1. If p₁ and p₂ are the per unit prices of goods 1 and 2, determine the utility maximizing demand of consumer B for each good as a function of p₁ and p₂ .
2. If p₁ and p₂ are the per unit prices of goods 1 and 2, determine the profit maximizing demand of the firm for good 1 as a function of p₁ and p₂.
3. If p₁ and p₂ are the per unit prices of goods 1 and 2, determine the utility maximizing demand of consumer A for each good as a function of p₁ and p₂.
4. Treat good 1 as the numeraire and set p₁ = 1. Determine the value of p₂ which clears the market, i.e., supply equals demand.