Question

In: Economics

Consider the following economy C = 0.85 (Y – T) + Ca ; Ca = 600...

Consider the following economy C = 0.85 (Y – T) + Ca ; Ca = 600 – 25 R ; T = 450 + 0.225 Y; IP = 1500 – 30 R ; G =1900; NX = 950 – 0.0625 Y. a) What are the values of the autonomous net export NXa and the autonomous taxes Ta (hint: see the formulas and compare) b) Compute the multiplier c) Derive the equation of the autonomous spending. d) Derive the equation of the IS curve e) Compute the values of the AP and YIS for R =3.25 f) Compute the values of the Ca, C, T, IP, and NX for income Y = 20,000 and R = 3.25 . Is this country a net importer or net exporter?

Solutions

Expert Solution

(a)

Autonomous net exports = 950 (the component independent of Y)

Ta = 450 (the component independent of Y)

(b)

Multiplier = 1 / [1 - MPC x (1 - t) + MPM] where MPC = 0.85, t = 0.225, MPM = 0.0625

Multiplier = 1 / [1 - 0.85(1 - 0.225) + 0.0625] = 1 / [1.0625 - (0.85 x 0.775)] = 1 / (1.0625 - 0.65875) = 1 / 0.40375 = 2.48

(c)

C = 0.85[Y - (450 + 0.225Y)] + 600 - 25R = 0.85(Y - 450 - 0.225Y) + 600 - 25R = 0.85(0.775Y - 450) + 600 - 25R

C = 0.65875Y - 382.5 + 600 - 25R

C = 0.65875Y + 217.5 - 25R

Total autonomous spending (Sa) = Autonomous consumption + Autonomous investment + G + Autonomous net exports

Sa = 217.5 - 25Y + 1500 - 30R + 1900 + 950

Sa = 4567.5 - 55R

(d)

In goods market equilibrium, Y = C + Ip + G + NX

Y = 0.65875Y + 217.5 - 25R + 1500 - 30R + 1900 + 950 - 0.0625Y

(1 + 0.0625 - 0.65875)Y = 4567.5 - 55R

0.40375Y = 4567.5 - 55R

Y = (4567.5 - 55R) / 0.40375 [Equation of IS curve]

NOTE: As per Answering Policy, 1st 4 parts are answered.

Rahul Sunny answered 1 year ago
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