Question

Suppose in the country A, the velocity of money in the country A is always stable. Answer the following questions:

a. What is the quantity equation? (Please indicate and explain each variable) (2%)

b. Suppose the price level in the period t-1 is P_t-1, and the price level In the period t is P_t in the country A.Please use P_t and P_t-1to represent the inflation rate during the period t-1 and the period tin the country A. (2%)

c. Suppose in the country A, the money supply was $2 million and real GDP was $4 million in 2005.In 2006, the money supply increased by 10 percent, real GDP increased by 5 percent and nominal GDP equaled $8.8 million. How much was the inflation rate between 2005 and 2006 in the country A? (Please use the percentage to represent your answer, and calculate to the second digit below, e.g. 0.456-0.46) (6%)

Answer 1

a. Quantity theory of money states that the money supply in an economy is directly proportional to the and price level in an economy i.e. any change in money supply leads to a proportional change in price level in the economy. The equation is given by:
M*V= P*Y
where,
M = Money supply
V = Velocity of money (number of times money changes hand)
P = Price level
Y = Real Gross Domestic product (GDP)

b. Rate of inflation is defined as the rate of change in price level in an economy. It is represented by π and is calculated using the following formula:

π = [(P_t -P_t-1)/P_t-1]*100

c) M*V= P*Y

P = MV/Y

taking log both sides, we get, LogP = LogM + Log V - Log Y

differentiating both sides w.r.t to time to get equation in growth rates, we get,

(dP/dt)/P = (dM/dt)/M +(dV/dt)/V - (dY/dt)/Y

(dP/dt)/P = π

(dM/dt)/M = g_m = 10%

(dY/dt)/Y = g_y = 5%

Since, velocity is stable in country A, therefore, (dV/dt)/V = g_v = 0
Hence, π = (dM/dt)/M +(dV/dt)/V - (dY/dt)/Y = 10-5 = 5%