Question

Recall the formula that states that $V = 1/P, where V is the value of the dollar and P is the price level. If the price level falls from 1 to 0.75, what will happen to the value of the dollar?

a. It will rise by a third (33.3 percent).

b. It will rise by a quarter (25 percent).

c. It will fall by a quarter (−25 percent).

d. It will fall by a third (−33.3 percent).

Short answer

The correct answer is option a) It will rise by a third (33.3 percent).

Step-by-step solution

Step 1. Value of money

Value of money refers to the total quantity of goods that can be exchanged or one unit of money. Value of money and price level have an inverse relationship; when the price level rises, the value of money decreases. The sudden and radical changes in the value of money will cause economic issues.

Step 2. Explanation for the correct answer

As the price level falls, the value of money increases. The value of money when the price level fell to 0.75 is:

Initial value of money, when price level was 1

$$\begin{gathered} Valueofmoney=\frac{1}{P} \\ =\frac{1}{1} \\ =1 \end{gathered}$$

The value of money when P=1 is 1.

Value of money when price level fell to 0.75 is:

$$\begin{gathered} Valueofmoney=\frac{1}{P} \\ =\frac{1}{0.75} \\ =1.33 \end{gathered}$$

The value of money when the price level fell to 0.75 is 1.333.

The value of money increased from 1 to 1.33, and the percentage rise was 33.3%.