country of Utopia

an you please verify the answers below are correct, or else outline how to do any of the questions I’ve

done incorrectly?

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)

Where Y is the level of real GDP in the economy, DI denotes the disposable income in the economy, C represents the level of consumption in the economy, C0 is the autonomous consumption level, mpc denotes the marginal propensity to consume, I is the level of investment in the economy, I0 characterizes the autonomous investment, mpi is the marginal propensity to invest, G characterizes the level of government expenditure, X is the level of export from the country, M represents the amount of import in the country, M0 is the level of autonomous import, mpm denotes the marginal propensity to import, T is the amount of tax imposed in the country, and t represents the average tax rate in the economy.

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.

2. What is the value of the overall multiplier? Please show your calculations and explain the value.

Utopia’s overall multiplier value is calculated using the equation  1 / [1 – MPC (1 – t) – MPI + MPM (1 – t)]; and therefore, 3.63.