Question

Assume that an economy is characterized by the following equations: C = 0.5(Y - T) T = 150 I = 700 - 40 r G = 150 Ms/P = Md/P = 0.8 Y - 80 r Ms = 930 P = 1

Part 1: Write the equation for the IS curve, expressing Y as a function of r: (include a negative sign where appropriate) = Number Number

Answer 1

To find the equilibrium, we equate aggregate expenditure with national income, solve for Y, and adjust government spending to achieve a set potential GDP. Two methods can be used: direct substitution and utilizing the fiscal multiplier.

Step-by-step explanation:

To find the equilibrium for this economy, we set aggregate expenditure (AE) equal to national income (Y). We'll solve for Y after substituting T (taxes) into the AE equation.

The aggregate expenditure is given by:

AE = C + I + G + X - M

Where:

• C = Consumption = 400 + 0.85(Y - T)
• I = Investment = 300
• G = Government spending = Assumed to be 200 initially for equilibrium calculation
• X = Exports = 500
• M = Imports = 0.1(Y - T)
• T = Taxes = 0.25Y

Plugging in the values:

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

AE = 400 + 0.85(0.75Y) + 300 + 200 + 500 - 0.1(0.75Y)

This simplifies to:

AE = 1400 + 0.6375Y - 0.075Y

AE = 1400 + 0.5625Y

Setting AE = Y for equilibrium:

Y = 1400 + 0.5625Y

This simplifies to Y/0.4375 = 1400, solving for Y gives us the equilibrium income.

To achieve a potential GDP of 3,500, we need to adjust G. First method is direct substitution, and the second is using the multiplier.

For the multiplier method, firstly calculate the multiplier (k) which is 1/(1- MPC(1-Tax rate)).

k = 1 / (1 - 0.85(1 - 0.25))

Then, calculate the increase in G needed to reach the potential GDP of 3,500 by using the formula ΔY = k * ΔG.