Question

nour likes green pens. Yesterday, she opened his desk drawer and found no green pens. So, bought three green pens without worrying too much about their price. Assume that nour’s budget is M, denote X for green pens, and denote Y for all other goods.

a) Apply the Slutsky equation to nour’s demand for green pens as a Giffen good.

b) Graphically show nour’s demand for green pens using Marshallian and Hicksian demand curves from nour’s indifference curves.

c) On your graph, show the following very clearly: the Hicksian monetary compensation, the Hicksian substitution effect, the Marshallian income effect, and the total Marshallian demand effect

Answer 1

A. The Slutsky equation to nour’s demand for green pens as a Giffen good.

The Slutsky equation (or Slutsky identity) in economics, named after Eugen Slutsky, relates changes in Marshallian (uncompensated) demand to changes in Hicksian (compensated) demand, which is known as such since it compensates to maintain a fixed level of utility. There are two parts of the Slutsky equation, namely the substitution effect, and income effect. In general, the substitution effect is negative. He designed this formula to explore a consumer's response as the price changes. When the price increases, the budget set moves inward, which causes the quantity demanded to decrease. In contrast, when the price decreases, the budget set moves outward, which leads to an increase in the quantity demanded. The equation demonstrates that the change in the demand for a good, caused by a price change, is the result of two effects:

A 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.

B. Graphically show nour’s demand for green pens using Marshallian and Hicksian demand curves from nour’s indifference curves.

Marshallian and Hicksian demands

Marshallian and Hicksian demands stem from two ways of looking at the same problem- how to obtain the utility we crave with the budget we have. Consumption duality expresses this problem as two sides of the same coin: keeping our budget fixed and maximising utility (primal demand, which leads us to Marshallian demand curves) or setting a target level of utility and minimising the cost associated with it (dual demand, which gives us Hicksian demand curves). We must also look at the Lagrangian functions where we obtain the first derivatives.

This leads us to the main difference between the two types of demand: Marshallian demand curves simply show the relationship between the price of a good and the quantity demanded of it. Hicksian demand curves show the relationship between the price of a good and the quantity demanded of it assuming that the prices of other goods and our level of utility remain constant. This makes sense when we look at consumption duality: for dual (Hicksian) demand, we maintain a fixed level of utility, and so our level of wealth, or income, must remain constant. We simply cannot be as satisfied if we do not maintain equal purchasing power.

Marshallian and Hicksian demand curves meet where the quantity demanded is equal for both sides of the consumer choice problem (maximising utility or minimising cost). For prices above this equilibrium point, consumer wealth is higher with Hicksian demand curves than Marshallian demand curves, because to maintain utility constant, Hicksian demand curves assume real wealth remains unchanged. Marshallian demand assumes only nominal wealth remains equal. The opposite is true for prices below this point: Marshallian demand assumes that as nominal wealth remains the same but price levels drop (negative inflation), the consumer is better off. Hicksian demand assumes real wealth is constant, so the individual is worse off. This is why Marshallian demand curves are more ‘stable’: they reflect both rent effect and substitution effect. Hicksian demand curves only show substitution effects (utility is constant, therefore rent must remain constant), which means that demand varies with price only because other options become more attractive.

C. graph, show the following very clearly: the Hicksian monetary compensation, the Hicksian substitution effect, the Marshallian income effect, and the total Marshallian demand effect