April 2004 Q6

You have the following data on the price of good X and the quantity sold of good X.
If the market price is set at £12 what is the total value of consumer surplus?

Price of good X Quantity of good X sold
£15, 1
£14, 2
£13, 3
£12, 4
£11, 5


Can someone please explain how to calculate this, since I really do not seem to understand this.
(The total expenditure for each would be price x quantity (i.e. 15*1, 14*2,...11*5).
I'm not sure how to work out the total utility.

Since I know that after calculating the total utility of the above quantities, I would difference these to find the marginal utility. Then I would see which were higher than £12 and difference these with the £12, and sum these differences up to get the total consumer surplus....)


This is my thinking, and even if it is correct/incorrect, could you please give a FULL explanation as would like to see how someone else thinks about this type of question.

Thanks!

 

Answer is £6.

Total expenditure is 4 x £12 = £48.
Total utility is £15 + £14 + £13 + £12 = £54.
So total consumer surplus is £54 - £48 = £6.

It has nothing to do with marginal utilities.





Think of it this way:

If the price is £16, no one will buy it (this is not stated, but we can assume this is the case since demand curves slope downwards).

If the price is £15, one person will buy it (call this person Alan)

If the price is £14, two people will buy it (one of which is Alan, the other is now Bob)

If the price is £13, three people will buy it (Alan, Bob, and now Charlie)

If price is £12, four people will buy it (Alan, Bob, Charlie, David)

If the price is £11, five people will buy it (Alan, Bob, Charlie, David, Eric)

Now, price is £12, then ABCD will buy it.

A would have paid £15 (A's total utility), but ended up paying £12, so his consumer surplus is £3.
B would have paid £14 (B's total utility), but ended up paying £12, so his consumer surplus is £2.
C would have paid £13 (C'stotal utility), but ended up paying £12 so his consumer surplus is £1.
D paid the maximum he would have paid anyway (D's total utility is £12).
(For E, he would have paid £11, but since price is £12 he won't purchase it).

Total consumer surplus is £3 + £2 + £1 = £6.





Alternatively, if you look at it on a graph, you can quickly draw the demand curve, which is a straight line starting at (0, £16) and going down to (5, £11).

Then draw a horizontal line at the market price, £12.

The total consumer surplus is the area between the market price and the demand curve, which is a triangle of area 6.


You can apply the same principle if you are looking at the demand curve of just one person. E.g. if you were asking for Alan's consumer surplus, knowing that the price and quantity figures presented in the question were relating to him only (i.e. he would buy one unit if price were £15, two units if it were £15, and so on), then on the first unit he would have received a consumer surplus of £3, on the second he would have received a consumer surplus of £2, £1 on the third, and £0 on the fourth unit. If market price is £12 he won't buy a fifth unit. So again his individual consumer surplus is £6.

 

Just to fill in a bit on marginal utility ...

Marginal utility is the extra utility (or satisfaction) from consuming an additional unit. Marginal utility falls as consumption increases. So, in this question, the person's marginal utility of the first unit in money terms is £15, the marginal utility of the subsequent units is £14, £13, £12 and so on.

The rational consumer will not consume a unit if the price he or she has to pay is greater than the extra satisfaction gained from the unit, so if the price is £15, he will only demand 1 unit.

If the price is £12, the consumer will demand 4 units. He will get total utility of £15 from the first unit, £14 from the second, £13 from the third and £12 from the fourth, making a total of £54 worth of utility. He will pay £12 x4 = £48.

His consumer surplus is total utility - expenditure = £6.

Alternatively, you can see consumer surplus as the sum of the consumer surpluses gained from each of the 4 individual units, ie (£15-£12) +(£14-£12) + (£13-£12) +(£12-£12) = + £3 +£2 +£1 +£0 = £6.

 

But that is if the demand curve is for one consumer and not for the whole market, which it appears to be from the question, right?

 

I guess from the very low number purchased that the market might just consist of one person! As the price falls, the consumer buys more.

To get to the market demand curve we have to add up all the individual demands at each price.

Suppose we have two consumers with the following marginal utility schedules:

Q (per day): 1 2 3 4 5
MU(A) in £: 15 14 10 5 0
MU(B) in £: 13 12 9 6 2

MU is the extra satisfaction gained from consuming the extra unit, so it is measuring how much the extra product is worth to the consumer.

If the price is £15, A will buy one but B won't buy any (since he won't pay more than it is worth to him).
If the price falls to £14, A will buy two but B is still not interested.
If the price falls to £13, A will still only buy 2 because the MU of the third is only £10, but B will now buy one, so the total demand is three.
If the price falls to £12, A will buy two and B will buy two, so the total demand is four per day.

So when the price is £12, (ie everyone pays £12) A will get £3 + £2 consumer surplus, and B will get £1 + £0 consumer surplus, so total consumer surplus is £6.

(The total utility of A is £15 + £14 = £29; and the total utility of B is £13 +£12 = £25; so the total utility of A and B is £29 + £25 = £54; the total expenditure is £12 x 4 = £48; so the consumer surplus is £6.)