Money Demand, Consumption, and Stock Market - Essay Example

The stock market of the American S&P 500 given in the graph below, predicts recession since the prices of stocks were stable and steadily growing until 2002-2003 and also in the year 2008-2009. These years were characterized by a great recession due to a fall in demand for goods hence the failure in the stocks to pick favorable prices. The peak in 2000 and 2007 represent a boom in the economy while the troughs of  2002-2003 and between 2008-2009 characterize a great recession.

Figure 1: S&P 500 stock market indexes from 1960 to 2012

3. Consumption and Investment

 Y = Cd+Id+G

National savings=Y- Cd-G=Id

Sd= Y-(4000-4000r+0.2Y)-2000

=Y-4000+4000r-0.2Y-2000

=0.8Y+4000r-6000

1. b) For the goods market to be cleared, it means that consumption and income equalize; Id=0

Sd=0

0.8Y+4000r-6000=0

0.8(10000)+4000r-6000=0

8000=6000-4000r

2000=4000r

r=0.5%

When Y = 12,000

0.8(12000)+4000r-6000=0

9,600=6000-4000r

3600=4000r

r=0.8%

An increase in income shifts the IS curve to the right.

1. When the government purchases increase to 2400, then the national savings will reduce

Sd= Y-(4000-4000r+0.2Y)-2400

        0= 10000-(4000-4000r+0.2Y)-2400

       0=10000-4000+4000r-8000-2400

      0=4000r-4400

      r=1.1%

The IS curve shifts to the right since the interest rates are increased. Again, an increase in government purchases reduces disposable national income hence shifting the IS curve to the left.

4. Real Money Demand and Supply

The real interest rate where

MV=PQ

Md=(3000+0.1Y-10000i)P*0.02

For the asset market to clear, money demanded should equal money supplied. Therefore,

Md=Ms=6000= [3000+0.1(8000)-10000i) 2* where r= (i+π) hence i= r- π (Fischer’s Model)

6000= (3000+800-10000(r-0.02)]*2

6000= (3800-10000r+200)*2

3000=4000-10000r

Real interest rate r=0.10 or10%

1. b) When Y=9000

6000= (3000+900-10000(r-0.02)]*2

6000= (3900-10000r+200)*2

3000=4100-10000r

Real interest rate r=0.11 or 11%

The interest rate decreases and shifts the LM curve

When M=6600, then Md=Ms=6600

For Y=8000, the interest rate is;

6600=(3000+800-10000(r-0.02)]*2

6600=(3800-10000r+200)*2

3300=4000-10000r

Real interest rate r=0.07 or7%

For Y=9000

6600=(3000+900-10000(r-0.02)]*2

6600=(3900-10000r+200)*2

3300=4100-10000r

Real interest rate r=0.08or 8%

The interest rates increase with the increase in the money supply

1. c) When inflation increases to 0.03, then

For Y=8000, the interest rate is;

6000=(3000+800-10000(r-0.03)]*2

6000=(3800-10000r+300)*2

3000=4100-10000r

Real interest rate r=0.11 or 11%

For Y=9000, the interest rate is;

6000=(3000+900-10000(r-0.03)]*2

6000=(3900-10000r-300)*2

3000=4200-10000r

Real interest rate r=0.12 or 12%

5. National income= consumption +Investment +Taxes

For equilibrium to occur, the money supply should equal the money demand

Real interest rates are where consumption, and government purchases equal to investment under full employment

Y=200+0.8[1000-(20+0.25(1000))-500r +200-500r +196

Y=200+0.8(730)-1000r+200+196

1000=784-1000r+196

1000=980-1000r

r=20/1000

=0.02 or 2%

The price level is obtained where Md=M=9890

Therefore, 9890= 0.5(1000)-250(0.02+0.1)P

9890=500-250(0.12)P

9890=470P

P= 21

Consumption Cd=200+0.8(1000-270)-500(0.02)

=200+584-10

=774

Investment Id will be;

Id =200-500r

Id=200-500(0.02)

Id=190

1. b) When G=216, then

Y=200+0.8[1000-(20+0.25(1000))-500r +200-500r +216

Y=200+0.8(730)-1000r+200+216

1000=784-1000r+216

1000=1000-1000r

r=0/1000

r=infinite (∞)

The price level is obtained where Md=M=9890

Therefore, 9890= 0.5(1000)-250(0.1)P

9890=500-250(0.1)P

9390=470P

P= 20

The price level reduces

Consumption Cd=200+0.8(1000-270)

=200+584

=774

Investment Id will be;

Id =200-500r

Id=200-500(∞)

Id=200

6. Levels of real wage under full employment

Under full employment, the wage rate is determined by the production and supply of labor

Production will be Y=10N-0.0025N2

The marginal product of labor will dY/dN=10-0.005N

At full employment, the marginal product of labor equals zero

dY/dN=10-0.005N=0

Therefore N; 10=0.005N

N=10000/5=2000

The wage rate will be;

Labor supply curve will be; Ns=55+10(1-0.5) w=2000

55+5w=2000

5w=1945

w=389

Full Employment means labor demand equals labor supply

Employment rate =389/2000=19.45%

Outputs will be given by the production function

Y=10N-0.0025N2

Where n=2000

Therefore y=10(2000)-10000

Y=20000-10000

Output =10000

1. b) At full employment, the real interest rates occur consumption equals investment

Y=300+0.8(10000-(20+0.5*10000)-200r +258.5-250r+G

10000=300+0.8(10000-5020)-200r+258.5-250r+50

10000=300+0.8*4980-200r+258.5-250r+50

5407.5=450r

The real interest rate is 12.01%

Consumption Cd= 300+0.8(10000-20-0.5*10000) -200(0.12)

=300+0.8(4980)-240

=4044

Investment is given by;

Id =258.5-250(0.12)

=258.5-30

=238.5

IS curve

1. Full employment value of the price level produces

Demand for money equals the supply of money. Therefore;

Md=Ms=0.5Y-250(r+π)

9150=0.5(10000)-250(0.12+0.02)P

9150= (5000-250)P

P=9150-4750

P=4400

72. d) When the government purchases increase to G=72.5

Y=300+0.8(10000-(20+0.5*10000)-200r +258.5-250r+G

10000=300+0.8(10000-5020)-200r+258.5-250r+72.5

10000=300+0.8*4980-200r+258.5-250r+72.5

5407.5=450r

The real interest rate is 11.9%

Consumption Cd= 300+0.8(10000-20-0.5*10000) -200(0.12)

=300+0.8(4980)-238

=4046

Investment is given by;

Id =258.5-250(0.119)

=258.5-29

=229.5

1. d) In the long run at full employment, the inflation will have been reduced to zero. Therefore

Demand for money equals the supply of money. Therefore;

Md=Ms=0.5Y-250(r)

9150=0.5(10000)-250(0.12)P

9150= (5000-30)P

P=9150-4970

P=4180

Y=300+0.8(10000-(20+0.5*10000)-200r +258.5-250r+G

10000=300+0.8(10000-5020)-200r+258.5-250r+50

10000=300+0.8*4980-200r+258.5-250r+50

5407.5=450r

The real interest rate is 12%

Consumption Cd= 300+0.8(10000-20-0.5*10000)-200(0.12)

=300+0.8(4980)-238

=4046

Investment is given by;

Id =258.5-250(0.12)

=258.5-30

=228.5

At full employment, interest rates are lower while investment increases.