types of utility functions and homothetic prrefrences
These notes will give you an introduction to different types of utility fuctions . These notes will be helpful to any student doing graduation with economics major.
TYPES OF UTILITY FUNCTIONS
Cobb-Douglas Utility
utility = U(x,y) = xayb
where a and b are positive constants
–The relative sizes of a and b indicate the relative importance of the goods
Perfect Substitutes
utility = U(x,y) = ax + by
The indifference curves will be linear. The MRS will be constant along the indifference curve.
Perfect Complements
utility = U(x,y) = min (ax, by)
The indifference curves will be L-shaped. Only by choosing more of the two goods together can utility be increased.
CES Utility (Constant elasticity of substitution)
utility = U(x,y) = xg/g + yg/g
when g is not = 0
utility = U(x,y) = ln x + ln y
when g = 0
–Perfect substitutes g = 1
–Cobb-Douglas g = 0
–Perfect complements g = - infinity
Homothetic Preferences
If the MRS depends only on the ratio of the amounts of the two goods, not on the quantities of the goods, the utility function is homothetic.
Perfect substitutes MRS is the same at every point
Perfect complements
MRS = infinity if y/x > a/b
undefined if y/x = a/b,
MRS = 0 if y/x < a/b
For the general Cobb-Douglas function, the MRS can be found as
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TYPES OF UTILITY FUNCTIONS
Cobb-Douglas Utility
utility = U(x,y) = xayb
where a and b are positive constants
–The relative sizes of a and b indicate the relative importance of the goods
Perfect Substitutes
utility = U(x,y) = ax + by
The indifference curves will be linear. The MRS will be constant along the indifference curve.
Perfect Complements
utility = U(x,y) = min (ax, by)
The indifference curves will be L-shaped. Only by choosing more of the two goods together can utility be increased.
CES Utility (Constant elasticity of substitution)
utility = U(x,y) = xg/g + yg/g
when g is not = 0
utility = U(x,y) = ln x + ln y
when g = 0
–Perfect substitutes g = 1
–Cobb-Douglas g = 0
–Perfect complements g = - infinity
Homothetic Preferences
If the MRS depends only on the ratio of the amounts of the two goods, not on the quantities of the goods, the utility function is homothetic.
Perfect substitutes MRS is the same at every point
Perfect complements
MRS = infinity if y/x > a/b
undefined if y/x = a/b,
MRS = 0 if y/x < a/b
For the general Cobb-Douglas function, the MRS can be found as
hope your doubts regarding the types of utility functions are now clear. do subscribe to our blog also do subscribe idea tutors on youtube and stay updated with new educational videos,
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