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Problem set – Introduction to the business cycles theory (short-run vs. long-run)
Economics 2 (Macroeconomics)
Lecturer: Tamás Fazekas
1
Problem
The firm has the following production function:
Y = AK 0.5 L0.5
The initial supply of capital is 4 and the supply for labour is 25 units. The initial nominal money supply is
4 units. The velocity of money is 5 units. The A technology parameter in basis case is 1 unit.
1.1
Inital case
1. What is the equation of AD curve?
2. What is the equation of long-run supply curve?
3. What is the equilibrium value of output and price level in the long run?
4. We suppose that the price will be unchanged in short run. What is the equilibrium value of output and
price level in the short run?
1.2
Demand shock
1. The nominal money supply is increased to 5 units by centeral bank. What is the equation of AD curve?
2. What is the equilibrium value of output and price level in the short run?
3. What is the equilibrium value of output and price level in the long run?
1.3
Supply shock
1. The price level increases by 5 percetage for a technologycal shock compare to initial case. What is the
equation of short-run supply curve?
2. What is the equilibrium value of output in the short run if the central bank will not influence this economics
situation?
3. Yielding to the labor union’s perssure the government would like to restore the output previous levels of
supply shocks. How much the money supply should be increased by?
1.4
Technology shock
1. Because of the new technological development can produce with same labour- and capital expenditure
twice more product and services in this economy. The A technology parameter increases to 2 units compare
to initial case. What is the new equation of long-run supply curve?
2. What is the new equation of short-run supply curve?
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2
Problem
An economy can be described as follows: the quantity of money is M = 100, the velocity of money is V = 6,
the value of output is Y = 10.
1. What is the equation of AD curve?
2. What is the equilibrium value of output and price level in the short and in the long run?
3. The state decides to increase M to M 0 = 150. What happens in the long-run and short-run?
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Problem - Homework
An economy can be described as follows: the quantity of money is M = 1, 500, the velocity of money is V = 2,
the value of output is Y = 2, 000.
1. What is the equation of AD curve?
2. What is the equilibrium value of output and price level in the short and in the long run?
3. The state decides to decrease M to M 0 = 1, 000. What happens in the long-run and short-run?
4
Problem
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.
1. If the economy is initially in long-run equilibrium, what are the values of P and Y ?
2. What is the velocity of money in this case?
3. If money supply increases to 2,000, what are the new short-run values of P and Y ?
4. Once the economy adjusts to long-run equilibrium at M = 2, 000, what are P and Y ?
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Problem - Homework
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.
1. If the economy is initially in long-run equilibrium, what are the values of P and Y ?
2. What is the velocity of money in this case?
3. 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 ?
4. What is the velocity of money in this case?
5. With the new aggregate demand function, once the economy adjusts to long-run equilibrium, what are P
and Y ?
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