a) We have a consumer who maximizes her utility at a certain point on the budget line. In that point, the budget line must be a tangent to an indifference curve. We therefore have an indifference curve such as I1 and a budget line such as BL1 in Figure S.2.4. The point of utility maximization is point A.
If the price of good 1 is cut by, say, half, the consumer can maximally buy twice the amount she could before. The budget line therefore rotates outwards to BL2, and intersects the X-axis at twice the distance.
Suppose that the consumer buys more of good 1 if the price falls. The new point of utility maximization, where another indifference curve just about touches the budget line BL2, must then be to the right of point A. For instance, it could be at point B. The total effect of the price fall is that the consumer shifts from consuming the quantity q11 of good 1 to the quantity q12. q12 must then be larger than q11.
We will now split the total effect into the substitution- and income effects. We start with the former. The substitution effect is the change in demand on good 1 that only depends on the change in relative prices and not on the increase in the level of utility. To find the size of that effect, we construct an imaginary budget line, BL*. Two things are important with BL*. First, the relative prices must be the same as after the price decrease, implying that BL* must have the same slope as BL2. Second, the level of utility at the point of utility maximization on BL* must be the same as the one the consumer originally had (since the substitution effect does not measure the increase in utility). BL* must consequently be a tangent to the same indifference curve to which the original budget line, BL1, is a tangent: I1.
However, since BL* and BL1 have different slopes, the point of tangency will not be the same for both of them. For BL1 it is point A; for BL* it is point C. From the graph, we see directly that the substitution effect must be positive for price decreases and negative for price increases: If BL* has a slope that is smaller than that of BL1, the point of tangency must be to the right of the previous point. (Note however that the substitution effect can be zero.)
The substitution effect is the increase in consumption of good 1 that corresponds to the distance between point A and point C along the X-axis. The consumer has the same level of utility but consumes more of good 1 since it is cheaper than before in relative terms. Instead, she consumes less of good 2. Note that this is not something you can observe.
BL* and point C are theoretical constructs.
The income effect is the part of the total effect that remains after the substitution effect has been subtracted. It corresponds to the part of the change in demand on good 1 that depends on the fact that the consumer increases her utility; in this case, that she moves from the indifference curve I1 to I2. If BL* would have been a real budget line, an increase in income that had shifted BL* to BL2 would have given the same increase in the demand of good 1. Therefore the name "the income effect."
b) If the good were an inferior good, there would be a slight difference. An inferior good is a good one buys less of when income increases, since one shifts over to other goods of higher quality. Regarding the substitution- and income effects, the inferior good must have a negative income effect. In Figure S.2.4 that would mean point B would have been somewhere to the left of C instead. To construct such a graph, draw the indifference curve such that BL2 is a tangent to it to the left of C, for instance as I3 in the graph.
c) A Giffen good is a special type of inferior good. The odd thing about it is that the income effect is so large that it dominates over the substitution effect. To construct such a graph, draw the indifference curve such that BL2 is a tangent to it to the left of point A. See I4 in the graph.