In an economy operating under Fisher's Quantity Theory of Money (MV = PT), the initial sto… — JAMB UTME

In an economy operating under Fisher's Quantity Theory of Money ( $MV = PT$ ), the initial stock of money ( $M$ ) is ₦500 million, the velocity of money circulation ( $V$ ) is 4, and the total volume of transactions ( $T$ ) is 100 million units. If the money supply increases by $25\%$ , the velocity of circulation decreases by $10\%$ , and the volume of transactions increases by $25\%$ , what is the new price level ( $P$ )?

Cevap: 18 ₦

Cevap

The new price level

P

is ₦18.

Applying Fisher's Quantity Theory of Money (

MV = PT

), the updated variables are

M = 625

V = 3.6

, and

T = 125

. Substituting these values into

P = \frac{MV}{T}

gives

P = \frac{625 \times 3.6}{125} = \frac{2250}{125} = 18

. Alternatively, notice that the

25\%

increase in money supply (

M

) is exactly offset by the

25\%

increase in real transaction volume (

T

), meaning the price level changes solely due to the

10\%

decrease in velocity (

V

). Reducing the initial price level of ₦20 by

10\%

gives

20 \times 0.90 = 18

Adım Adım Çözüm

Calculate the updated values for money supply (

M_2

), velocity (

V_2

), and transaction volume (

T_2

) following the specified percentage changes.

M_2 = 500 \times 1.25 = 625

million Naira,

V_2 = 4 \times 0.90 = 3.6

, and

T_2 = 100 \times 1.25 = 125

million units.

The parameters of Fisher's equation must be adjusted according to their relative percentage increases or decreases.

Substitute the updated parameters into Fisher's Equation of Exchange (

MV = PT

625 \times 3.6 = P_2 \times 125

, simplifying to

2250 = 125 P_2

According to the Quantity Theory of Money, total monetary expenditure (

MV

) equals total nominal transaction value (

PT

Solve the linear equation for the unknown new price level (

P_2

P_2 = \frac{2250}{125} = 18

Dividing total money expenditure by total volume of transactions yields the average price per unit.

Anahtar Kavram

Fisher's Quantity Theory of Money (Equation of Exchange)

Tahmini Süre:2m 0s

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