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3. The "cost" to banks of accidentally being caught short of reserves is equal to the rate charged by the Fed on discount loans. The higher a bank's excess reserves, the lower its likely need for borrowing. The benefit to a bank of keeping excess reserves small is that it eams interest on more loans. Thus, it makes sense to claim that the excess-reserves-to-deposits ratio depends on the difference between the loan rate of interest and the discount rate. Of course this ratio must lie in the (0,1) interval. Assume that the specific functional form is the following! ER 1 D 1+ exp 100 li,-) (This is a "sigmoid function which maps the difference between loan and discount rates of interest onto the bounded (0,1) interval. As the difference goes to infinity, the function approaches 0; as the difference goes to negative infinity, the function approaches 1). a) Assume the discount rate is 5% (.05). Calculate the ER/D ratio for values of the loan rate of interest of i) 6% ii) 7% iii) 8% iv) 9% v) 10% 3. The "cost" to banks of accidentally being caught short of reserves is equal to the rate charged by the Fed on discount loans. The higher a bank's excess reserves, the lower its likely need for borrowing. The benefit to a bank of keeping excess reserves small is that it eams interest on more loans. Thus, it makes sense to claim that the excess-reserves-to-deposits ratio depends on the difference between the loan rate of interest and the discount rate. Of course this ratio must lie in the (0,1) interval. Assume that the specific functional form is the following! ER 1 D 1+ exp 100 li,-) (This is a "sigmoid function which maps the difference between loan and discount rates of interest onto the bounded (0,1) interval. As the difference goes to infinity, the function approaches 0; as the difference goes to negative infinity, the function approaches 1). a) Assume the discount rate is 5% (.05). Calculate the ER/D ratio for values of the loan rate of interest of i) 6% ii) 7% iii) 8% iv) 9% v) 10%