Question

A consumer always spends 50% of his monthly income on food. Introduction of value added tax on food items has led to a 20% increase in food prices while his monthly income remained unchanged. The consumer’s price elasticity of demand for food is __________. (in integer) 
 

Hint:

If a consumer spends a constant fraction of income on a good, the demand is unit elastic ($E_p = -1$).

Answer 1

Correct Answer: -1

Step 1: Recall the property of constant expenditure share.
If the consumer spends a constant proportion of income on a good, the expenditure share remains fixed despite price changes.
Step 2: Use elasticity relationship.
Let $P$ = price, $Q$ = quantity, and total expenditure $E = P \times Q$. If $E$ is constant, then \[ P \times Q = \text{constant} \Rightarrow Q \propto \frac{1}{P}. \] Hence, \[ \text{Price elasticity of demand} = \frac{\%\Delta Q}{\%\Delta P} = -1. \]
Step 3: Conclusion.
\[ \boxed{\text{Elasticity of demand} = -1.} \]