Okay we're going to do a similar exercise
to what we did in the previous spreadsheet
but now we are going to vary the price of
good X rather than varying income which we
did in the previous spreadsheet. The preferences
that are here are a little bit different than
the ones before. Before we were actually in
a quadratic world. That's how I was able to
derive inferior goods and be able to plot
the income consumption path. To enable me
to plot this price consumption curve here
I've changed the preferences. We're now in
what's called a Stone-Geary world. So the
preferences are a little different. And as
a result the controls have changed a bit.
So let me show that for a second. Let's move
over here and move down. You have two different
controls. You can change income and you can
change price. That is you can affect the budget
line. But there is no control now for the
preferences. So the preferences are going
to stay fixed in this exercise. And what I
am going to do now is vary the price of X.
Let's raise the price a little bit. Let's
raise it a lot. That moves the intercept on
this axis in. Notice that the choice point
as I raise it stays on this dotted curve which
is the price consumption curve. So the price
consumption curve shows the choice point as
we vary the price of X. And there I'm raising
it. And now let's lower it back again. And...when
you lower the price of X you're getting more
X.
You can show that relationship here. Let's
move further to the right here. So here's
that same choice point. Now I'm plotting the
price of X against the quantity of good X.
And as I lower the price.... Let's lower it
again. I get more of good X. As I raise the
price... I get less of good X. So the demand
curve for X as we expect slopes down.
Let's go back to the original diagram. I want
to make one more observation about this price
consumption curve. You can actually infer
elasticity of demand for good X by the following.
Along the price consumption curve for changes
in the price of X, the price of Y is staying
fixed. So the expenditure on Y depends on
the amount of Y consumed. And you can't really
tell this but this curve is actually sloping
down throughout. As I lower the price of X
I'm actually buying less Y. And therefore
I'm spending less on Y. Income is also not
changing. So I must be spending more income
on good X as I lower its price which means
demand is actually elastic for good X. So
again, you can infer demand elasticity of
X from the.... slope of the price consumption
curve by first looking at the consumption
of Y. And Y consumption is falling as the
price of X falls. So expenditure on X must
be rising as the price of X falls.
