Topic 3 - Marginal Rate of Substitution Flashcards
Define MRS
The rate at which the consumer is just willing to substitute one good for the other
AKA ratio of marginal utilities
(if we reduce consumption of one good, utility reduce so in order to stay on same IC must increase consumption of other good but how by how much)
change in x2/change in x1
What is MRS graphically
- change in x1 is small hence it is MARGINAL rate of substitution
- Slope of IC at a particular point
- it is negative but we dont we really show negative sign (we know this from monotonicity)
MRS of perfect substitutes and perfect complements
perfect substitutes:
u(c,p) = aC +bP
MRS = -a/b
Perfect complements:
u (r, l) = min (aR , bL)
MRS is :
- undefined at the kink
- negative infinity on the vertical section
- 0 on the horizontal section
What happens if you monotonically transform a utility function
- Utility function changes but the preference and order of ranking does not
- infinite number of utility functions will show the same preferences
How does MRS change along the curve for diff types of utility functions
- perfect substitutes: same throughout and slope is constant so MRS same everywhere
- perfect complements: diff at horizontal seciton, vertical section and kink
- imperfect substitutes: represented by a cobb douglas function and this shows diminshing MRS (convex to origin)
Explain diminishing MRS
- MRS falls in absolute value as you go down the MRS curve
- the more you have of a good, the more willing you are to sacrifice it to gain an extra unit of another good
- hence MRS falls as you go down
What are homothetic tastes
- A situation where the consumers preferences depend solely on the ratio of good 1 to good 2
- homothetic taste give rise to Indifference maps where the MRS is constant along any ray from the origina
- AKA SIMPLE TERMS:
if income increases you continue to consumer goods x1 and x2 in the same ratio; demand for these goods rises by the same proportion so MRS at a higher income is same as it was at a lower income.
Expand on homothetic tastes
- The relative quantity of each good and MRS remains
constant along any ray from the origin - When income is scaled up or down by t > 0, the demanded bundle scales up or down by the same
amount.
What are quasilinear tastes
- the utility function is non-linear in at most one good in the bundle
- tastes are linear in one good but may not be in the other good
e.g u(x1,x2) = v(x1) +x2 - consumption of one goods does not vary with income and increase in income is spent on all other consumption
What are IC curves like for quasilinear tastes
- indifference curves arevertically shifted versions of the same indifference curve (assuming the good
that is independent of income is on the horizontal axis). - Such preferences have the same MRS on vertical rays
– we have utility functions that are linear in one good but non-linear in
another.
What is MRS like for quasilinear tastes
constant along any vertical line from the x axis
examples of quasliniear goods
- one of the goods are independent of income e.g salt and pepper, bread - change in income doesn’t cause a change in how much we consume of these goods
What is elasticity of substitution for diff types of goods
perfect substitutes: infinity
perfect complements: no substitutability so 0
cobb-douglas: 1
what is elasticity of substitution
The degree of substitutability measures how responsive the
bundle of goods along an IC is to changes in the MRS
Exaplin elastcity of substitution
- Consider a 1% change in the MRS
- The less curved the IC, the more x2 has to fall and the more
x1 has to increase for the MRS to have changed by 1% - Thus, the less curvature in the IC, the greater is the
% ∆x2
/x1 required for the MRS to change by 1%, which implies a higher elasticity of substitution σ – i.e. Perfect Substitutes
