Question

Lisa has an income of $1000 per month. She buys only food and non-food item. In...

Lisa has an income of $1000 per month. She buys only food and non-food item. In this question, treat non-food as a numeraire, letting the price equal to 1, while the price of food is p. Suppose Lisa’s preference is to consume exactly 3 units of non-food for every 1 unit of food.

1. Derive her demand for food.

2. If p = 2, how much food does she buy? Suppose the price of food increased by 50%, how much food does she buy now? Is her food demand elastic or inelastic? (confirm by calculating the price elasticity of demand: Ed = ∂x1 ∂p1 p1 x1 )

3. Suppose her income doubles, what is the quantity demanded of food and non-food after the income doubles? If there is any change, explain the change in 1-2 sentences.

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Answer #1

a) 1 unit of food and 3 units of Non-food are perfect complements.
F = M/(3+ P) = 1000/(3 + P)

b) F =  1000/(3 + 2) = 200

New price = 2 x 1.5 = 3

F =  1000/(3 + 3) = 166.67

Elasticity = Percentage change in quantity/percentage change in price = 16.67/50
This is less than 1. Hence, the demand is inelastic.

c) New income is 2000
F = 2000/(3 + 2) = 400
NF = 3 x 400 = 1200

Doubling of income leads to doubling of quantity demanded of food and non-food items.

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