Money demand in an economy in which no interest is paid on money is: M^d/P = 500
ID: 1218992 • Letter: M
Question
Money demand in an economy in which no interest is paid on money is: M^d/P = 500 + 0.2Y - 1000i
a. Suppose that P = 100, Y = 1000, and i = 0.10. Find real money demand, nominal money demand, and velocity.
b. The price level doubles from P = 100 to P = 200. Find real money demand, nominal money demand, and velocity.
c. Starting from the values of the variables given in Part (a) and assuming that the money demand function as written holds, determine how velocity Is affected by an increase in real income, by an increase in the nominal interest rate, and by an increase in the price level.
Explanation / Answer
a) Real money demand is
Md/ P = 500 + 0.2Y – 1000i
= 500 + (0.2 ×1000) – (1000 ×0.10)
= 600.
Nominal money demand is Md = (Md/P) × P = 600 × 100 = 60000.
Velocity is V = PY / Md = 100 × 1000 / 60 000 ~ 1.67.
b) Real money demand is unchanged, because neither Y nor i has changed.
Nominal money demand is Md = (Md / P) * P = 600 × 200 = 120,000.
Velocity is unchanged, because neither Y nor Md / P has changed, and we can write the equation for velocity as
V = PY / Md = Y / (Md / P).
c) Effect of increase in real income:
When i = 0.10,
V = Y / [500 + 0.2Y – (1000 * 0.10)]
= Y / (400 + 0.2Y)
= 1 / [(400 / Y) + 0.2].
When Y increases, 400 / Y decreases, so V increases.
Effect of increase in the nominal interest rate:
When Y = 1000,
V = 1000 / [500 + (0.2 * 1000) – 1000i]
= 1000 / (700 – 1000i)
= 1 / (0.7 – i).
When i increases, (0.7 - i) decreases, so V increases.
Effect of increase in the price level:
There is no effect on velocity, This is because, we can only write velocity as a function of Y and i. What happens is that nominal money demand changes proportionally with the price level, so that real money demand, and hence velocity, is unchanged.
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