Suppose that this year\'s money supply is $500 billion, nominal GDP is 10 trilli

Question

Suppose that this year's money supply is $500 billion, nominal GDP is 10 trillion and real GDP is $5 trillion.

a) What is the price level? what is the velocity of money?
b) Suppose that velocity is constant and the economy's output of good and services rised by 5% each year, what will happen to nominal GPD and the price level next year if the Fed keeps the money supply constant?
c) what money supply should the Fed set next year if it wants to keep the price level constant?
d)What money supply should the fed set next year if it wants inflation of 10%?

Explanation / Answer

a) Assuming monetary equation M/P=Y/V: M=500b NGDP=10'000b RGDP=5'000b NGDP = RGDP x P = PY 10'000 = 5'000 x P P = 10'000/5'000 = 2 V = PY/M = 10'000/500 = 20 b) ?M=0 ; ?V=0 ; ?Y=+5% c) (1+?M) / (1+?P) = (1+?Y) / (1+?V) 1 / (1+?P) = (1+5%) / 1 1/ (1+?P) = 1.05 1+?P = 1/1.05 ?P = (1-1.05)/1.05 = -0.05/1.05 ˜ -0.0476 ˜ -4.76% ?NGDP = ?PY = ((1+?P)(1+?Y)) - 1 = = ((1/1.05)(1.05)) - 1 = 1-1 = 0 Nominal GDP will remain the same (no change) - because growth in RGDP will be offset by fall in price level. Price level will fall thus delfator will decrease. d) p=?P%=0 ; ?V%=0 ; ?Y%=+5% (1+?M) / (1+?P) = (1+?Y) / (1+?V) (1+?M) / 1 = (1+5%) / 1 1+?M = 1+5% ?M = +5% M = 500 billion +5% = 500x1.05 = 525 billion p=?P%=+10% ; ?V%=0 ; ?Y%=+5% (1+?M) / (1+?P) = (1+?Y) / (1+?V) (1+?M) / 1.1 = 1.05 / 1 1+?M = 1.05x1.1 = 1.155 ?M% = +15.5% M = 500 billion +15.5% = 500x1.155 = 577.5 billion ?M=+77.5 billion

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