In: Finance
Suppose the old bankers on the central island own $5,000,000 of fiat money and creditors are owed $7,500,000. a. Compute the price at which creditors be able to sell the debt they own. b. How much interest will a banker be willing to pay after the debtors have arrived in order to have one more dollar of fiat money? C. Suppose the central bank is willing to purchase $2,000,000 worth of debt, what will the price of the debt be in this case?
Return earned by bankers buying up debt :-
Each unit of debt costs banker ξt and pays him $1 for a gross rate of return of $1/$ξt or 1/ξt . Therefore bankers can make a non-negative profit by borrowing from the central bank as long as the interest rate charged by the central bank does not exceed 1/ξt . Recall that the price of the debt ξt is determined by the ratio of currency owned by bankers to the size of the debt. As bankers borrow and supply more currency to creditors, the price at which creditors can sell their debt ξt rises. In this, arbitrage induces banks to borrow from the central bank until 1/ξt = Ψt . By choosing Ψt , the central bank can determine ξt , the extent to which bankers lack the fiat money balances needed to purchase the debt of others. The lower the rate of interest, at the discount window, (Ψ > = 1) , the more money clearinghouse bankers will borrow and supply to the creditors. This simple discount window policy of setting Ψ = 1 allows bankers as much fiat money as they need to purchase the debt of early leaving creditors at par (ξ = 1).