Answer to Question #117029 in Macroeconomics for Konlan Roland

Question

Assignment 1
As a member of Ghana’s economic planning team for the 2020 fiscal year, answer the under
listed questions (a & b) given that:
Y = C + I + G + X - M....................................................... (1)
C = 0.8Yd............................................................................ (2)
M = 0.2Yd........................................................................... (3)
Yd = (1-t)Y.......................................................................... (4)
Additional information: t = 0.2Y (tax rate), G = 400 (government spending), X = 280
(exports) and I = 300 (investment)
(a) Solve for the equilibrium level of national income
(b) Assume a marginal propensity to import (my) of 0.3 and solve for the new
equilibrium national income

Answer 1

(a) Solve for the equilibrium level of national income

$$Y = C + I + G + X - M$$

But:

$C = 0.8Yd \\ M = 0.2Yd \\ Yd = (1-t)Y\\ t = 0.2\\ G = 400 \\ X = 280 \\ I = 300$

Therefore

$$Y = 0.8(1 - 0.2)Y + 300 + 400 + 280 - 0.2(1 - 0.2)Y\\ Y = 0.64Y + 980 - 0.16Y\\ 0.52Y = 980\\ Y^* = \dfrac{980}{0.52} = \color{red}{1,884.62}$$

(b) Assume a marginal propensity to import (my) of 0.3 and solve for the new

equilibrium national income

$$Y = 0.8(1 - 0.2)Y + 300 + 400 + 280 - 0.3(1 - 0.2)Y\\ Y = 0.64Y + 980 - 0.24Y\\ 0.6Y = 980 Y^* = \dfrac{980}{0.6} = \color{red}{1,633.33}$$