Question: Problem 2 Endowment equilibrium: Farmers and miners (54 points) Suppose an economy consists of 2 people: A farmer and a miner. The two individuals have

Problem 2 Endowment equilibrium: Farmers and miners (54 points) Suppose an economy consists of 2 people: A farmer and a miner. The two individuals have identical preferences, u (f,g) = fg, where f is a kilo of food, and g is a gram of gold. The farmer is endowed with 20 kilos of food and no gold. The miner is endowed with no food and one gram of gold. The farmer and the miner can trade food and gold at prices py and p,. In the following, choose food to be the numeraire good, so set py = 1 and equilibrium will determine the price of gold p,. 1. For given prices (py = 1 and p,), solve for the farmer's optimal demand for food and gold given that the farmer has an endowment that has value 20. For given prices (py = 1 and p,), solve for the miner's optimal demand for food and gold given that the miner has an endowment that has value 1 x p,. Determine the equilibrium price of gold, p;. How does the value of the miner's endowment compare to that of the farmer? Illustrate the equilibrium outcome in an Edgeworth Box. Determine the contract curve for the economy. Illustrate the contract curve in the same Edgeworth Box. Now, suppose 8 more farmers identical to the first enter the economy. Determine the endow- ment equilibrium for the economy with 9 farmers and 1 miner. The 9 farmers each have an endowment of 20 kilos of food and no gold. The miner has a gram of gold and no food. Keep that food is the numeraire good, py = 1. (a) What is the equilibrium consumption bundle of a farmer? ) (b) What is the equilibrium consumption bundle of the miner? (c) What is the equilibrium price of gold? ) (d) What happened to the value of the miner's endowment upon the entry of more farmers? Explain

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