Microeconomic Analysis ECON203
Microeconomic Analysis ECON203 Consumer Preferences and the Concept of Utility Consumer Preferences Consumer Preferences portray how consumers would compare the desirability any two combinations or allotments of goods, assuming these allotments were available to the consumer at no cost at a particular time and place (this may change as circumstances alter). These combinations are referred to as baskets or bundles. Assumptions: 1. Preferences are complete if the consumer can rank any two baskets of goods • A preferred to B or indifferent between A and B. 2. Preferences are transitive if a consumer prefers basket A to basket B and basket B to basket C, they also prefer basket A to C. 3. More is be/Non-Satiety: Having more good is better for a consumer.
The Utility Function The 3 assumptions about preferences allow us to represent preferences with a utility function: • • •
A function that measures the level of satisfaction a consumer receives from any basket of goods and services Assigns a number to each basket so that more preferred baskets get a higher number than less preferred baskets. U = u(y)
Implications: • • •
An ordinal concept: the precise magnitude of the number that the function assigns has no significance. Utility not comparable across individuals. Monotonicity: Any transformation of a utility function that preserves the original ranking of bundles is an equally good representation of preferences. o E.g. U = y0.5 vs. U = y0.5 + 2 represent the same preferences. This is called Monotonic Transformation
Marginal Utility Marginal utility of a good y is additional utility that the consumer gets from consuming a little more of y. • • •
The rate at which total utility changes as the level of consumption of good y rises MUy = U/Y = dU/dy MUy is the slope of the utility function with respect to y
Diminishing Marginal Utility The principle of diminishing marginal utility states that the marginal utility falls as consumer consumes more of a good.
Multiple Goods The marginal utility of a good x is the additional utility that the consumer gets from consuming a little more of x when the consumption of all the other goods in the consumer’s basket remain constant.
• •
More is better more y and more x indicate more U Diminishing marginal utility: o MU of x is not dependent of x. So MUX does not increase as x increases o MU of y increases with increase in number of y o Neither exhibits diminishing returns
Indifference Curves An Indifference Curve or Indifference Set: Is the set of all baskets for which the consumer is indifferent An Indifference Map: Illustrates a set of indifference curves for a consumer
Marginal Rate of Substitution (MRS) The marginal rate of substitution (MRS): the rate at which the consumer would be willing to give up one good to get more of another, holding the level of utility constant. MRS is the negative of the slope of the indifference curve.
Implications of MRS: •
•
Indifference curves are negatively‐sloped, bowed out from the origin, preference direction is up and right. o Averages preferred to extremes Indifference curves do not intersect the axes.
Diminishing MRS:
Types of Indifference Curves
• • • •
IC for normal goods IC for perfect substitutes IC for perfect compliments Quasi Linear Indifference Curves
Special Function Forms Cobb-Douglas curves bow towards the origin. They are used for IC of normal goods but may take on other forms.
1. Special Cobb-Douglas Utility Function: One Special Cobb-Douglas Utility Function is written as
Thus, alpha + beta will equal to 1. By changing alpha (a), we can generate a wide variety of indifference maps using this function.
When a = 0.5, the indifference curves are symmetric around the 45 degree line When a ≠ 0.5, they converge faster to the axis representing the good with the higher exponent.
2. Perfect Substitutes: U = Ax + By
3. Perfect Compliments: U = min (Ax, By)
4. Quasi-Linear U = v(x) + Ay
The only thing that determines your personal trade off between x and y is how much x you already have. This curve can be used to ‘add up’ utilities across individuals.
Examples of Curves when assumptions are violated:
The Utility Function The 3 assumptions about preferences allow us to represent preferences with a utility function: • • •
A function that measures the level of satisfaction a consumer receives from any basket of goods and services Assigns a number to each basket so that more preferred baskets get a higher number than less preferred baskets. U = u(y)
Implications: • • •
An ordinal concept: the precise magnitude of the number that the function assigns has no significance. Utility not comparable across individuals. Monotonicity: Any transformation of a utility function that preserves the original ranking of bundles is an equally good representation of preferences. o E.g. U = y0.5 vs. U = y0.5 + 2 represent the same preferences. This is called Monotonic Transformation
Marginal Utility Marginal utility of a good y is additional utility that the consumer gets from consuming a little more of y. • • •
The rate at which total utility changes as the level of consumption of good y rises MUy = U/Y = dU/dy MUy is the slope of the utility function with respect to y
Diminishing Marginal Utility The principle of diminishing marginal utility states that the marginal utility falls as consumer consumes more of a good.
Multiple Goods The marginal utility of a good x is the additional utility that the consumer gets from consuming a little more of x when the consumption of all the other goods in the consumer’s basket remain constant.
• •
More is better more y and more x indicate more U Diminishing marginal utility: o MU of x is not dependent of x. So MUX does not increase as x increases o MU of y increases with increase in number of y o Neither exhibits diminishing returns
Indifference Curves An Indifference Curve or Indifference Set: Is the set of all baskets for which the consumer is indifferent An Indifference Map: Illustrates a set of indifference curves for a consumer
Marginal Rate of Substitution (MRS) The marginal rate of substitution (MRS): the rate at which the consumer would be willing to give up one good to get more of another, holding the level of utility constant. MRS is the negative of the slope of the indifference curve.
Implications of MRS: •
•
Indifference curves are negatively‐sloped, bowed out from the origin, preference direction is up and right. o Averages preferred to extremes Indifference curves do not intersect the axes.
Diminishing MRS:
Types of Indifference Curves
• • • •
IC for normal goods IC for perfect substitutes IC for perfect compliments Quasi Linear Indifference Curves
Special Function Forms Cobb-Douglas curves bow towards the origin. They are used for IC of normal goods but may take on other forms.
1. Special Cobb-Douglas Utility Function: One Special Cobb-Douglas Utility Function is written as
Thus, alpha + beta will equal to 1. By changing alpha (a), we can generate a wide variety of indifference maps using this function.
When a = 0.5, the indifference curves are symmetric around the 45 degree line When a ≠ 0.5, they converge faster to the axis representing the good with the higher exponent.
2. Perfect Substitutes: U = Ax + By
3. Perfect Compliments: U = min (Ax, By)
4. Quasi-Linear U = v(x) + Ay
The only thing that determines your personal trade off between x and y is how much x you already have. This curve can be used to ‘add up’ utilities across individuals.
Examples of Curves when assumptions are violated:
