Problem 2. Suppose that the following economy consists of two types of people, A

Question

Problem 2. Suppose that the following economy consists of two types of people, A and B, with population 100 for each type. Time is infinite and labeled as t = 1, 2, ,00 Type A can only work in the even-period while type B can only work in the odd-period. When they work, thev can produce 1 unit of apple. Eating an apple will vield 1 unit of utility. An apple is nonstorable and cannot be divided. Type A value apples more than Type B in the odd-period, i.e., they want to eat the apple more than Type B do However, Type B value apples more than type A in the even-period

Explanation / Answer

Part-a)

In the economy with two types of individuals,A and B and indefinite time period T,type A values and consumes the apples more than type B during odd periods which is the employment period for type B.Alternatively,type B demands and consumes more apples than type A during the even periods which is the employment period for type A individuals.

Now,in every time period both types of individuals would like to smooth their consumption pattern by maximizing total utility of apple consumption from each time period.In this context,considering a fixed income level for both types of individuals and a constant price level for the apples(which is the main product in this case) it can be assumed that the individuals would maximize their lifetime utility by equalizing the Marginal Utilities(MU) obtained from additional apple consumption in each of the time periods which in this case is given as 1 unit.It can be mathematically denoted as MU(1)=MU(2)=MU(3)=........MU(infinity)

Now,realistically,we have to consider the income level of each types of individuals and any inflationary expectations(individual's expectation regarding changes in price level of apples for subsequent time periods) during the successive time peiods.The income level in each time period ideally depends on the savings from the previous time period and the income obtained from current time period.Now,observe that the type A individuals only work in even periods and consumes apples during odd time periods.Thus,type A's consumption depends on his/her income level during the even periods(assuming that savings equal to income level as type A individuals don't consume any apple during even periods) and during the odd time periods when he/she doesn't work.Thus,type A individual's intertemporal utility maximization and optimal choice of apple consumption depends on mainly the income level or savings level from the even time periods and equalization of MU obtained from apple consumption in each odd time period.

Similarly,type B individuals would earn income level and save entirely during the odd time periods as he/she works only during odd time periods and consumes apples only during even time periods(considering apple is the product in the economy).Hence,type B's intertemporal utility maximization would depend on the income/savings level from the odd periods as he/she doesn't earn any income during even periods and the equalization of MU obtained from apple consumption during the even time periods.

Part-b)

Now,if the mint stops money supply at the present time,it will consequently increase the value of coins/money assuming that coin/money demand is constant.Type-A agents are endowed with 1 unit of silver coins each at the beggining of time period t.With no more coin/money supply and increase in value of coin/money,the savings or storage of money would increase in time period t.Therefore,the consumption of coins/money would decrease alternatively as increase in the value of coins/money would raise the cost of borrowing money(can be also thought of as increase in interest rate).This would encourage people to reduce borrowing and coin circulation/use or coin consumption will reduce as a result.Thus,the savings level of coin or money would increase in the economy due to contractionary monetary policy by the mint.

Part-c)

Thus,the increase in the value of money/coins or cost of coin/money borrowing would also reduce the money/coin demand in the economy.Now,the increase in the interest rate or value of coin/money would induce higher intentions of lending with expectations of higher interest earnings on coin/money lending.But reduction in coin/money demand would decrease the consumption of coins and as a result the utility obtained coin/money consumption would also drop.An increase in the cost of borrowing now leads to higher interest payment on coin/money consumption.Hence,the marginal value of coin consumption is not 1 unit of utility anymore and will be less.

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