Question

Rob consumes two goods, x and y. He has an allowance of $50 per week and is not endowed with either of the goods. If the price of good x increases and his substitution and income effects change demand in opposite directions,

a. good x must be a Giffen good.

b. good x must be an inferior good.

c. WARP is violated.

d. good x must be a normal good.

e. There is not enough information to judge whether good x is a normal or inferior good.

PLEASE SHOW ALL WORK

Answer 1

The correct answer is (b) good x must be an inferior good

Suppose price of good X increases and hence in order to buy more of good X we have to sacrifice more of good Y(because P_x/P_y increases) and hence substitution is more costly now. Hence due to substitution effect demand of X decreases and as it is given that his substitution and income effects change demand in opposite directions. Hence this means that Income effect will result in increase in demand of X.

As price increases this means that her real income(decreases because With this income he can buy less of goods). Note real income is calculated in terms of goods he can buy and now he can buy less of goods because of increase in price X.

Hence Real income decreases and as discussed above Income effect resulted in increase in demand of X.

A good is a normal good if income decreases resulted in decrease in demand and A good is an inferior good if income decreases resulted in Increase in demand.

Here, A decrease in Real income resulted in increase in demand of X and hence Good X is an inferior good.

(Note that a good is a Giffen good if substitution effect and income works in different direction and Size of Income effect > Size of substitution effect and in this case we have not given the size of income and substitution effect. So, we can not say about whether X is a Giffen good or not)

Hence, the correct answer is (b) good x must be an inferior good.