Microeconomics 3: Income-Substitution Effect (Slutsky), Revealed Preferences and Edgeworth box

Question 1

You’ll need the demand function

Describe and interpret what the inverse demand function is

Answer 1

For a utility function 𝑈(𝑥, 𝑦) = 𝑥^𝑐 x 𝑦^𝑑, the solution for optimal consumption of
good 𝑥 is:
𝑥 = 𝑐 / 𝑐+𝑑 x 𝑚/𝑝bottom right𝑥
 We can transform it and then:
𝑝bottom right𝑥 = 𝑚𝑐/𝑥(𝑐 + 𝑑)
 The first representation is a demand function, the second – is the inverse
demand function.
 Interpretation: the downward sloping inverse demand function shows also the
willingness to pay more when the amount of good x is little and less as x grows
larger.

Question 2

Describe the inverse demand function graphically

Answer 2

If the demand curve is viewed measuring price as a function of quantity, we
have the inverse demand function
Graph with “Pbottom rightx” y-axis and “X” x-axis and a negative curve that’s decreasing less & less. Curve labelled “Inverse demand curve Pbottom rightx(x)

Question 3

Illustrate & describe the overall effect from a change in price of a good. Then illustrate & describe the substitution effect. Then illustrate & describe the income effect

Answer 3

Graph with “y”-axis and “x”-axis and 2 straight budget constraint lines. Both start at same point on y-axis but one has steeper gradient than another. Each budget constraint has a tangent to an IC. The ICs are parallel to each other. The tangent at the steeper budget constraint is “A” and the other is “B”. The difference between A and B is “Total increase in x”.
Suppose the consumer is
maximising utility at point A.
If the price of good x falls, the
consumer will maximise utility
at point B.

On previous graph, there’s now a purple dotted budget constraint line, parallel to the previous budget constraint with less steep slope, going through A (imaginary budget constraint). There’s a new IC that matches for this budget constraint as the lowest point of this IC touches this imaginary line and is point “C”. The difference between A and C, labelled at x-axis is “Substitution effect”.
To isolate the substitution effect, we
hold purchasing power constant but allow
the relative price of good x to change:
➢The substitution effect is the
movement from point A to point C;
➢The individual substitutes good x for
good y because x is now relatively
cheaper

There’s a difference showing between point C and B, at x-axis it’s labelled “Income effect”
The income effect occurs because the
individual’s “real” income changes
when the price of good x changes:
- The income effect is the
movement from point C to
point B;
 If x is a normal good, the
individual will buy more
because “real” income
increased

Question 4

Describe the price changes for normal goods and inferior goods

Also, compare in what direction substitution effect operates vs income effect

Answer 4

If a good is normal, substitution and income effects reinforce one another
 when price falls, both effects lead to a rise in quantity demanded;
 when price rises, both effects lead to a drop in quantity demanded.

If a good is inferior, substitution and income effects move in opposite directions
and the combined effect is indeterminate:
 when price rises, the substitution effect leads to a drop in quantity demanded, but the
income effect is opposite;
 when price falls, the substitution effect leads to a rise in quantity demanded, but the
income effect is opposite

Substitution effect always operates in the same direction - we’re substituting towards the relatively cheaper good. Income effect can work in either direction