Consider an OLG economy with an infinite horizon where individuals live for two periods. Suppose number...

  

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Consider an OLG economy with an infinite horizon where individuals live for two periods. Suppose number of young born in a period is constant at N= N (i.e. n = 1). There is a constant stock of f money M.= M (i.e. z=1). In each young generation there are three types of individuals born: worke bankers and entrepreneurs. Workers and entrepreneurs both have y units of time available and use all of this time to work. Each unit of time spent working produces one unit of the consumption good. Here we assume that individuals only care about consuming when old. Each worker produces a different amount (some are more productive than others). Denote the amount produced by each young worker by s. Entrepreneurs have an additional ability to create capital, which has a one period return of x> 1 (an matures after one period). Finally, bankers have no endowment and do not care about consumption. Bankers in this economy simply take deposits and promise a one-period return r, and make loans at the rate r. Bankers can perfectly locate entrepreneurs to make loans and can be easily located by depositors. Finally, when a depositor needs to make a withdrawal, there is a fixed cost op that ifiey must pay to do this that does not depend on the size of the withdrawal. You can think of this cost as the cost of going to the bank, periodically answering security questions, signing-in to your account etc. (a) Young workers can either acquire money or deposit with a banker. How many goods do they receive in the next period if they acquire fiat money? (b) How many goods do they acquire in the next period if they deposit? (c) What is the rate that must be offered by bankers? (d) What are the average real rates of return on money and deposits? (e) Explain why some individuals will deposit and others will acquire money. (f) What does the banker do with deposits? (g) At what rate r does the banker lend to entrepreneurs? (h) What do entrepreneurs do with the goods they produce? (1) Assume bankers loan at rate r=x and pay rate r=x on deposits and do not consume. Why do we include them in our model? (1) Suppose the total deposits in the economy are H, and total currency is Q What is the price of the good? (k) Find a relationship between the monetary base M, and the money stock (M1).. Consider an OLG economy with an infinite horizon where individuals live for two periods. Suppose number of young born in a period is constant at N= N (i.e. n = 1). There is a constant stock of f money M.= M (i.e. z=1). In each young generation there are three types of individuals born: worke bankers and entrepreneurs. Workers and entrepreneurs both have y units of time available and use all of this time to work. Each unit of time spent working produces one unit of the consumption good. Here we assume that individuals only care about consuming when old. Each worker produces a different amount (some are more productive than others). Denote the amount produced by each young worker by s. Entrepreneurs have an additional ability to create capital, which has a one period return of x> 1 (an matures after one period). Finally, bankers have no endowment and do not care about consumption. Bankers in this economy simply take deposits and promise a one-period return r, and make loans at the rate r. Bankers can perfectly locate entrepreneurs to make loans and can be easily located by depositors. Finally, when a depositor needs to make a withdrawal, there is a fixed cost op that ifiey must pay to do this that does not depend on the size of the withdrawal. You can think of this cost as the cost of going to the bank, periodically answering security questions, signing-in to your account etc. (a) Young workers can either acquire money or deposit with a banker. How many goods do they receive in the next period if they acquire fiat money? (b) How many goods do they acquire in the next period if they deposit? (c) What is the rate that must be offered by bankers? (d) What are the average real rates of return on money and deposits? (e) Explain why some individuals will deposit and others will acquire money. (f) What does the banker do with deposits? (g) At what rate r does the banker lend to entrepreneurs? (h) What do entrepreneurs do with the goods they produce? (1) Assume bankers loan at rate r=x and pay rate r=x on deposits and do not consume. Why do we include them in our model? (1) Suppose the total deposits in the economy are H, and total currency is Q What is the price of the good? (k) Find a relationship between the monetary base M, and the money stock (M1)..