Question

1. Suppose that:

MDP=800+0.2Y-5000r+π
MS=1000+0.1Y-3000π

1. If π=0.1 ;r=0.1 ;Y=2000, in equilibrium, what is the price level?
2. What is the velocity? (using the same parameters as in a.)
3. If output increases so that Y=3000, what is the price level?
4. What is the velocity? What is the change rate of the velocity? What does this number mean?
5. Now, if π=0.1 ;Y=2000; and price level is forced to be P=6, what is the equilibrium interest rate?
6. What is now the velocity?

Answer 1

(a) (MD / P) =800+0.2Y-5000(r+π)
Put π=0.1 ;r=0.1 ;Y=2000

=> (MD / P) = 800 + 0.2Y - 5000(r + π)

=> (MD / P) = 800 + 0.2(2000) - 5000(0.1 + 0.1)

=> (MD /P) = 800 + 400 - 5000 (0.2)

=> (MD/P) = 1200 - 1000

=> (MD/P) = 200

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MS=1000+0.1Y-3000π

Put π=0.1 ;r=0.1 ;Y=2000

=> MS = 1000 + 0.1(2000) - 3000(0.1)

=> MS = 1000 + 200 - 300

=> MS = 900

At equilibrium, MD = MS

=> (MD/P) = 200

=> (900 / P) = 200

=> P = (900 / 200)

=> P = 4.5

Price level is 4.5

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(b) MV = PY

Where M is the money supply

V is the velocity

P is price level

Y is real GDP

--

MV = PY

=> 900 * V = 4.5 * 2000

=> 900 * V = 9000

=> V = (9000 / 900)

=> V = 10

velocity is 10.

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(c) Now Y = 3000.

(MD / P) =800+0.2Y-5000(r+π)
Put π=0.1 ;r=0.1 ;Y=3000

=> (MD / P) = 800 + 0.2Y - 5000(r + π)

=> (MD / P) = 800 + 0.2(3000) - 5000(0.1 + 0.1)

=> (MD /P) = 800 + 600 - 5000 (0.2)

=> (MD/P) = 1400 - 1000

=> (MD/P) = 400

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MS=1000+0.1Y-3000π

Put π=0.1 ;r=0.1 ;Y=3000

=> MS = 1000 + 0.1(3000) - 3000(0.1)

=> MS = 1000 + 300 - 300

=> MS = 1000

At equilibrium, MD = MS

=> (MD/P) = 400

=> (1000 / P) = 400

=> P = (1000 / 400)

=> P = 2.5

Price level is 2.5

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(d)

MV = PY

Where M is the money supply

V is the velocity

P is price level

Y is real GDP

--

MV = PY

=> 1000 * V = 2.5 * 3000

=> 1000 * V = 7500

=> V = (7500 / 1000)

=> V = 7.5

velocity is 7.5

Velocity decreases from 10 to 7.5

% change in velocity = [(7.5 -10) / 10]*100

=> % change in velocity = -25%

Velocity of money measured the rate at which money exchanged in an economy.

Velocity equals to 7.5 means on an average one unit of currency is exchanged 7.5 times during a given period of time.

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(e) MS=1000+0.1Y-3000π

Put π=0.1 ;Y=2000

=> MS = 1000 + 0.1(2000) - 3000(0.1)

=> MS = 1000 + 200 - 300

=> MS = 900

At equilibrium; MD = MS

=> (MD / P) = 800+0.2Y-5000(r+π)

Put MD = 900, P = 6, Y = 2000 and π = 0.1

=> (900 / 6) = 800 + 0.2(2000) - 5000 (r + 0.1)

=> 150 = 800 + 400 - 5000r - 500

=> 150 = 700 - 5000r

=> 5000r = 700 - 150

=> 5000r = 550

=> r = (550 / 5000)

=> r = 0.11

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(f)

MV = PY

Where M is the money supply

V is the velocity

P is price level

Y is real GDP

--

MV = PY

=> 900 * V = 6 * 2000

=> 900 * V = 12000

=> V = (12000 / 900)

=> V = 13.33