Mila F.
asked 01/14/22Equation: M⋅V=P⋅Q.
The quantitative theory of money states that given dollars in circulation in a year, a monetary velocity of V, a price level of , and a real output of dollars, the above 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 ?
Answer choices:
A. M
B. Q
C. M/Q
D.Q/M
1 Expert Answer
Raymond B. answered 01/15/22
Math, microeconomics or criminal justice
M and Q are constants, so M/Q and Q/M are constants
as P increases by 1, what is the change in V?
MV = PQ
solve for V
V = P(Q/M)
new V = (P+1)(Q/M)
expand the right side
new V = P(Q/M) + Q/M = old V + Q/M
Q/M is the change in V. D is correct
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Vaughn R.
The question asks for the change in monetary velocity, or ▲V, which just means the final velocity (Vf) minus the initial velocity (Vi). If we solve the equation for V we get V = P*(Q/M), and we're given that M and Q are constant. Let's say Vi = P*(Q/M). Next, we can setup an equation for Vf like so: Vf = (P+1)*(Q/M), since our price level has been increased by 1, and our velocity will change as a result. Now if we distribute the constant (Q/M), we get Vf = P*(Q/M) + 1*(Q/M) = P*(Q/M) + (Q/M). But wait a second...earlier we said that Vi = P*(Q/M), so we can substitute that into our equation for Vf, giving us Vf = Vi + (Q/M). Subtract Vi from both sides gives us Vf - Vi = (Q/M), or ▲V = (Q/M), therefore the answer is D. Hope this helps!01/15/22