PLEASE DOUBLE-CHECK THE NUMBERS IN THE GIVEN QUESTION! In the country of Utopia,

Question

PLEASE DOUBLE-CHECK THE NUMBERS IN THE GIVEN QUESTION!

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

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 = 0.65; I0 = $200; mpi = 0.15; G = $400; X = $300; M0 = $100; mpm = 0.05; 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. Is the overall Utopian economy now in equilibrium? Elaborate your answer.

3. If the economy is not in equilibrium now, what will happen eventually? Explain your answer.

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

Y = C + I + G + (X – M) C = C0 + (mpc)(DI) I = I0 + (mpi)(Y) M = M0 + (mpm)(DI) DI = Y – T T = (t)(Y)

Explanation / Answer

Consider the given problem here the consumption function is given by.

=> C = C0 + MPC*(Y-T) = 500 + 0.65*(Y-0.25*Y) = 500 + 0.65*0.75*Y = 500 + 0.49*Y.

The Investment function is given by, “I = I0+MPI*Y = 200+0.15*Y.

The import function is given by, “M=M0+MPM*Y=100+0.05*Y.

So, at the equilibrium the following condition must hold.

=> Y=C+I+G+X-M = (500+0.49*Y)+(200+0.15*Y)+400+300-(100+0.05*Y).

=> Y = 1,300+0.59*Y, => 0.41*Y = 1,300, => Y=3,170.73. SO, here the goods market equilibrium is “Y*=3,170.73”.

2).

As the potential GDP of “Utopia” is “4,000 > 3,170.73”, => the economy is not in equilibrium. Since the potential GDP of that economy is more than the actual equilibrium GDP.

3).

So, here for “Y=4,000”, the total demand for that economy is “C+I+G+X-M=1,300+0.59*Y”, => 3,660 < 4,000.

So, the “AD < Y”, => the level of inventory is a positive, => the production will decreases until the equilibrium GDP will reach.

4).

So, at the equilibrium the following condition will hold.

=> Y=C+I+G+X-M=1,300+0.59*Y, => the value of the multiplier is “1/1-0.59 = 2.44”.

So, here the value of the multiplier is “2.44”.

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