Answer to Question #82915 in Macroeconomics for marion kileges

Question

15.10.18, 21:21
Given the following equations for a certain economy: Y = C + I + G + X (Income identity) C =100 +0.9Yd (Consumption function) I = 200 –500r (Investment function) X = 100 – 0.12Y –500r (Net export) G = 200 (Government purchases) T = 0.2 (Tax rate) L = Y-100r (Real money demand) M = 800 (Real money supply).
Derive equations for IS and LM curves . Determine the r and y pair at which the two markets are clearing iii) Compute the values of C, I, X and L

Answer 1

Y = C + I + G + X, C = 100 + 0.9Yd, I = 200 – 500r, X = 100 – 0.12Y – 500R, G = 200, t = 0.2, M = 800, L = Y - 100r.

1) What is the IS curve?

Substitute C, I and X in the income identity: Y = 100 + 0.9(Y - 0.2Y) + 200 – 500r + 200 + 100 - 0.12Y – 500r,

0.4Y = 600 – 1000r,

IS curve: Y = 1500 – 2500r.

2) What is the LM curve?

Derive from the equation for money demand:

M = (0.8Y - 2000r),

800 = 0.8Y - 2000r,

0.8Y = 800 + 2000r,

So, LM curve: Y = 1000 + 2500r.

3) What are the values of Y and r if spending balance occurs and the demand for money equals the supply for money?

Y (from IS curve) = Y (from LM curve) = 1500 – 2500r = 1000 + 2500r,

500 = 500r, r = 0.10 (10%)

Substitute R into IS or LM: Y = 1250

4) What are the values of consumption, investment and net exports?

C = 1000, I = 150, X = 100.