M*V=P*Q The quantitative theory of money states that given M dollars in circulation in a year, a monetary velocity of V, a price level of P, and a real output of Q dollars, the given equation is correct. An economist considers the case where the dollars in circulation and the real output are known constants. Which of the following expressions is the change in monetary velocity as the price level increases by 1 ? Choose 1 answer: (A) M (B) Q (C) (M)/(Q) (D) (Q)/(M)

Question

M*V=P*Q The quantitative theory of money states that given  M dollars in circulation in a year, a monetary velocity of  V, a price level of  P, and a real output of  Q dollars, the given equation is correct. An economist considers the case where the dollars in circulation and the real output are known constants. Which of the following expressions is the change in monetary velocity as the price level increases by 1 ? Choose 1 answer: (A)  M (B)  Q (C)  (M)/(Q) (D)  (Q)/(M)

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Start with equation: We start with the equation M*V = P*Q. To find how V changes with P, we need to solve for V. V = (P*Q) / MFind new price level: Now, we need to find the change in V when P increases by 1. Let's call the new price level P + 1. The new V, which we'll call V_new, is: V_new = ((P + 1)*Q) / MCalculate change in V: To find the change in V, we subtract the original V from V_new. Change in V = V_new - V Change in V = (((P + 1)*Q) / M) - (P*Q) / MSimplify expression: Simplify the expression by combining the terms over a common denominator. Change in V = ((P*Q + Q) / M) - (P*Q) / M Change in V = (P*Q + Q - P*Q) / MCancel out terms: Cancel out the P*Q terms. Change in V = (Q) / MFinal answer: The change in monetary velocity (V) as the price level (P) increases by 1 is Q/M. So, the correct answer is (D) (Q)/(M).

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