Problem1

Y= A*K^{0.5}*L^{0.5}

=15* 100^0.5*25^0.5

=15*10*5

=750

MPK= __Changein Y__ = 750-0/10-0 = 75

Changein K

MPL= Change in Y/ Change in L =750-0/5-0= 150

Y=A*K^0.3*L^0.3

=15*100^0.3*25^0.3

=15*3.981*2.626

=156.814

MPK= Change in Y/Change in K =156.814-750/3.981-10 = -593.185/-6.019 =98.55

MPL=Change in Y/Change in L = 156.814- 750/ 2.626 -5 = -593.185/-2.374 =249.86

MPKincreased from 75 to 98.55, MPL also increased from 150 to 249.86.However, Y decreased from 750 to 156.814.

BothK and L decreased in reference to part a. K decreased from 10 to3.981 which translates to a 60.19% decrease while L decreased from 5to 2.626 which translates to a 47.48% decrease.

Y=A*K^0.5*L^0.5

=15*120^0.5*30^0.5

=15*10.954*5.477

=900

MPK= Change in Y/ Change in K = 900 – 156.814/10.954-3.981=743.186/6.973 = 106.58

MPL= Change in Y/ Change in L = 900 – 156.814/5.477- 2.626 =743.186/2.851 = 260.68

MPKincreased from 75 to 106.58 while MPL increased from 150 to 260.68.Y, total production output also increased from 750 to 900.

BothK and L increased in reference to part a. K increased from 10 to10.954, which is a 9.54% increase while L increased from 5 to 5.477which is a 4.77% increase.

Problem2

Disposableincome, Y_{d}= Y – Tax + G_{s}

= 1200 -100 + 100

= 1200

Consumption= 80% of Y_{d}=1200*0.8

= 960

Savings= 1-Consumption Rate

=1-(0.8) = 0.2*1200 = 240

Ifthe Government spending increases by 20, then the following willoccur

Disposableincome = 1200 -100 +120

= 1220

Thex axis is investment y axis is the real interest rate. The demandcurve represents the investment demand while the supply curverepresents the savings. In this case the equilibriumsavings/investment will be at 4% since the savings will be equal tothe investment.

Savings= 1 – consumption

=0.2*1220=244

Savingsincreases by 1.667%. As a result, the equilibrium real interest ratedecreases as savings increases by the same percentage.

Problem3

MV= PY

600*V= 5*1000

V= 5*1000/600 = 8.333

Ifthe money supply goes up to 1200, P would also increase when thevelocity of money and the price level do not change.

MV= PY

1200*8.33= 1000P

P= 1200*8.333/1000 = 10

Ifthe money supply would be 1200 while P and Y are 5 and 1000 as frompart a, the velocity of money would decrease.

MV= PY

1200V= 5*1000

V= 5*1000/1200

=4.167