C0 = $500; mpc = 0.8; I0 = $200; mpi = 0.2; G = $400; X = $300; M0 = $100; mpm =

Question

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.

The country of Utopia is probably experiencing a recessionary pressure in its economy now. The economists are suspecting that, since the latest estimates of mpc, mpi, and mpm indicate that their estimated values have gone down to 0.65, 0.15, and 0.05 respectively.

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

Is the overall Utopian economy now in equilibrium? Elaborate your answer.

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

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

Explanation / Answer

Answer:

(1) In demand side equilibrium,

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 - 0.25Y)]

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)Y = 1,300

0.275Y = 1,300

Y = $4,727

(2) Since demand-side equilibrium GDP is higher than potential GDP, the economy is not in equilibrium.

(3) Since demand-side equilibrium GDP is higher than potential GDP, price level will be higher than at potential GDP level, causing an inflationary gap. In the long run, higher price level will increase the cost of inputs, which will make firms lower output, reducing aggregate supply. Therefore, short-run aggregate supply will fall, which will further increase the price level but will restore the demand-side equilibrium GDP to the potential GDP of $4,000.

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

= 1 / [1 - (0.25 x 0.8) + 0.2 + 0.1] = 1 / (1 - 0.2 + 0.2 + 0.1) = 1 / 1.1

= 0.91

This signifies that as consumption, investment and import demands each increases by 1 unit, total output of the economy will increase by 0.91 units.

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