The demand for good x is x IPxPy Is X an inferior or normal

The demand for good x is

x= I/(Px+Py)

Is X an inferior or normal good? Show work.

Is good Y a substitute or complement for good X? Show work.

Solution

(a)

X is a normal good if, with increase in I (income), demand for X increases.

Here, if I increases, ceteris paribus X (demand) increases (from the left side). So X is a normal good.

(b)

As price of Y increases, (Px + Py) increases and [I / (Px + Py)] decreases, or X decreases. So, X and Y are complements (for complements, higher price of one good will lower demand for the other good).