(c)
Y = C + I + G0
Y = b(Y - T0) + hF0 + g0 - g1r0 + G0
Y = bY - bT0 + hF0 + g0 - g1r0 + G0
(1 - b)Y = hF0 + g0 - g1r0 + G0 - bT0
Y = (hF0 + g0 - g1r0 + G0 - bT0) / (1 - b)
Impact of change in r0 on Y = dY/dr0 = -g1 / (1 - b)
Since g1 > 0 and 0 < b < 1,
(-g1) < 0 and (1 - b) > 0. Therefore
(dY/dr0) < 0.
As interest rate increases (decreases), output decreases (increases).
(d)
MPC = b = 0.8
(i) Tax multiplier = -b / (1 - b) = -0.8 / (1 - 0.8) = -0.8 / 0.2 = -4
When T increases by $10 billion, Y decreases by ($10 billion x 4) = $40 billion.
(ii) Government spending multiplier = 1 / (1 - b) = 1 / (1 - 0.8) = 1 / 0.2 = 5
When G increases by $10 billion, Y increases by ($10 billion x 5) = $50 billion.
(iii) When both T and G increases by $10 billion,
Net increase in Y = Decrease in Y due to increase in T + Increase in Y due to increase in G = $(-40 + 50) billion = $10 billion
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