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?