Part a) i: Calculate the equilibrium level of income and the multiplier in this model

Here's a step-by-step solution for Question 5:

Part a) i: Calculate the equilibrium level of income and the multiplier in this model

Given functions:
$C = 50 + 0.8Y^d$
$I = 70$
$G = 200$
$TR = 100$
$t = 0.20$

First, define disposable income ($Y^d$):

$$Y^d = Y - T + TR$$

Since $T = tY$:

$$Y^d = Y - tY + TR = (1-t)Y + TR$$

Substitute the given values for $t$ and $TR$:

$$$$