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Difficulty: MediumValue of Money and Quantity Theory of Money

In an economy, the general price index increases from 100100 to 125125 over a given period. Based on the relationship between price level and purchasing power in the Quantity Theory of Money, what is the percentage change in the value of money?

  1. A decrease of 20%20\%Answer
  2. B
    A decrease of 25%25\%
  3. C
    An increase of 25%25\%
  4. D
    An increase of 20%20\%

Answer

A decrease of 20%20\%
According to the Quantity Theory of Money, the value of money (VmV_m) is inversely related to the general price level (PP), defined by Vm=1PV_m = \frac{1}{P}. When the price index rises from 100100 to 125125, the initial value of money is 0.010.01 and the new value is 0.0080.008. The percentage change in purchasing power is 0.008−0.010.01×100%=−20%\frac{0.008 - 0.01}{0.01} \times 100\% = -20\%, which signifies a 20%20\% decrease.

Step-by-Step Solution

1
Express the relationship between price level (PP) and the value of money (VmV_m)
Vm=1PV_m = \frac{1}{P}
The value of money measures purchasing power and is the reciprocal of the price level.
2
Calculate initial and final values of money
Initial Vm1=1100=0.01V_{m1} = \frac{1}{100} = 0.01; Final Vm2=1125=0.008V_{m2} = \frac{1}{125} = 0.008
Substitute the price indices (100100 and 125125) into the formula.
3
Calculate the percentage change in the value of money
Percentage Change=0.008−0.010.01×100%=−0.0020.01×100%=−20%\text{Percentage Change} = \frac{0.008 - 0.01}{0.01} \times 100\% = \frac{-0.002}{0.01} \times 100\% = -20\%
Apply the standard percentage change formula: New Value−Old ValueOld Value×100%\frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100\%.

Key Concept

Inverse relationship between price level and the value of money (Vm=1PV_m = \frac{1}{P})
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Topics

Value of Money and Quantity Theory of Money

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