5. AD-AS Numerical Analysis (10 points). Assume that the long-run aggregate supply curve is vertical at Y = 3,000 while the short-run aggregate supply curve is horizontal at P = 1.0. The aggregate demand curve is Y = 2 × M / P, and M = 1,500. a. If the economy is initially in long-run equilibrium, what are the values of P and Y? (2 points) b. What is the velocity of money in this case? (2 points) c. Suppose because banks start paying interest on checking accounts, the aggregate demand function shifts to Y = 1.5 × M / P. What are the short-run values of P and Y? (2 points). d. What is the velocity of money in this case? (2 points) e. With the new aggregate demand function, once the economy adjusts to long-run equilibrium, what are P and Y? (2 points).

a.Y=3000.   P = 1

b.The velocity of money is 2

c.P = 1. Y= 2250

d.V = 1.5

e.Y = 3000 .  P = 0.75

Explanation:

a. If the economy is in long run equilibrium , Y is equal to Y of long run supply curve, hence,Y=3000.

Therefore If economy is in equilibrium Price = price of short run supply curve , so P = 1

b.  In order to calculate the velocity of money we have to use the following equation:

MV = PY

M = 1500 , P = 1 , Y = 3000

1500*V = 1*3000

V = 3000/1500 = 2

The velocity of money is 2

c.  According to the given data the Short run supply curve is still the same so P = 1  and MV = PY  and M = 1500 , V = 1.5 , P = 1

Hence, Y = MV/P = 1500*1.5/1 = 2250

d.  Becuse the new Ad is Y = (1.5)(M/P  and slope of AD is 1.5

Therefore, V = 1.5

e.  Because, the economy is in long run equilibrium and the long run supply curve is at Y = 3000 , So Y = 3000

Therefore, MV = PY

M = 1500 , V = 1.5 , Y = 3000

P = MV/Y = 1500*1.5/3000 = 2250/3000 = 0.75

answer(b) revenue account which increases;