Finding consumer surplus without a graph

This post goes over one example of finding consumer surplus, if you would like more information on consumer surplus, including what it is, and how to calculate it using a general form, check out this other post.

Here is the actual question we are going to discuss in this economics post:

Nick can purchase each milkshake for $2. For the first milkshake purchased Nick is willing to pay $4, for the second milkshake $3, for the third milkshake $2 and for the fourth milkshake $1. What is the value of Nick's consumer surplus?
a.$2
b.$9
c.$3
d.$10


Most people are able to remember that consumer surplus is the difference between the demand curve and the price paid by the consumer.  However, the trick for this question is to remember that the demand curve is equal to the willingness to pay of the consumer.  It is also possible that the marginal consumer surplus (the consumer surplus from the next unit) is negative.

So we can go through each decision that Nick makes, and figure out what the associated consumer surplus is for that choice.  First, we know that Nick ONLY pays $2 for each milkshake, regardless of the number of milkshakes he purchases.  For the first milkshake, Nick is willing to pay $4, but only has to pay $2, so his surplus is $2.  For the next, he is willing to pay $3, but pays $2 for a surplus of $1.  The third purchase results in no surplus because $2=$2, and for the last purchase he actually has a negative surplus, because he is willing to pay is less than the price he is paying.  This means he gets -$1 surplus from the transaction ($1-$2).

When we add together the surplus from the 1st, 2nd, 3rd, and 4th milkshake we get:

2 + 1 + 0 - 1 = 2

So his total surplus is $2.