A consumer has the following utility function

U (x₁, x₂) = x₁(x₂ + 4)

Prices of the two goods x₁ and x₂ respectively are p₁ and p₂ and the consumer has income m. We assume that all prices and income are strictly positive. Furthermore, throughout this question we assume that m > 4p₂.

Consumer expenditure data in developing countries show that individuals

• spend more than half of their income on food
• proportion of income spent on food declines as income increases.

(i) Can either of the two goods - x₁ or x₂ - represent food? Explain your answer.

(ii) Compute the missing values of elasticities in the following table assuming M=10,p₁ =2, and p₂ =1.

	x2
Income elasticity
Absolute value of own price elasticity
Cross price elasticity

(iii) While x₂ is produced locally, x₁ is transported from a different region. Assume p₂ = 1. Building a new railroad (that connects the regions) will reduce transportation cost which in turn will reduce the price of good 1 from p₁ = 2 to p₁ = 1. Railroad will be funded by taxes which will reduce each consumer's disposable income from m = 10 to m = 10 - T. A utility-maximizing consumer will accept higher taxes as long as

T _____________.