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Suppose that the only deposits requiring reserves are checkable deposits (D), that the reserve requirement on...

Suppose that the only deposits requiring reserves are checkable deposits (D), that the reserve requirement on deposits (rr) is 10 percent, and that the public always holds 40 percent as much currency as they hold in checkable deposits.

A. If high-powered money (B) equals $100 billion, what is the level of M1?

B. If high-powered money is increased by $50 billion (so ?B = $50b), by how much does M1 change? By how much do checkable deposits change (?D)?

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Answer #1

Suppose that the only deposits requiring reserves are checkable deposits (D), that the reserve requirement on deposits (rr) is 10 percent, and that the public always holds 40 percent as much currency as they hold in checkable deposits.

A. If high-powered money (B) equals $100 billion, what is the level of M1?

Money multiplier = (1 + c)/(rr + c) = (1 + 40%)/(10% + 40%) = 2.8

M1 = Money multiplier x HPM

M1 = 2.8*100 = 280 billion

C + D = 280 billlion

40% of D + D = 280 billion

D = 280/1.4 = 200 billion and C = 80 billion.

B. If high-powered money is increased by $50 billion (so ?B = $50b), by how much does M1 change? By how much do checkable deposits change (?D)?

M1 will change by 50 x 2.8 = 140 billion.

M1 = Currency + deposits

140 + 280 = 40%of D + D

420 billion = 1.4D

D = 300 billion

Deposits are increased by 100 billion from 200 billion to 300 billion.

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