Question

1. Write down the Slutsky equation.  (10)
2. Use the Slutsky equation to explain why it is unlikely that there could be a Giffen good.  (15)

Answer 1

Answer a: There are two parts of the Slutsky equation, namely the substitution effect, and income effect.

The equation demonstrates that the change in the demand for a good, caused by a price change, is the result of two effects as said earlier:

• substitution effect: the good becomes relatively cheaper, so the consumer purchases other goods as substitutes
• income effect: the purchasing power of a consumer increases as a result of a price decrease, so the consumer can now afford better products or more of the same products, depending on whether the product itself is a normal good or an inferior good

Slutsky managed to do was find an equation that decomposes this effect based on Hicksian and Marshallian demand curves

Mathematically, it is based on the derivatives of Marshallian and Hickisan demands:

The left hand side of the equation is the total effect- that is, the derivative of x (quantity) respect p (price). It shows us how much the total quantity of x that we consume varies when we change price. The next part is the substitution effect- how much the variation is due to us finding similar options. It is obtained from the derivative of the Hicksian demand with regards price. The right hand side is the income effect, how much changes in our purchasing power affect the amount we consume of a certain good. It is the derivative of the Marshallian demand with regards wealth (multiplied by the quantity).

Detailed derivation of slutsky Equation:

Answer b:  Giffen good is a product that is in greater demand when the price increases, which are also special cases of inferior goods.

In the extreme case of income inferiority, the size of income effect overpowered the size of the substitution effect, leading to a positive overall change in demand responding to an increase in the price. Slutsky's decomposition of the change in demand into a pure substitution effect and income effect explains why the law of demand doesn't hold for Giffen goods.

∂x /∂I < 0, ∂x/ ∂p | U=U<0 .

Similar to a conventional inferior good, the income and substitution effects are countervailing. But what’s special about a Giffen good is that the income effect dominates the substitution effect (in some range): a rise in the price of a Giffen good causes the consumer to buy more of the good (so, demand is effectively upward sloping). Even though a price increase reduces demand due to the substitution effect holding utility constant, the consumer is effectively so much poorer due to the income loss that her demand for the inferior good rises.