Answer to Question #231152 in Microeconomics for Nee

Question

Define and discuss local examples for the following within the context:

a. Indifference Curves

b. Marginal rate of substitution

c. Indifference curves and transitivity

d. Convexity of indifference curve

e. Utility and the marginal rate of substitution

f. Non Homothetic Preferences

g. Homothetic Preferences

h. Optimisation Principle

I. Lump Sum Principle

J. Homogeneity of Expenditure functions

Answer 1

An indifference curve depicts goods combinations providing an equal satisfaction level.

For example, Figure 1 below illustrates three indifference curves that show Lilly’s preferences for the tradeoffs that she faces in her two main relaxation activities: eating doughnuts and reading paperback books. Each indifference curve (Ul, Um, and Uh) represents one level of utility. First we will explore the meaning of an individual indifference curve and then we will look at the relationship between different indifference curves.

b)

The marginal rate of substitution (MRS) is the quantity of a commodity a consumer is willing to consume in relative to another good, as far as the new commodity is equally satisfying. MRS is utilized in indifference for consumer behavior analysis.

For example, a consumershould decide between consuming hamburgers and hot dogs. The consumer is asked the preferred combinations of hamburgers and hot dogs that provide same satisfaction level to determine the marginal rate of substitution.

c)

Preferences are said to be transitive if they are consistent internally. For example, if A is preferred to B and B is preferred to C, then A is preferred to C.

d)

Indifference curve convexit shows that the marginal rate of substitution of X for Y reduces as more of X is substituted for Y. Therefore, indifference curves are convex to the origin in the case where principle of diminishing marginal rate of substitution holds.

e)

The marginal rate of substitution (MRS) refers to the rate that a consumer is willing to give up in exchange with another good good while maintaining the same satisfaction level.

f)

Non-homothetic preferences capture Engel's law, i.e. the relationship between between expenditure and its proportion spent on food is inverse. These preferencesmean that the rates of net investment rise with the income level as the steady state is approached.

g)

A preference relation is considered homothetic if the indifference curve slope is constant along any ray from the origin. When preferences take this form, the knowledge the indifference curve shape tells the shape of all indifference curves, because they are “radial blowups” of each other.

h)

The optimization principle states that 'the entity will act so as to maximize the value of a specific combination of abstract functions'. Specifying what the functions are obtains different specific scientific laws.

i)

The lump sum principle states that 'a tax on a person's general purchasing power is more efficient than a tax on specific goods.'

j)

If a function u(x) is continuous, strictly quasi-concave and non-satiated, it follows that the associated expenditure function c(p, u) is homogeneous with degree 1 in p, concave, strictly increasing in u, and contains partial derivatives which are the Hicksian demand functions.