Price Changes,x2,x1,p1,x1*,Fixed p2 and y.,p1,p1 = p1 p2,Fixed p2 and y.,Own-Price Changes,x2,x1,p1,x1*,Fixed p2 and y.,p1,p1 = p1 = p2,Fixed p2 and y.,Own-Price Changes,x2,x1,p1,x1*,Fixed p2 and y.,p1,p1 = p1 = p2,Fixed
15、 p2 and y.,Own-Price Changes,x2,x1,p1,x1*,Fixed p2 and y.,p1,p1 = p1 = p2,Fixed p2 and y.,Own-Price Changes,x2,x1,p1,x1*,Fixed p2 and y.,p1,p1 = p1 = p2,p2 = p1,Fixed p2 and y.,Own-Price Changes,x2,x1,p1,x1*,Fixed p2 and y.,p1,p1,p2 = p1,Fixed p2 and y.,Own-Price Changes,x2,x1,p1,x1*,Fixed p2 and y.
16、,p1,p2 = p1,p1,p1 price offer curve,Ordinarydemand curvefor commodity 1,Own-Price Changes,Usually we ask “Given the price for commodity 1 what is the quantity demanded of commodity 1?”But we could also ask the inverse question “At what price for commodity 1 would a given quantity of commodity 1 be d
17、emanded?”,Own-Price Changes,p1,x1*,p1,Given p1, what quantity isdemanded of commodity 1?,Own-Price Changes,p1,x1*,p1,Given p1, what quantity isdemanded of commodity 1?Answer: x1 units.,x1,Own-Price Changes,p1,x1*,x1,Given p1, what quantity isdemanded of commodity 1?Answer: x1 units.,The inverse ques
18、tion is:Given x1 units are demanded, what is the price of commodity 1?,Own-Price Changes,p1,x1*,p1,x1,Given p1, what quantity isdemanded of commodity 1?Answer: x1 units.,The inverse question is:Given x1 units are demanded, what is the price of commodity 1? Answer: p1,Own-Price Changes,Taking quantit
19、y demanded as given and then asking what must be price describes the inverse demand function of a commodity.,Own-Price Changes,A Cobb-Douglas example:,is the ordinary demand function and,is the inverse demand function.,Own-Price Changes,A perfect-complements example:,is the ordinary demand function
20、and,is the inverse demand function.,Income Changes,How does the value of x1*(p1,p2,y) change as y changes, holding both p1 and p2 constant?,Income Changes,Fixed p1 and p2.,y y y,Income Changes,Fixed p1 and p2.,y y y,Income Changes,Fixed p1 and p2.,y y y,x1,x1,x1,x2,x2,x2,Income Changes,Fixed p1 and
21、p2.,y y y,x1,x1,x1,x2,x2,x2,Incomeoffer curve,Income Changes,A plot of quantity demanded against income is called an Engel curve.,Income Changes,Fixed p1 and p2.,y y y,x1,x1,x1,x2,x2,x2,Incomeoffer curve,Income Changes,Fixed p1 and p2.,y y y,x1,x1,x1,x2,x2,x2,Incomeoffer curve,x1*,y,x1,x1,x1,y,y,y,I
22、ncome Changes,Fixed p1 and p2.,y y y,x1,x1,x1,x2,x2,x2,Incomeoffer curve,x1*,y,x1,x1,x1,y,y,y,Engelcurve;good 1,Income Changes,Fixed p1 and p2.,y y y,x1,x1,x1,x2,x2,x2,Incomeoffer curve,x2*,y,x2,x2,x2,y,y,y,Income Changes,Fixed p1 and p2.,y y y,x1,x1,x1,x2,x2,x2,Incomeoffer curve,x2*,y,x2,x2,x2,y,y,
23、y,Engelcurve;good 2,Income Changes,Fixed p1 and p2.,y y y,x1,x1,x1,x2,x2,x2,Incomeoffer curve,x1*,x2*,y,y,x1,x1,x1,x2,x2,x2,y,y,y,y,y,y,Engelcurve;good 2,Engelcurve;good 1,Income Changes and Cobb-Douglas Preferences,An example of computing the equations of Engel curves; the Cobb-Douglas case.The ord
24、inary demand equations are,Income Changes and Cobb-Douglas Preferences,Rearranged to isolate y, these are:,Engel curve for good 1,Engel curve for good 2,Income Changes and Cobb-Douglas Preferences,y,y,x1*,x2*,Engel curvefor good 1,Engel curvefor good 2,Income Changes and Perfectly-Complementary Pref
25、erences,Another example of computing the equations of Engel curves; the perfectly-complementary case.The ordinary demand equations are,Income Changes and Perfectly-Complementary Preferences,Rearranged to isolate y, these are:,Engel curve for good 1,Engel curve for good 2,Fixed p1 and p2.,Income Chan
26、ges,x1,x2,Income Changes,x1,x2,y y y,Fixed p1 and p2.,Income Changes,x1,x2,y y y,Fixed p1 and p2.,Income Changes,x1,x2,y y y,x1,x1,x2,x2,x2,x1,Fixed p1 and p2.,Income Changes,x1,x2,y y y,x1,x1,x2,x2,x2,x1,x1*,y,y,y,y,Engelcurve;good 1,x1,x1,x1,Fixed p1 and p2.,Income Changes,x1,x2,y y y,x1,x1,x2,x2,
27、x2,x1,x2*,y,x2,x2,x2,y,y,y,Engelcurve;good 2,Fixed p1 and p2.,Income Changes,x1,x2,y y y,x1,x1,x2,x2,x2,x1,x1*,x2*,y,y,x2,x2,x2,y,y,y,y,y,y,Engelcurve;good 2,Engelcurve;good 1,x1,x1,x1,Fixed p1 and p2.,Income Changes,x1*,x2*,y,y,x2,x2,x2,y,y,y,y,y,y,x1,x1,x1,Engelcurve;good 2,Engelcurve;good 1,Fixed
28、 p1 and p2.,Income Changes and Perfectly-Substitutable Preferences,Another example of computing the equations of Engel curves; the perfectly-substitution case.The ordinary demand equations are,Income Changes and Perfectly-Substitutable Preferences,Income Changes and Perfectly-Substitutable Preferenc
29、es,Suppose p1 p2. Then,Income Changes and Perfectly-Substitutable Preferences,Suppose p1 p2. Then,and,Income Changes and Perfectly-Substitutable Preferences,Suppose p1 0.That is, the consumers MRS is the same anywhere on a straight line drawn from the origin.,(x1,x2) (y1,y2) (kx1,kx2) (ky1,ky2),p,p,
30、Income Effects - A Nonhomothetic Example,Quasilinear preferences are not homothetic.For example,Quasi-linear Indifference Curves,x2,x1,Each curve is a vertically shifted copy of the others.,Each curve intersectsboth axes.,Income Changes; Quasilinear Utility,x2,x1,Income Changes; Quasilinear Utility,
31、x2,x1,x1*,y,x1,Engelcurveforgood 1,Income Changes; Quasilinear Utility,x2,x1,x2*,y,Engelcurveforgood 2,Income Changes; Quasilinear Utility,x2,x1,x1*,x2*,y,y,x1,Engelcurveforgood 2,Engelcurveforgood 1,Income Effects,A good for which quantity demanded rises with income is called normal.Therefore a nor
32、mal goods Engel curve is positively sloped.,Income Effects,A good for which quantity demanded falls as income increases is called income inferior.Therefore an income inferior goods Engel curve is negatively sloped.,Income Changes; Goods1 & 2 Normal,x1,x1,x1,x2,x2,x2,Incomeoffer curve,x1*,x2*,y,y,x1,
33、x1,x1,x2,x2,x2,y,y,y,y,y,y,Engelcurve;good 2,Engelcurve;good 1,Income Changes; Good 2 Is Normal, Good 1 Becomes Income Inferior,x2,x1,Income Changes; Good 2 Is Normal, Good 1 Becomes Income Inferior,x2,x1,Income Changes; Good 2 Is Normal, Good 1 Becomes Income Inferior,x2,x1,Income Changes; Good 2 I
34、s Normal, Good 1 Becomes Income Inferior,x2,x1,Income Changes; Good 2 Is Normal, Good 1 Becomes Income Inferior,x2,x1,Income Changes; Good 2 Is Normal, Good 1 Becomes Income Inferior,x2,x1,Incomeoffer curve,Income Changes; Good 2 Is Normal, Good 1 Becomes Income Inferior,x2,x1,x1*,y,Engel curvefor g
35、ood 1,Income Changes; Good 2 Is Normal, Good 1 Becomes Income Inferior,x2,x1,x1*,x2*,y,y,Engel curvefor good 2,Engel curvefor good 1,Ordinary Goods,A good is called ordinary if the quantity demanded of it always increases as its own price decreases.,Ordinary Goods,Fixed p2 and y.,x1,x2,Ordinary Good
36、s,Fixed p2 and y.,x1,x2,p1 price offer curve,Ordinary Goods,Fixed p2 and y.,x1,x2,p1 price offer curve,x1*,Downward-sloping demand curve,Good 1 isordinary,p1,Giffen Goods,If, for some values of its own price, the quantity demanded of a good rises as its own-price increases then the good is called Gi
37、ffen.,Ordinary Goods,Fixed p2 and y.,x1,x2,Ordinary Goods,Fixed p2 and y.,x1,x2,p1 price offer curve,Ordinary Goods,Fixed p2 and y.,x1,x2,p1 price offer curve,x1*,Demand curve has a positively sloped part,Good 1 isGiffen,p1,Cross-Price Effects,If an increase in p2increases demand for commodity 1 the
38、n commodity 1 is a gross substitute for commodity 2. reduces demand for commodity 1 then commodity 1 is a gross complement for commodity 2.,Cross-Price Effects,A perfect-complements example:,so,Therefore commodity 2 is a grosscomplement for commodity 1.,Cross-Price Effects,p1,x1*,p1,p1,p1,Increase t
39、he price ofgood 2 from p2 to p2and,Cross-Price Effects,p1,x1*,p1,p1,p1,Increase the price ofgood 2 from p2 to p2and the demand curvefor good 1 shifts inwards- good 2 is acomplement for good 1.,Cross-Price Effects,A Cobb- Douglas example:,so,Cross-Price Effects,A Cobb- Douglas example:,so,Therefore commodity 1 is neither a grosscomplement nor a gross substitute forcommodity 2.,
