Final answer:
When the quantity of money triples and the price level increases by 50 percent with velocity constant, real output (Y) increases but not in a strict proportional relationship. A specific calculation is needed to ascertain the exact increase in real output which could be closest to a 50 percent increase as per the given options.
Step-by-step explanation:
In the equation of exchange, which is represented by MV = PT (Money Supply x Velocity = Price Level x Real GDP), when the quantity of money (M) triples, price levels (P) increase by 50 percent, and velocity (V) remains constant, we can calculate the impact on real output (Y). For an example calculation, if the initial money supply (M) is $4 trillion and there's an $800 billion increase:
The new money supply becomes $4.8 trillion.
Given the velocity of money is 3, the initial nominal GDP was $12 trillion (4 trillion x 3).
After the increase in money supply and if velocity remains constant, the new nominal GDP will be $14.4 trillion (4.8 trillion x 3).
With the price level increasing by 10 percent (from 100 to 110), the adjusted price level isn't merely the inflation percentage increase, but the factor of price levels which is 1.10 after increase (110/100).
Now we can solve for the new Real GDP: 14.4 trillion / 1.10 = approximately $13.09 trillion.
That's about a 9.09 percent increase in real output from the initial $12 trillion.
To answer the student's question specifically, real output (Y) would increase in a way that is closest to option (a) - increases by 50 percent, though a precise calculation is necessary to find the exact increase.