Question

Consider the UNILUS economy in the long-run described by the following equations:

Y = C + I + G, Y = 5,000, G = 1,000, T = 1,000, C = 250 + 0.75(Y − T), I = 1,000 − 50r. C=100+b(Y-50-0.25Y);

Compute private saving, public saving, and national saving.

(5 Marks)

Find the equilibrium interest rate. (5 Marks)

Now suppose that G rises to 1,250. Compute private saving, public saving, and national savings. (5 Marks)

Find the new equilibrium i

Answer 1

$Part\space (a)$

$Y=C+I+G$

 $C=250+0.75(5000-1000) =250+3000=3250$

$5000=3250+1000-50r+1000$

$5000=5250-50r$

$50r=250$

$r=250\div50=5$

$I=1000-(50\times5)=1000-250=750$

Private savings.

$S=Y-C-G=I=5000-3250-1000=750$

Public savings

$Sg=T-G=1000-1000=0(Balanced\space budget)$

 $Sp=-250+(1-0.75)(Y-T)=-250+0.25(5000-1000)=-250+1000=750$

National savings

$S=Sp=Sg=750+0=750 (National)$

$Part (b)$

$S=I$

$750=1000-50r$

 

$r=5\%$

$Part (c)$

$Y=C+I+G$

$C=3250$

$5000=3250+1000-50r+1250$

 $5000=5500-50r$

 $50r=500$

$r=500\div50 =10$

 $I=1000-(50\times10)=1000-500=500$

 $S=Y-C-G=I=5000-3250-1250=500$

Public savings

 $Sg=T-G=1000-1250=-250 \space(Budget\space deficit)$

$Public$

Private savings

$Sp=Y-T-C=5000-1000-3250 =750$

$Sp=750\space (Private)$

 National savings

$S=Sp+Sg=750-250=500\space (National)$

 $Part\space (d)$

New equilibrium interest

$Y=C+I+G$

$5000=3250+1000−50r+1250$

$5000=5500-50r$

 $50r=500$

$r=500\div50 =10$

$r=10\%$