Exam 4: Demand Relationships Among Goods

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With only two goods,x and y,if x and y are gross substitutes,a rise in px must necessarily:

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Use the following definitions for an individual who consumes only two goods,x and y: sx = share of income spent on x. sy = 1-sx.​ Use the following definitions for an individual who consumes only two goods,x and y: s<sub>x</sub> = share of income spent on x. s<sub>y</sub> = 1-s<sub>x</sub>.​   = price elasticity of demand for x.​   = price elasticity of demand for y. ​e<sub>x,I</sub> = income elasticity of demand for x. ​ e<sub>y,I</sub> = income elasticity of demand for y.​   = cross price elasticity of demand for x.​   = cross price elasticity of demand for y. -If the demand for x is given by   ,which of parameter values hold? = price elasticity of demand for x.​ Use the following definitions for an individual who consumes only two goods,x and y: s<sub>x</sub> = share of income spent on x. s<sub>y</sub> = 1-s<sub>x</sub>.​   = price elasticity of demand for x.​   = price elasticity of demand for y. ​e<sub>x,I</sub> = income elasticity of demand for x. ​ e<sub>y,I</sub> = income elasticity of demand for y.​   = cross price elasticity of demand for x.​   = cross price elasticity of demand for y. -If the demand for x is given by   ,which of parameter values hold? = price elasticity of demand for y. ​ex,I = income elasticity of demand for x. ​ ey,I = income elasticity of demand for y.​ Use the following definitions for an individual who consumes only two goods,x and y: s<sub>x</sub> = share of income spent on x. s<sub>y</sub> = 1-s<sub>x</sub>.​   = price elasticity of demand for x.​   = price elasticity of demand for y. ​e<sub>x,I</sub> = income elasticity of demand for x. ​ e<sub>y,I</sub> = income elasticity of demand for y.​   = cross price elasticity of demand for x.​   = cross price elasticity of demand for y. -If the demand for x is given by   ,which of parameter values hold? = cross price elasticity of demand for x.​ Use the following definitions for an individual who consumes only two goods,x and y: s<sub>x</sub> = share of income spent on x. s<sub>y</sub> = 1-s<sub>x</sub>.​   = price elasticity of demand for x.​   = price elasticity of demand for y. ​e<sub>x,I</sub> = income elasticity of demand for x. ​ e<sub>y,I</sub> = income elasticity of demand for y.​   = cross price elasticity of demand for x.​   = cross price elasticity of demand for y. -If the demand for x is given by   ,which of parameter values hold? = cross price elasticity of demand for y. -If the demand for x is given by Use the following definitions for an individual who consumes only two goods,x and y: s<sub>x</sub> = share of income spent on x. s<sub>y</sub> = 1-s<sub>x</sub>.​   = price elasticity of demand for x.​   = price elasticity of demand for y. ​e<sub>x,I</sub> = income elasticity of demand for x. ​ e<sub>y,I</sub> = income elasticity of demand for y.​   = cross price elasticity of demand for x.​   = cross price elasticity of demand for y. -If the demand for x is given by   ,which of parameter values hold? ,which of parameter values hold?

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In the Slutsky equation for In the Slutsky equation for   ,the income effect is given by: ,the income effect is given by:

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Quasi-concavity of utility functions insures that with only two goods,these goods must be:

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If a rise in the price x causes less y to be demanded:

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If goods x and y are complements,then the cross price elasticity of demand between them will be:

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The attributes model of consumer choice explains the possibility that an individual does not purchase a particular good,z by assuming:

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Use the following definitions for an individual who consumes only two goods,x and y: sx = share of income spent on x. sy = 1-sx.​ Use the following definitions for an individual who consumes only two goods,x and y: s<sub>x</sub> = share of income spent on x. s<sub>y</sub> = 1-s<sub>x</sub>.​   = price elasticity of demand for x.​   = price elasticity of demand for y. ​e<sub>x,I</sub> = income elasticity of demand for x. ​ e<sub>y,I</sub> = income elasticity of demand for y.​   = cross price elasticity of demand for x.​   = cross price elasticity of demand for y. -Homogeneity of the demand function is shown by: = price elasticity of demand for x.​ Use the following definitions for an individual who consumes only two goods,x and y: s<sub>x</sub> = share of income spent on x. s<sub>y</sub> = 1-s<sub>x</sub>.​   = price elasticity of demand for x.​   = price elasticity of demand for y. ​e<sub>x,I</sub> = income elasticity of demand for x. ​ e<sub>y,I</sub> = income elasticity of demand for y.​   = cross price elasticity of demand for x.​   = cross price elasticity of demand for y. -Homogeneity of the demand function is shown by: = price elasticity of demand for y. ​ex,I = income elasticity of demand for x. ​ ey,I = income elasticity of demand for y.​ Use the following definitions for an individual who consumes only two goods,x and y: s<sub>x</sub> = share of income spent on x. s<sub>y</sub> = 1-s<sub>x</sub>.​   = price elasticity of demand for x.​   = price elasticity of demand for y. ​e<sub>x,I</sub> = income elasticity of demand for x. ​ e<sub>y,I</sub> = income elasticity of demand for y.​   = cross price elasticity of demand for x.​   = cross price elasticity of demand for y. -Homogeneity of the demand function is shown by: = cross price elasticity of demand for x.​ Use the following definitions for an individual who consumes only two goods,x and y: s<sub>x</sub> = share of income spent on x. s<sub>y</sub> = 1-s<sub>x</sub>.​   = price elasticity of demand for x.​   = price elasticity of demand for y. ​e<sub>x,I</sub> = income elasticity of demand for x. ​ e<sub>y,I</sub> = income elasticity of demand for y.​   = cross price elasticity of demand for x.​   = cross price elasticity of demand for y. -Homogeneity of the demand function is shown by: = cross price elasticity of demand for y. -Homogeneity of the demand function is shown by:

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Use the following definitions for an individual who consumes only two goods,x and y: sx = share of income spent on x. sy = 1-sx.​ Use the following definitions for an individual who consumes only two goods,x and y: s<sub>x</sub> = share of income spent on x. s<sub>y</sub> = 1-s<sub>x</sub>.​   = price elasticity of demand for x.​   = price elasticity of demand for y. ​e<sub>x,I</sub> = income elasticity of demand for x. ​ e<sub>y,I</sub> = income elasticity of demand for y.​   = cross price elasticity of demand for x.​   = cross price elasticity of demand for y. -The elasticity of the compensated demand curve   Can be computed as: = price elasticity of demand for x.​ Use the following definitions for an individual who consumes only two goods,x and y: s<sub>x</sub> = share of income spent on x. s<sub>y</sub> = 1-s<sub>x</sub>.​   = price elasticity of demand for x.​   = price elasticity of demand for y. ​e<sub>x,I</sub> = income elasticity of demand for x. ​ e<sub>y,I</sub> = income elasticity of demand for y.​   = cross price elasticity of demand for x.​   = cross price elasticity of demand for y. -The elasticity of the compensated demand curve   Can be computed as: = price elasticity of demand for y. ​ex,I = income elasticity of demand for x. ​ ey,I = income elasticity of demand for y.​ Use the following definitions for an individual who consumes only two goods,x and y: s<sub>x</sub> = share of income spent on x. s<sub>y</sub> = 1-s<sub>x</sub>.​   = price elasticity of demand for x.​   = price elasticity of demand for y. ​e<sub>x,I</sub> = income elasticity of demand for x. ​ e<sub>y,I</sub> = income elasticity of demand for y.​   = cross price elasticity of demand for x.​   = cross price elasticity of demand for y. -The elasticity of the compensated demand curve   Can be computed as: = cross price elasticity of demand for x.​ Use the following definitions for an individual who consumes only two goods,x and y: s<sub>x</sub> = share of income spent on x. s<sub>y</sub> = 1-s<sub>x</sub>.​   = price elasticity of demand for x.​   = price elasticity of demand for y. ​e<sub>x,I</sub> = income elasticity of demand for x. ​ e<sub>y,I</sub> = income elasticity of demand for y.​   = cross price elasticity of demand for x.​   = cross price elasticity of demand for y. -The elasticity of the compensated demand curve   Can be computed as: = cross price elasticity of demand for y. -The elasticity of the compensated demand curve Use the following definitions for an individual who consumes only two goods,x and y: s<sub>x</sub> = share of income spent on x. s<sub>y</sub> = 1-s<sub>x</sub>.​   = price elasticity of demand for x.​   = price elasticity of demand for y. ​e<sub>x,I</sub> = income elasticity of demand for x. ​ e<sub>y,I</sub> = income elasticity of demand for y.​   = cross price elasticity of demand for x.​   = cross price elasticity of demand for y. -The elasticity of the compensated demand curve   Can be computed as: Can be computed as:

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Use the following definitions for an individual who consumes only two goods,x and y: sx = share of income spent on x. sy = 1-sx.​ Use the following definitions for an individual who consumes only two goods,x and y: s<sub>x</sub> = share of income spent on x. s<sub>y</sub> = 1-s<sub>x</sub>.​   = price elasticity of demand for x.​   = price elasticity of demand for y. ​e<sub>x,I</sub> = income elasticity of demand for x. ​ e<sub>y,I</sub> = income elasticity of demand for y.​   = cross price elasticity of demand for x.​   = cross price elasticity of demand for y. -A generalization of Engel's Law is given by: = price elasticity of demand for x.​ Use the following definitions for an individual who consumes only two goods,x and y: s<sub>x</sub> = share of income spent on x. s<sub>y</sub> = 1-s<sub>x</sub>.​   = price elasticity of demand for x.​   = price elasticity of demand for y. ​e<sub>x,I</sub> = income elasticity of demand for x. ​ e<sub>y,I</sub> = income elasticity of demand for y.​   = cross price elasticity of demand for x.​   = cross price elasticity of demand for y. -A generalization of Engel's Law is given by: = price elasticity of demand for y. ​ex,I = income elasticity of demand for x. ​ ey,I = income elasticity of demand for y.​ Use the following definitions for an individual who consumes only two goods,x and y: s<sub>x</sub> = share of income spent on x. s<sub>y</sub> = 1-s<sub>x</sub>.​   = price elasticity of demand for x.​   = price elasticity of demand for y. ​e<sub>x,I</sub> = income elasticity of demand for x. ​ e<sub>y,I</sub> = income elasticity of demand for y.​   = cross price elasticity of demand for x.​   = cross price elasticity of demand for y. -A generalization of Engel's Law is given by: = cross price elasticity of demand for x.​ Use the following definitions for an individual who consumes only two goods,x and y: s<sub>x</sub> = share of income spent on x. s<sub>y</sub> = 1-s<sub>x</sub>.​   = price elasticity of demand for x.​   = price elasticity of demand for y. ​e<sub>x,I</sub> = income elasticity of demand for x. ​ e<sub>y,I</sub> = income elasticity of demand for y.​   = cross price elasticity of demand for x.​   = cross price elasticity of demand for y. -A generalization of Engel's Law is given by: = cross price elasticity of demand for y. -A generalization of Engel's Law is given by:

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For the Cobb-Douglas utility function with two goods,the sum of the own price elasticities of demand must be:

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"Hicks' Third Law of Demand" states that "most" goods must be:

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Two goods are Hicks (net)substitutes if a rise in the price of one causes a(n):

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With the Cobb-Douglas utility function With the Cobb-Douglas utility function   ,x and y are: ,x and y are:

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For the "Composite Commodity Theorem" to hold,all goods in the composite must:

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The primary additional insight provided by expanding the theory of demand from two to three goods is that a pair of goods may now be:

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Symmetry of net substitution effects is one of the principal conclusions of the theory of utility maximization.Which two mathematical theorems are used to prove this symmetry?

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If utility is separable in a three-good utility function x3 If utility is separable in a three-good utility function x<sub>3 </sub> <sub> </sub>    Then for changes in   Must: Then for changes in If utility is separable in a three-good utility function x<sub>3 </sub> <sub> </sub>    Then for changes in   Must: Must:

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