If your demand for some good X is X I PxPy X equals Income

If your demand for some good X is:

X = ___I__

Px+Py

( X equals Income divided by Price of x + Price of y) (ie Px*X+Py*Y=I)

a) Is X a normal or inferior good? Show me how you know.

b) Is good Y a substitute or complement for good X? Show me how you know

a) X is a normal good because as Income will increase, price remaining same; demand for X will increase and vice versa.

Say when I = 100

Px = 2

Py = 3

Demad for X = 100/2+3 = 100/5 = 20 units.

If income increased ot 200, it will be 200/5 = 40 units. If with increase in income, demand for a good increases and vice verca, it is a normal good.

b) X and Y are complementary because with increase in price of Y, demand of X is decreasing and vice verca.

In above case, suppose all else remaining same, PY increases to 4 new demand will be

100/6 = 16.66 units.

With increase in price of Y, demand for X decreased from 20 units to 16.66 units. Hence X and Y are complementary goods.