Consider a commodity money model economy with the following features: - There are 100 identical people in each generation.

- Each individual is endowed with 15 units of the consumption good when young.

- To keep things simple, assume that each of the young wants to acquire money balances worth 1/3^rdof hisyoungendowment, regardless of the rate of return.

- The initial old own 200 units of gold and 100 units of silver. Both gold and silver could be used for consumption or as a medium of exchange or both.

- Assume that individuals are indifferent between consuming 1 unit of gold and consuming 3 units of the consumption good and also indifferent between consuming 1 unit of silver and consuming 2 units of the consumption good.

Let number of units of gold purchased by each individual is given by,m_g^t,price of gold is given byv_g^t,number of units of silver purchased by each individual is given by,m_s^t,price of gold is given byv_s^t. Both gold and silver can be stored and easily exchanged.

(a)Write down the lifetime budget constraint of an individual by including the information above. Show your steps. (4 marks)

(b)Consider the economy with gold only for parts b, c and d of the question.Suppose the initial old choose to sell their gold for consumption goods instead of consuming it. Write equation that represents the equality of supply and demand for gold. Use it to find the number of units of gold purchased by each individual and the price of gold. Explain your steps. (2+2+2 = 6 marks)

(c)At this price of gold, will the initial old actually choose to consume any of their gold? Explain. (1 mark)

(d)Now consider both gold and silver available in the economy. Find the money market clearing condition if both gold and silver are used as money. For what range of values of silver, is there an equilibrium in which both silver and gold are used only as money (and not consumed)? Explain your steps. (2+2 = 4 marks)