Tutorial Question 3 (for reference)

Consider a two-person (A and B), two-commodity (1 and 2) pure exchange economy. Suppose that individual A's preferences can be represented by the utility function U^A(q₁^A, q₂^A) = q₁^A + ln(q₂^A), where q₁^A is individual A's consumption of commodity one and q₂^A is individual A's consumption of commodity two. Similarly, suppose that individual B's preferences can be represented by the utility function U^B(q₁^B, q₂^B) = q₁^B + 2ln(q₂^B), where q₁^B is individual B's consumption of commodity one and q₂^B is individual B's consumption of commodity two. Individual A is endowed with one units of commodity one and two units of commodity two, while individual B is endowed with two units of commodity one and one unit of commodity two.

Tutorial Question 4 (this is the question I need help in)

Consider once again the economy that was described in Tutorial Question 3. Suppose that both individuals are price takers who face the common price vector (p₁, p₂), where both prices are strictly positive and finite. Let commodity two be the numeraire for this economy, so that we can normalise the price of commodity two to be "one". This allows us to write the price vector for this economy as (p₁, p₂) = (p, 1), where the price ratio (p = p₁/p₂) is strictly positive and finite.

1. What is the budget constraint that faces individual A? What about individual B?
2. What is the budget-constrained utility maximisation problem for individual A? What about individual B?
3. What are individual A's uncompensated demands for commodity one and commodity two? What about individual B.
4. What are the market clearing conditions for commodity one and commodity two? Use one of these conditions to solve for the competitiveequilibrium price ratiop*. Confirm that this equilibrium price ration also ensures that the other market clears.
5. Use the uncompensated demands for each commodity by each individual and the competitive equilibrium price ratio to find the competitive equilibrium commodity allocation of commodities to each individual.
6. Illustrate your answers in an Edgeworth-Bowley box diagram.