Suppose your engle curve for X is given by the equation XabI

Suppose your engle curve for X is given by the equation: X=a+bI, where I is income and a and b are constants.

A. If you income increases from I to I+delta I, by how much does X increase?

B. Write down the formula in terms of X and I for your income elasticity of demand for X.

C. Use the equation X=a+bI to eliminate I from your formula and write a formula for income elasticity in terms of X alone.

D. As you consumption of X increases, what happens to your income elasticity of demand for x?

E. If you engle curve is a line through the origin, what is your income elasticity of demand for x?

Solution

Part A.

When I becomes I + delta, then X\' = a + b (I + delta) = a + bI + b* delta = X + b* delta

So, increase in X = b* delta

Part B:

Income elasticity of demand is calculated as per the following:

Ln X = Ln (a + bI)

Differenting both sides,

dX/X = dI/I [b / (a + bI)]

(dX/X)/(dI/I) = b / (a + bI)

Income elasticity of demand = b / (a + bI)

Part C:

Income elasticity of demand in terms of X is given by b / X.

Part D:

As X increases, income elasticity of demand will fall, as X is in the denominator of the elasticity formula.

Part E:

As in the original equation, \"a\" will change to zero, if the line goes through origin. As it is not a part of the elasticity formula, then the formula will remain unchanged. It will be b / X or 1 / I.