**please answer all question, ste**ps as detail as possible.

**QUESTION 1 (Total: 15 marks)**

**Chapter 1: **Consider an economy where *n = 1.25 *and *y _{t} =1.1y_{t-1} *(an economy where both population and endowment are growing. Assume old people do not receive any endowments. Assume that a young person’s preferences are such that they want to consume two-thirds of their endowment such that

*C _{1.t} = 0.66y_{t}.*

**Refer to the discussion posted on A2L regarding “A RECORD** **– KEEPING EQUILIBRIUM) **involving intergenerational transfers.

Given above:

a)Show the equation for supply of transfers by a young individual at time t. (2 marks)

b)Show the equation for demand of transfers by an old individual at time t (Note and old person in t is young at time t-1). (2 marks)

c)Using the equilibrium for transfers find the rate of transfer between young and the old. (4 marks)

d)Now suppose population growth rate is 1.2. Calculate and find the new rate of transfer. Given your answer **explain intuitively **the impact of population growth on rate of transfer. (1 +3 = 4 marks). (NOTE: Grade is allocated for the quality of the explanation).

e)In the current Covid-19 scenario, there is a decline in older generation combined with economic slowdown. Explain in few sentences, what impact would these have on the rate of transfer. (3 marks) (NOTE: Grade is allocated for the quality of the explanation).

**SHOW YOUR STEPS TO AVOID GRADE PENALTY.**

** **

**QUESTION 2 (Total: 15 marks)**

**Chapter 2 (Appendix): ** Suppose utility equals *ln(c _{1,t}^{1/2}) +b ln(c_{2,t+1}^{1/2})*. Using the steps explained in the appendix:

a)Find an expression for real demand for money in terms of *b *and *y *at the point where utility is maximized. (4 marks)

b)Derive expressions for life time consumption pattern corresponding to utility maximization denoted by *c ^{*}_{1,t }*and

c)Suppose the economy experiences economic growth leading to a rise in endowments. Show the impact of this on the expressions you have derived for parts a and b. Provide intuitive explanation for each of the impacts. (3×2 =6 marks). (NOTE: Grade is allocated for the quality of the explanation).

d)Will population growth have any effect on the expressions derived in parts a and b? Explain why? (NOTE: Grade is allocated for the quality of the explanation).

**SHOW YOUR STEPS TO AVOID GRADE PENALTY.**

** **

**QUESTION 3 (Total: 15 marks)**

Consider a commodity money model economy like the one described in **Chapter 3** but 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 ^{rd} of his **young **endowment, 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 by

(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 an 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)

**SHOW YOUR STEPS TO AVOID GRADE PENALTY.**

**QUESTION 4 (15 marks)**

This is a question from Chapter 4. Consider an overlapping generations model with the following characteristics: Each generation is composed of 100 individuals. The fiat money supply changes according to *Mt *= 1.25*Mt-*1. The initial old own a total of 50 units of fiat money (*M*0 = $50). Each period, the newly printed money is given to the young of that period as a lump-sum transfer (subsidy). Each person is endowed with 10 units of the consumption good when born and nothing when old. Preferences are such that individuals wish to save 5 units when young at the equilibrium rate of return on fiat money.

(a) What is the real rate of return on fiat money in this economy? (5 marks)

(b) How many goods does a young individual receive as a subsidy in period 1? (5 marks)

(c) What is the price of the consumption good in period 1, *p*1, in dollars? (5 marks)

**SHOW YOUR STEPS TO AVOID GRADE PENALTY.**

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