Intermediate Microeconomics

4. [40 marks] Consider an exchange economy with two goods (salad and milk) and two types of consumers (farmers and cowboys). All consumers have the same utility function 2 Hi = (#3313 + 21/37::M) Farmers are endowed with 2 units of salad and no milk. Cowboys are endowed with 1 unit of milk and no salad. Normalize the price of salad to p3 = $1. First, suppose that there is exactly one farmer and one cowboy. (a) Find all Pareto efcient allocations. (b) Find a competitive equilibrium. (c) Draw a clearly labeled Edgeworth box with the initial allocation, the equilib- rium allocation, the set of all Pareto eicient allocations, and the equilibrium budget line. Now, suppose that there are n > U farmers and m > U cowboys. (e) 'Write down the equations needed to nd an equilibrium. (E) If you want the relative price of milk to be equal to 1, do you need to have more farmers, more cowboys, or exactly the same amount