Question

Consider an IS/LM model of an economy with the following equations

C = 220 + 0.75Yd

I = 165 – 10i

G bar = 490

TR bar= 300

T = .15Y

L = .2Y – 3i

M bar / P bar = 550

(a) Using the above data, derive the equation for the IS curve.

Answer 1

The equation for the IS curve in the given IS/LM model is derived by equating total planned spending (AE) to national income (Y). By solving the equation, the equilibrium level of output (Y) is calculated to be 3923.

Step-by-step explanation:

The IS curve represents the equilibrium condition in the goods market. To derive the equation for the IS curve, we equate total planned spending (aggregate expenditure) to national income (output or Y). The aggregate expenditure (AE) equals consumption (C), investment (I), government spending (G), and net exports (X-M).

Thus, the equation for the IS curve can be written as:

Y = C + I + G + (X - M)

Substituting the given values into the equation:

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

Simplifying the equation gives:

Y = 140 + 0.9(Y - 0.3Y) + 500 + 800 + 600 - 0.15Y

Solving for Y:

Y - 0.48Y = 2040

0.52Y = 2040

Y = 3923