In a national economy, the initial money supply (M) is \text{N}800 billion and the velocit… — JAMB UTME

In a national economy, the initial money supply ( $M$ ) is $\text{N}800$ billion and the velocity of circulation ( $V$ ) is $5$ . The total volume of physical transactions ( $T$ ) is $200$ million units. If the monetary authority increases the money supply by $25\%$ while the velocity of circulation declines by $10\%$ , assuming the general price level ( $P$ ) remains constant, what is the new total volume of transactions ( $T$ ) in millions of units?

Cevap: 225 million units

Cevap

The new total volume of transactions is 225 million units.

According to Fisher's Quantity Theory of Money (

MV = PT

), total expenditure (

MV

) equals total transaction value (

PT

). The initial expenditure is

800 \text{ billion} \times 5 = 4,000 \text{ billion}

. Since

T = 200 \text{ million}

, the general price level

P = 20,000

. After adjustments, the new money supply

M' = 800 \times 1.25 = 1,000 \text{ billion}

and the new velocity

V' = 5 \times 0.90 = 4.5

. The new expenditure

M'V' = 1,000 \times 4.5 = 4,500 \text{ billion}

. Holding

P

constant at

20,000

, the new volume of transactions is

T' = \frac{4,500,000 \text{ million}}{20,000} = 225 \text{ million units}

. Alternatively, using proportional change:

T' = T \times 1.25 \times 0.90 = 200 \times 1.125 = 225 \text{ million units}

Adım Adım Çözüm

State the initial relationship using Fisher's Equation of Exchange:

MV = PT

Initial total turnover

MV = 800 \text{ billion} \times 5 = 4,000 \text{ billion}

. With

T = 200 \text{ million}

, the baseline price level

P = \frac{4,000,000 \text{ million}}{200 \text{ million}} = 20,000

Establishes the quantitative relationship between money supply, velocity, price level, and physical volume of transactions.

Calculate the updated values of money supply (

M'

) and velocity of circulation (

V'

M' = 800 \text{ billion} \times 1.25 = 1,000 \text{ billion}

;

V' = 5 \times 0.90 = 4.5

Applies the specified

25\%

increase to money supply and

10\%

decrease to velocity.

Determine the new total monetary expenditure (

M'V'

M'V' = 1,000 \text{ billion} \times 4.5 = 4,500 \text{ billion}

Finds the new aggregate money payments flow in the economy.

Solve for the new total transaction volume (

T'

) keeping price level (

P

) constant.

T' = \frac{M'V'}{P} = \frac{4,500,000 \text{ million}}{20,000} = 225 \text{ million units}

Re-arranges Fisher's equation to isolate

T'

when

P

is unchanged.

Anahtar Kavram

Fisher's Quantity Theory of Money (

MV = PT

)

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