3 Consider a close economy supply and demand model Y denote

3. Consider a close economy supply and demand model. Y denote GDP, C denotes Consumption, I denotes Investment, r is the real rate of interest in percent, T denotes Taxes, and G stands for Government Spending. Suppose the aggregate production function of the economy is Y AK L with K denotes capital and L denotes labor input. Assume now K-900, L-900 and A-10. The variables in the model taking these forms: C-600 + 0.70,-7) 1 = 2000-100r T-500 G = 500 a. Calculate the national income. How much of the GDP goes into paying labor and capital input? (6 points) b. What are the real wage rate and real rental rate of the capital? (6 points) c. What are the equilibrium values of C, I, and r? (6 points) d. What are the values of private saving, public saving, and national saving? (6 points) e. If government spending rises to 1,000, what are the new equilibrium values of c, , and r? (6 points) f. What are the new equilibrium values of private saving, public saving, and national saving? (6 points)

Solution

Ans a)

Y=A(KL)^1/2=10(900*900)^9.5=10*900=9000

Cost function =wL+rK

Marginal Product of Labour=0.5A(K/L)^0.5 and Marginal Product of Capital=0.5A(L/K)^0.5

MPL=0.5*10*(K/L)^0.5=5 similarly MPK=5

We know at equilibrium MPL=w and MPK=r

Hence wL=5*900=$4500 gors into paying Labour and $9000-$4500=$4500 goes into paying capital

Ans b)

Real Wage Rate and Rental Rate of the Capital is as calculated above would be equal to 5 & 5 respectively

Ans c)

Equilibrium value of C

=600+0.7(9000-500)=600+0.7(8500)=$6550

Equilibrium value of r

Y=C+I+G=6550+2000-100r+500

9000=9050-100r

100r=50

r=0.5

Equilibrium I=2000-100(r)=2000-100(0.5)=$1950

Ans 1/d)

Private Saving=Y-T-C=9000-6550-500=$2050

Public Saving=T-G=500-500=0

National Savings=Private Savings+Public Savings=2550+0=$2050