Econ 101: Income, and Substituion with Indifference curves

HEY, Before anything else happens, we should all ask our TAs why indifference curves are convex to the origin (I think it has something to do with diminishing marginal rates of substitution- basically, a combination of goods with a major defficiency in one product requires a LOT of compensation in terms of the other product in order to get the same total utility as you would with a balanced combination of goods).

Alright: It's a shorter lecture today.

We know that we can use the budget line and the indifference curves for any two products to predict a different quantiy which will be purchased at each price.


Now we're going to look at how to graphically represent the substitution and income effects using budget lines and marginal utility analysis.

Remember: whenever the price of one good drops, our real income (purchasing power) rises. For theory's sake, in order to isolate the substitution effect, we must change the budget line to reflect changing price ratios while keeping real income constant. In order to do this, we take the budget line and rotate it around the point where it originally intersects with it's original indifference curve.

We look at where this new, streched budget line is tangent to a greater indifference curve. The change in the quantity of product A is caused by the substituion effect: consumers substituting into the cheaper good to maximize total utility (reach a greater indifference curve).

Now let's look at income effect: If total income increases when the price of a NORMAL GOOD decreases, that will also cause us to purchase more of that good. In order to look at the income effect, we take the restricted budget line (with the new price ratio) and shift it up and to the right to reflect the increase in real income.

The point where this new, inflated budget line is tangent to the highest indifference curve represents the new quantity purchased as a result of both substitution AND income effect.


Remember:
-The total effect is the substitution effect + the income effect
-The substitution is a change in quantity purchased due to a change in relative prices. It is always negative (except for conspicious consumption goods), which means that price and quantity purchased change in opposite directions
-Income effect is a change in quantity purchased due to a change in purchasing power.
It can be positive (for normal goods) or negative (for inferior goods)

If the income effect is greater than the substitution effect, the product in question is a Giffen Good


NOW: let's put it all together!

Indifference curve analysis yields the same conditions for total utility maximization as marginal utility analysis!

We know that for Utility to be maximized in indifference curve analysis, the budget line must be tangent to the indifference curve.

BUDGET LINE EQUATION: PxQx +PyQy = Income
BUDGET LINE SLOPE: -Px/Py (Marginal rate of tranformation)

INDIFFERENCE CURVE EQUATION: /\Qx(MUx) + /\Qy(MUy) = 0
INDIFFERENCE CURVE SLOPE: -MUx/MUy (Marginal rate of substitution)

Maximazation condition: The budget line must be tangent to the indifference curve

or

the slope of the budget line must equal the slope of the indifference curve

or

-Px/Py must = -MUx/MUy

or

MUx/Px = MUy/Py WHICH IS MARGINAL UTILITY ANALYSIS

Brilliant, non?

Econ 101 Indifference Curves:

Indifference curves are graphs which incorporate the idea of tastes or preferences.


We assume that consumers are rational thinkers, and that they can rank their preferences. There are three parts to this 'rationality':

1- COMPLETE the consumer must either prefer good A to good B, good B to good A, or be indifferent
2- REFLEXIVE A is always as good as A. Preferences don't change based on exogenous variables
3- TRANSITIVE If A > B and B > C, then A > C

THESE SUBJECTIVE PREFERENCES ARE INDEPENDANT (EXOGENOUS).
-We cannot make comparisons between different people (because you can't compare my happiness to yours)
-We cannot make comparisons between different times
-This shows us that psychology is the basis of microeconomics!

HOKAY! Now that the background stuff is out of the way, let's actually look at one of these again.

FUNCTION OF A UTILITY CURVE: U = U(x,y) higher number = higher utility...

All of the different points on one indifference curve show different combined quantities of 2 goods (x and y) which yield a constant total utility.
Because the utility derived from any product is different for different people, the indifference curve shows PERSONAL PREFERENCES.

CHARACTERISTICS:
For any two products, there are an infinite number of indifference curves expanding outward. The total utility for each progressive curve is higher than the last one, because each progressive curve represents a greater combined quantity of goods x and y, and in most cases, we prefer to have MORE (more goods = greater total utility).

Two indifference curves for the same product cannot cross, because that would suggest that we can achieve the same total utility with a set combination of x and y as we could with the same quantity of x, but fewer of y. Also the point of intersection would imply two different total utilities for the same combination of goods. That's illogical.

EQUATION: Change in X (Marginal utility of X) + Change in Y (Marginal utility of Y) = 0

Why? Because if two points are on the same indifference curve, the utility lost on one axis is gained on the other axis.

utility lost = Change in X (Marginal utility of X)
utility gained = Change in Y (Marginal utility of Y)

The slope of the indifference curve = change in X/change in Y

OR

negative marginal utility of X/marginal utility of Y

OR

the marginal rate of substitution!

COMBINING BUDGET LINES AND INDIFFERENCE CURVES:
both budget lines and indifference curves have the same axes: quantities of different products. Budget lines show us possible combinations of different products, and indifference curve show us desired combinations of different products!

REMEMBER, price changes are represented as rotations or stretches of the budget line. SO, if the price of soda falls, the budget line for soda stretches out further along the x-axis, and the possible quantity of soda increases. Consumers want to maximize total utility, so places where the indifference line meets the budget line represent the demanded combinations of goods, given the prices of both products. As the prices of a good falls, consumers substitute into that good in order to reach higher indifference curves with the stretched budget line.
.
In this way, we can see the formation of a demand curve- consumers buy greater quantities of a product as the price decreases in order to maximize total utility (intersect with the highest indifference curve). This results in a negatively sloped demand curve.

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