Econ 101: Substitution and Income Effects

How to be happy: You make your decision according to what maximizes your happiness.

Remember, given two products, in order to maximize total utility, simply equate the marginal utilities (factoring in price).

Here's another way of looking at it: we're going back to opportunity cost. The condition for total utility maximization is that you must consume the good until the marginal benefit is equal to the marginal cost. In other words, when consuming something like coke, you continue to consume it until the money we use to buy that coke is of greater benefit to us than the coke itself: ie- the marginal cost of the coke exceeds the marginal benefit.

Okay, now let's look at it mathematically:
The condition for maximum total utility is (MarginalUtilityX/MarginalUtilityY) must equal (PriceX/PriceY)

We can't control prices, but we can control marginal utilities. We control marginal utilities by purchasing more or less of a particular good. Changing consumption ratios CHANGES marginal utilities.

The less you buy of a product, the higher it's marginal utility will be. The more you buy of a product, the lower it's marginal utility will be. This is the law of diminishing marginal utility.

So if the price of one product X is greater than product Y, you can simply buy less of product X and more of product Y to balance out the two ratios mathematically so they will remain equal.

This can also be seen on a diagram!
If you Measure Marginal utility per price on the Y axis, and quantity purchased on the X axis, and then you have two mirrored diminishing utility curves, you can draw a horizontal line across the two graphs at any point to find out the quantities where marginal utility is equal, and therefore total utility is maximized. This is a really quick way of determining the ratio of quantities to purchase in order to maximize utility.

Also, you can notice that at the points of maximized utility, the utility gained from purchasing more of one product is less than the utility lost from purchasing one less of the other product.

Basically, buy whatever has a higher marginal utility until that difference disappears due to the law of diminishing incomes.

HOW TO DERIVE DEMAND FROM MARGINAL UTILITY ANALYSIS:

Expenditure on one good is small compared to all other goods (or income). A change in the marginal utility of one good will probably not affect the marginal utility of all other goods. As such, we can treat all other goods as income (Y).

(MarginalUtilityX/MarginalUtilityY) must equal (PriceX/PriceY) for utility maximization.

If price of X rises while income remains constant, then the marginal utility of X must also rise. This means the quantity bought of X must decrease (doe to the law of dimishing marginal utility).

Let's link this: when prices rise, quantity demanded falls, which is why we have a negative sloped demand curve!

SUBSTITUION AND INCOME EFFECTS:
Why do people want to buy more as the price falls?

First we need to understand real income. Real income is what you can really buy- in other words, your purchasing power (for instance, you could make a million dollars a year, but if it costs thousands of dollars to purchase basic consumer goods, your real income is very low)

Substitution Effect: A change in the quantity demand due to a change in the relative price, holding real income constant. AKA: original purchasing power, new prices.

IE: I have a $10 allowance for pocky. The price of pocky falls by 1/2 (from $1 to 50 cents). My allowance is also cut in half to just five dollars, BUT in order to maximize my utility, I must buy more pocky (I have to lower it's marginal utility, because the price has fallen)

THE SUBSTITUION EFFECT IS ALWAYS NEGATIVE: AS THE PRICE DROPS THE CONSUMER WILL ALWAYS SUBSTITUTE INTO THE CHEAPER GOOD

Income effect: A change in the quantity demanded due to a change in REAL INCOME (ie purchasing power), holding NEW RELATIVE PRICES CONSTANT

IE: I now receive my old allowance again ($10), but to maximize my utility, if pocky is a normal good, I will still want to buy more of them

(NOTE: Normal goods- income elasticity of demand is positive
Inferior goods- income elasticity of demand is negative)

The magnitude of the income effect depends on:
1- the porportion of income which is spend on the product in question (the greater the porportion, the greater the effect)
2- The magnitude of the price change

THE TOTAL EFFECT OF PRICE CHANGES IS A COMBINATION OF THE SUBSTITUION EFFECT AND THE INCOME EFFECT

BOTH OF THE ARE CAUSED BY CHANGES IN PRICE

Normal Goods + income elasticity of demand
Inferior Goods - income elasticity of demand
Ordinary Goods - price elasticity of demand
Giffen GOods + price elasticity of demand
Ie: Bread as a stable in the 1800s

2 reqs
-Inferior Good
-Large proportion of household income

In other words, the income effect must offset the substitution effect

Ordinary Ordinary Giffen
Sub Effect - - -
Inc Effect - + ++
Inc Elast + - --
Price Elast - - +

NOTE: both sub and inc effect result from PRICE CHANGES
Giffen Goods: Income rises and quantity demanded falls. Price falls and quantity demanded falls.

THIS IS BECAUSE
-income elasticity is negative
-the income effect is positive
-so price elasticity will be positive

THATS SO COOL!