Consider an individual who moves from Asia to the United States and brings with

Question

Consider an individual who moves from Asia to the United States and brings with him his life savings of $40,000, which he deposits in a U.S. bank. For each of the cases below, compute the overall change in deposits and reserves in the U.S. banking system as a result of this new deposit. a. 10 percent target reserve ratio; no cash drain; no excess reserves b. 10 percent target reserve ratio; 5 percent cash drain; no excess reserves c. 10 percent target reserve ratio; 5 percent cash drain; 5 percent excess reserves

Explanation / Answer

In this question, let X be the injection of cash into the Canadian banking system ($40 000). Ultimately, this new cash will be held either as reserves by the banks, R, or as cash by the public, C. That is, C + R = X. If deposits are given by D, the change in reserves is given by R = vD, where v is the reserve requirement. The change in the public's cash holding is C = cD, where c is the cash drain. Substituting into the above equation we get, cD + vD = X D = X/(v + c) R = [v/(v + c)] X

a) For v= 0.10 and c = 0, we have D = $400 000 and R = $40 000.

b) For v = 0.10 and c = 0.05, we have D = $266 667 and R = $26 667.

c) For v = 0.10 + .05 and c = 0.05, we have D = $200 000 and R = $30 000

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