I have done the first question but I would like help with the multiplier - see below in bold.

 

In the country of Utopia, the structure of the economy is described as the following:

 

Y = C + I + G + (X - M)

C = C0 + (mpc)(DI)

I = I0 + (mpi)(Y)

M = M0 + (mpm)(DI)

DI = Y - T

T = (t)(Y)

 

After extensive research, the economists in Utopia believe that the following values (all the dollar values are in number of millions) can be assigned to the structure of the economy,

C0 = $500; mpc = 0.8; I0 = $200; mpi = 0.2; G = $400; X = $300; M0 = $100; mpm = 0.1; and t = 0.25. The Utopian economists further believe that the level of potential GDP in the country is $4,000.

 

1. What is the demand side equilibrium level of real GDP in the country? Please show your calculations.

 

Y = C0 + [MPC x (Y - tY)] +I0 + (MPI x Y) + G + X - M0 - [MPM x (Y - tY)]

 

Y ($) = 500 + [0.8 x (Y - 0.25Y)] + 200 + 0.2Y + 400 + 300 - 100 - [0.1 x (Y - 0.25)]

 

Y = 500 + (0.8 x 0.75Y) + 200 + 0.2Y + 400 + 300 - 100 (0.1 x 0.75Y)

 

Y = 1,300 + 0.6Y + 0.2Y - 0.075Y

 

(1 + 0.075 - 0.8) = 1,300

 

0.275Y = 1,300

 

Y = $4,727

 

Under Scenario 1.  mpc=0.80, t=0.25, mpi=0.20, and mpm=0.10; What is the value of the overall multiplier? Please show your calculations and explain the value.

 

 

**This is what I have so far - I'm not sure if I'm on the right track.

 

Multiplier= 1/[1-(t x MPC) + MPI + MPM

                                (mpc(Y-tY)) + (mpi(Y)) + (mpm(Y-tY))

 

=1/[1 - (0.25 (0.8(Y - 0.8Y)+ (0.2(Y)) + (0.1(Y - 0.1Y)]

=1/[1 - (0.25 x 0.6) + 0.04 + 0.075]

=1/[1 - 0.15 + 0.04 + 0.075]

=1/0.965

=1.036

 

Overall multiplier= 1/1-MPC(1-t)-MPI+MPM(1-t)

Overall multiplier= 1/1-0.8(1-0.25)-0.2+0.1(1-0.25)

Overall multiplier= 1/1-0.8x0.75-0.2+0.1x0.75

1/0.275=3.64