a) Assume that the long-run aggregate supply curve is vertical at Y = 3,000 whil

Question

a) 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.

i) If the economy is initially in long-run equilibrium, what are the values of P and Y?

ii) What is the velocity of money in this economy?

b) 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 = 3(M/P) and M = 1,000.

i) Suppose a supply shock moves the short-run aggregate supply curve to P=1.5. What are the new short run P and Y? What will be the new long run P and Y?

ii) Suppose that immediately after the supply shock the Federal Reserve Bank wanted to hold output at its long-run level. What level of M would be required? If this level of M were maintained, what would be long-run equilibrium P and Y?

iii) If M increases to 2,000, what are the new short-run values of P and Y?

iv) Once the economy adjusts to long-run equilibrium at M = 2,000, what are P and Y?

c) Use the aggregate demand

Explanation / Answer

i)
Y = 3000 in the long-run
To find P in the long-run:
Y = 2(M/P)
Y = 2(1500/P)
3000 = 3000/P
P = 1

ii)
M * V = P * Y
V = (P * Y)/M
V = (1 * 3000) / 1500
V = 2

iii)
If M increases to 2000, in the short-run price will remain at 1. This is because even though the AD curve shifts, AS is vertical, and thus the price will not change. The new value of Y will be:
Y = 2(M/P) = 2(2000/1) = 4000

iv)
Once the economy adjusts to the long-run equilibrium at M = 2000, the new value of Y will be 3000, as the long-run Y is 3000. At the new aggregate demand, P will be:
Y = 2(M/P)
P = 2(M/Y) = 2(2000)/3000 = 1.33

b)
i)
The P in the short-run will be 1.5.

The Y is in the short-run will be:
Y = 3(M/P)
Y = 3(1000/1.5) = 3000/1.5 = 2000

The P in the long-run will be 1 and the Y in the long-run will be 3000. Notice these are the same values we found in part i of part a. This is because short-run equilibrium will tend to adjust toward the long-run equilibrium as the economy has time to recover from the supply shock.

ii)
The Y we use in this problem is the long-run 3000 and the price we use in this problem is the short-run 1.5. These are long-run equilibrium P and Y as well for this problem.
Y = 3(M/P) so:
M = (Y * P)/3
M = (3000 * 1.5)/3 =1500

c) See attached file

i) Price and output both increase, because aggregate demand shifts right
ii) Price and output both increase, because aggregate supply shifts left
iii) Price decreases and output increases, because aggregate supply shifts right

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