The area above the line isn't feasible to achieve given the prices of
the two goods and the budget available. If incomes were to increase, say
to £40 or the prices of both goods were to fall by the same percentage
we would see the budget line shift as is shown in this next diagram. The
rule is, changes in income or equal changes in price will cause the
budget line to shift parallel to the original curve. Here's the new
curve with an increased budget of £40:
The slope of the line here represents the relative price of the two
goods. So in the example above it was 30/15 = 2 for the first line and
40/20 = 2 for the second line. The rule of thumb for that is Price of Y /
Price of X. Prices can also change independently of each other, as we
well know. If one price changes and the other doesn't, this causes a
pivot on the diagram. If good X changed from £2 to £1 we'd see a pivot
around the initial point on the Y axis. This next diagram will show
that:
The pivot here is quite clear, as the price of good X decreases it means
more can be consumed while the consumption of good Y remains constant.
Next, we'll move on to a more complex concept - the optimum consumption
point! This is where we combine the budget line from above and the
indifference curves from the blog post I did a few days back. By
definition, the optimum consumption point will be where the budget line
touches the highest indifference curve on an indifference map. As with
most concepts, this is also much easier to understand when represented
on a diagram:
Here you can see that the budget line touches, or is tangential, to the
indifference curve L2, which is the highest one it touches. Therefore we
can say that the optimum consumption point for these two goods would be
X1 of good X and Y1 of good Y. We know the slope of the budget line is
Px / Py and we know from the previous blog post that the indifference
curve slope at any point is MuX / MuY. Therefore, the optimum
consumption point is the point where (Px / Py) = (MuX / MuY)!
A change in income will cause a change to the diagram. The budget line
will either shift out or in depending on whether incomes rose or incomes
fell. This new budget line would cross and indifference curve at a
different point, if you joined the new optimum consumption point and the
old one you'd have created a new line that we call the
income-consumption curve in economics. As with a change in price of one
of the goods, the budget line will pivot and a new optimum consumption
point will be formed. Connect the original point and the new point and
this line you've created is called the price-consumption curve.
Now for the exciting bit! Actually deriving a consumers demand curve for a good!
Ok, there is a demand curve derived for good X using the indifference
curves and budget lines. Look at it, take it in, see if you can see
what's going on. It's difficult, I know. Here's my explanation attempt:
On the top diagram we have used good X along the bottom and money for
all other purposes on the Y axis. We have a set budget and at varying
prices of X this budget line is pivoting. Each of these new pivoted
budget lines crosses indifference curves at different points to form a
price-consumption curve. The points of intersection of each budget line
translate down to as the quantities demanded of good X. Now, to work out
the prices for the second diagram. Lets look at the first budget line
for this. It crosses L1, we can see that. At that point it has
translated down to the bottom diagram as Q1. The price here is the same
as the slope of the curve.. so assuming we have a budget of £30 I'd say
the budget line hits the X axis at roughly 17. So, 30/17 = 1.76, which
is the roughly where the point is on the second diagram. If we did the
same for the other two budget lines we'd receive prices of 1.2 and 0.94.
These are those two other price points you can see on the diagram. Then
as with any other demand curve, join the dots to actually complete the
demand curve for good X. PHEW!