Consider a commodity-money economy like the one described in class. There are 100 identical people in every generation. Each person is endowed with 15 units of the consumption good when young and nothing when old. Assume that each young person wishes to consume 2/3 of their endowment when still young, regardless of the rate of return on money. The initial old own a total of 100 units of gold. Assume that people are indifferent between consuming 1 unit of gold or 1 unit of the consumption good.

1. a)Suppose the initial old choose to use their gold as money rather than con- sume it. Write a equation that represents the market clearing condition for gold. Use it to find the trading value of goldvtg. (5 pts)
2. b)At this value of gold, will the initial old actually choose to consume any of their gold? Why? (2 pts)
3. c)Calculate the rate of return on gold. (3 pts)
4. d)Define the quantity theory of money and the neutrality of money (in terms of the initial stock of gold). Do any of them hold under the current example? Explain. (5 pts)
5. e)Now assume that the initial stock of gold is multiplied by a factor ofk. What is the maximum allowable value of k for which money is still neutral (that is, compared to our starting point)? How about the minimum value? Show your work. (15 pts)
6. f)What is the value ofkfor which each of the intial old consume 2 units of gold? Show your work. (10 pts)