Assume that equilibrium GDP (Y) is 5,000. Consumption is given by the equation C = 500 + 0.6 (Y - T). Taxes (T) are equal to 600. Government spending is equal to 1,000. Investment is given by the equation I = 2,160 - 100r, where r is the real interest rate in percent. In this case, the equilibrium
Real interest rate is:
A)5 percent.
B)8 percent.
C)10 percent.
D)13 percent.

Question

Quizplus · Accepted Answer

To find the equilibrium real interest rate, we need to find the level of investment that will bring aggregate demand (AD) equal to equilibrium GDP (Y).

AD = C + I + G 
where C = 500 + 0.6(Y - T) = 500 + 0.6(Y - 600) = 500 + 0.6Y - 360 = 140 + 0.6Y 
I = 2,160 - 100r 
G = 1,000 
Y = AD

Substituting the values: 
Y = 140 + 0.6Y + 2,160 - 100r + 1,000 
Y = 3,300 - 100r + 0.6Y

Simplifying and rearranging: 
0.4Y = 4,460 - 100r 
0.4(5,000) = 4,460 - 100r 
2,000 = 4,460 - 100r 
2,460 = 100r 
r = 24.6

Therefore, the equilibrium real interest rate is 24.6 percent, which is closest to option D (13 percent).

Assume That Equilibrium GDP (Y) Is 5,000