What happens as our consumer's decision becomes more complex?
That is, how does Jim maximize his utility, when faced with choosing among multiple products,
and having to worry about prices?
Let's say that Jim stops off at the mall food court for some lunch, and for him, at this
moment, the marginal utility of the slice of pizza would be 100 units of utility; the
marginal utility of a small soda would be 50 units of utility.
To maximize utility, which should Jim pick first?
If he has no worries over income or price, he would choose the pizza.
But the fact is that prices do matter; in this case, let's say that the pizza is $2.50
and the small soda is $1.
If Jim considers how to get the most added satisfaction per dollar spent with each spending
decision, then he will achieve the maximum possible utility when all of his income's
been spent.
So, which product yields greater added satisfaction -- marginal utility -- per dollar?
If you take a look at the pizza, the marginal utility over the price is 100 utils (or units
of satisfaction) divided by $2.50; the pizza yields 40 units of utility per dollar.
The Coke gives 50 units of utility, and costs a dollar, so it yields 50 units of utility
per dollar.
Coke wins this one.
But hold on a minute -- once I buy the Coke, the marginal utility of Coke falls, and then
what?
Eventually, as the consumer continues the pattern of choosing the greatest marginal
utility per dollar spent, an equilibrium will be reached.
Consumer equilibrium occurs when the marginal utility per last dollar spent is equal across
all goods, and all income has been spent.
Think about it this way: what if this isn't true?
What if, say product K gives more satisfaction per dollar than any other product?
I’d do better to cut back elsewhere, and buy more of product K. Similarly, if product
W gives less marginal utility per dollar spent, you'd want cut back on W, until all were equal.
OK, look: assume a consumer has a weekly income of $100, which he spends completely on three
commodities: pizza, beer and cigarettes.
The price of pizza is $12, the price of beer is $8, and the price of cigarettes is $4.
What combination of pizza, beer and cigarettes is this consumer going to choose?
Right now, there just isn't enough information to answer this question.
It's not enough to know your consumer's budget; you also need to have information about his
or her preferences.
For example, if this were me I don't drink or smoke, so I’d spend all of my money on
pizza.
This means we need some additional information about our hypothetical consumer.
Remember when we went through the cookie activity?
The utility figures reflected the consumer's tastes and preferences.
I'm going to use the following table to determine our consumer's preferences.
Notice, that for each product, the Law of Diminishing Marginal utility holds.
And remember: our consumer has $100, price of pizza is $12, price of beer is $8, and
the price of cigarettes is $4.
Pretend for a moment that you are this consumer, and like all consumers, you’re a utility
maximizer.
What would you choose first?
The first pizza, the first beer, or the first cigarettes?
It's easy to go astray on this one, because the first pizza yields the greatest additional
utility.
The problem is that the 85 units of utility are also more expensive than the alternatives.
To figure out where to get the biggest bang for your buck, we're going to have to calculate
not just marginal utility, but marginal utility per dollar spent.
This isn’t too hard; all we need to do is divide each of the marginal utility figures
by the price of that product.
For example, that first pizza?
Yes, it yields 85 units of added utility, but those 85 units will cost you $12!
That means that the first pizza really yields 7.08 units of utility per dollar.
Is this the best you can do?
No; take a look at that first pack of cigarettes -- even though it has a lower added utility
than either pizza or beer, it's also cheaper than the other products.
Per dollar, the cigarettes yield more additional satisfaction.
So the consumer's first choice is to buy the first pack of cigarettes.
At $4, the consumer still has $96 left.
What will he choose next?
Now that the first pack of cigarettes has been consumed, the question is: will this
consumer choose the first pizza, the first beer, or the second pack of cigarettes?
At 12 units of utility per dollar, cigarettes still win out over the first pizza (7.08 units
of satisfaction per dollar), and the first beer (8.75 units of satisfaction per dollar).
So the consumer chooses the second pack of cigarettes, leaving him with $92.
And so the process goes: the consumer chooses a third pack of cigarettes, leaving $88, and
then switches to his first beer (apparently he's thirsty after three packs of cigarettes).
He still has $80 left, so he continues, going right back to cigarettes; next is the second
beer, then finally some food, with the first pizza.
Still having $56, our consumer keeps going.
The third beer, the fifth cigarettes, then second pizza, followed by the fourth beer.
Now stop for a minute.
What you notice about the next choice?
What would be the best option: the third pizza, the fifth beer, or the sixth cigarettes?
They all yield five additional units of utility per dollar.
Each of them would be an equally good choice.
Coincidentally enough, our consumer has $24 remaining -- exactly enough to purchase one
more of each commodity, with zero leftover income.
In the end, THIS consumer, given $100, will choose three pizzas, five beer, and six cigarettes,
for a total utility of 717 units of satisfaction.
I can tell this by adding up the marginal utilities from the units consumed.
You take a look at the pizza -- the first gave 85, the second gave 72, the third gave
60, for a total of 217 units of satisfaction from those three pizzas.
You can calculate for the cigarettes and beer as well; overall total 717 units.
This consumer has achieved consumer equilibrium, where the marginal utility per last dollar
spent for each good is equal.
No other combination gives greater utility.
Just to prove this to yourself, you could spend your hundred dollars in either of the
following ways but what would you total utility be?
NEXT TIME: Indifference curves TRANSCRIPT0 (MICRO) EPISODE 18: CONSUMER EQUILIBRIUM