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.

(0.5 marks) Find the consumer's MRS between the two goods (i.e., marginal utility of x₁ divided by marginal utility of x₂).

(0.5 marks) Write down the equation for the consumer's budget line and the slope of the budget line where x₁ is on the horizontal axis and x₂ is on the vertical axis.

(2 marks) Solve the consumer's optimization problem and express the demand for the two goods in terms of prices and income.

(5 marks) 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.

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

(3 marks) 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

(3 marks) 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 fromp₁ = 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 _____________.