Not always downward sloping these complications are

not always downward sloping. These complications are something we postpone for another
day.
5 Consumer°s surplus and the demand curve
9

is simply the area under the inverse demand curve between the points 0 and x on the x -axis:
u ( x ) =
Z
x
0
u
0
( x ) dx:
The second term, px , is the area of the rectangle below the price line and between the points
0 and x on the x -axis. The di/erence between these two terms is the area of the triangle
between the inverse demand curve and the price line. This is also the value of ° u ³ ° m , where
° u is the utility achieved at the optimum. In other words, this is another way of °nding
consumer°s surplus .
We can also use this approach to measure the change in utility that results when prices
change. For example, suppose that the price of the good falls from p = 1 : 2 to p
0
= 0 : 75 . How
much would the utility change? This is equivalent to asking, ±How much does the consumer³s
surplus change?²If the consumer³s surplus is always the area between the inverse demand
curve and the price line, the change in consumer surplus will just be the di/erence between
these areas for the two prices. In other words, it will be the area bounded by the two price
lines and the inverse demand curve.
0 1 2 3 4 5
0.0
0.5
1.0
1.5
2.0
2.5
x
p
Change in CS
Price and consumer surplus