Assume that the long-run aggregate supply curve is vertical at Y = 3,000 while t

Question

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? ANS: P=1 Y=3000

b.

What is the velocity of money in this case? ANS: V= 2

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? ANS: P=1 Y=2250

d.

What is the velocity of money in this case? ANS: V=1.5

e.

With the new aggregate demand function, once the economy adjusts to long-run equilibrium, what are P and Y? ANS: P=.75 Y=3000

f. What is the velocity now? ANS: V=1.5

I have all the answers listed after the question but I need to see all steps to understand where the answer is coming from please.

a.

If the economy is initially in long-run equilibrium, what are the values of P and Y? ANS: P=1 Y=3000

b.

What is the velocity of money in this case? ANS: V= 2

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? ANS: P=1 Y=2250

d.

What is the velocity of money in this case? ANS: V=1.5

e.

With the new aggregate demand function, once the economy adjusts to long-run equilibrium, what are P and Y? ANS: P=.75 Y=3000

f. What is the velocity now? ANS: V=1.5

I have all the answers listed after the question but I need to see all steps to understand where the answer is coming from please.

Explanation / Answer

a.

If the economy is initially in long-run equilibrium, what are the values of Pand Y?

ANS: Since the economy is in long run equilibrium , Y is equal to Y of long run supply curve , So,Y=3000.

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

b.

What is the velocity of money in this case? ANS: V= 2

MV = PY

M = 1500 , P = 1 , Y = 3000

1500*V = 1*3000

V = 3000/1500 = 2

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-runvalues of P and Y? ANS: P=1 Y=2250

Since the Short run supply curve is still the same so P = 1

and MV = PY

M = 1500 , V = 1.5 , P = 1

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

d.

What is the velocity of money in this case? ANS: V=1.5

Since the new Ad is Y = (1.5)(M/P

and slope of AD is 1.5

hence V = 1.5

e.

With the new aggregate demand function, once the economy adjusts to long-run equilibrium, what are P and Y? ANS: P=.75 Y=3000

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

MV = PY

M = 1500 , V = 1.5 , Y = 3000

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

f. What is the velocity now? ANS: V=1.5

Since the demand curve is the same and so does it's slope

So, V will still remain the same , v= 1.5

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