Question

An economy shows the following functions,

C=200+0.75(Y−T)
T=80+0.2Y
I=200−2000i
G=N$300
Mt =0.5Y
Mz =200−250i
Ms=N$400
​ Compute the equilibrium income and rate of interest?

Answer 1

To find the equilibrium income in an economy, we set aggregate expenditure equal to output and solve for national income. To adjust government spending to achieve a potential GDP of 3,500, we could either solve directly for G or use a multiplier approach.

Step-by-step explanation:

The question asks to find the equilibrium income for an economy given certain economic functions and then determine the change in government spending needed to achieve a potential GDP of 3,500. The equilibrium is where aggregate expenditure (AE) is equal to output (Y), meaning that AE = C + I + G + X - M.

To find the equilibrium income, set Y = AE, which translates to:

Y = 400 + 0.85(Y - 0.25Y) + 300 + 200 + 500 - 0.1(Y - 0.25Y)

Simplify this to find Y, the national income at equilibrium.

To find the change in government spending to achieve a potential GDP of 3,500, we first plug 3,500 into the equations to solve for G, and secondly, we calculate the multiplier to figure it out that way.

For the multiplier method:

The multiplier is calculated as 1/(1 - MPC(1 - tax rate) + MPM), where MPC is the marginal propensity to consume, and MPM is the marginal propensity to import. With this, we can determine the change in G needed to reach the full employment output of 3,500.