# elasticity of income if price changes by 10 percent

Arista always spends 10 % of her income on whatzits. Assume that her income increases by some percentage while the price of whatzits remains constant (and that all whatzits cost the same). What is her income elasticity of demand for whatzits?

I know elasticity of demand is either less than 1 or more than 1. Since the equation for elasticity of income is quantity divided by income I dont understand what number to put for the numerator.

? / 10 %. = 1

Will the answer be positive 1 or negative 1.

• "the equation for elasticity of income is quantity divided by income" This is false. – Giskard Oct 18 '19 at 6:08
• I would start by writing out the formula for income elasticity – Brennan Oct 26 '19 at 23:22

Try work it out step by step and don't just concentrate on the math.

Suppose Arista has income of $$w$$, and the price of whatzits is $$p$$. She spends 10% of that on whatzits, so how many whatzits does she buy? Let's call this $$q$$.

Now suppose income is now $$x \cdot w$$ (so if her income increases by 3% then $$x$$ is 1.03.) The price of whatzits is still the same, $$p$$. How many whatzits does she buy now? Let's call this $$q'$$.

The income elasticity of [quantity] demand[ed] is simply the percentage change in quantity demanded divided by the percentage change in income:

$$e = \frac{\frac{q' - q}{q}}{\frac{xw - w}{w}}.$$

You need to be clear on which one is the effect and which one is the cause in the elasticity formula. Also this formula relates two percent changes of x and y and not proportions (which is a different concept).

In this case, it seems that the income changes (and price remains constant), so we want to see the effect on the demand (quantity). Therefore Var%Income*e =Var%Demand, where e=elasticity.

• What do you mean by Var%Income*e =Var%Demand? – Art Nov 17 '19 at 8:52