The Slutsky-Equation and Various Elasticity Calculations
R. Pope
In Figure 5.3 of the text, a price change is decomposed into income and substitution
effects. This turns out to be a very important exercise so stay with it. In the Figure the
price of x falls. The original equilibrium is at x* and y*. As p
x
falls, the equilibrium
consumption changes to x** and y**. Thus, x isn’t a Giffen good. As p
x
falls more of the
good is consumed.

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The movement from x* to x** are two points on an ordinary demand curve.
Now, decompose the movement from x* to x** into an income effect and a substitution
effect. The substitution effect lets price change but keeps a person’s real income constant.
Here real income constant means that one is on the same indifference curve. It can be
thought of as the following: if p
x
falls, real income has gone up. Let the new price of x
prevail but take away enough income so that the individual is on the same indifference
curve. That level of income is shown as a dotted line in Figure 5.3. What would the
person consume in such an experiment: B in Figure 5.3 were the new budget (price ) line
is tangent to the original indifference curve. x
B
is a point on the compensated demand
curve x
c
(p
x
,p
y
,U) that we have seen before. It is not yet shown on the graph but we can
p
x
x(p
x
,p
y
,I)
p
x
2
p
x
1
x*
x
B
x**