Question 1.
Question 2.
Question 3.
i)
Y = C+I+G
𝐶 = 𝐶0 + 𝐶1 (𝑌 − 𝑇)
𝐼 = 𝑋0 − 𝑋1 𝑖
𝑌 = 𝐶0 + 𝐶1 (𝑌 − 𝑇) + 𝑋0 − 𝑋1 𝑖 + 𝐺
𝑌 = 𝐶0 + 𝐶1 𝑌 − 𝐶1 𝑇 + 𝑋0 − 𝑋1 𝑖 + 𝐺
𝑌(1 − 𝐶1 ) = 𝐶0 − 𝐶1 𝑇 + 𝑋0 − 𝑋1 𝑖 + 𝐺
𝑌=
1
(𝐶 − 𝐶1 𝑇 + 𝑋0 − 𝑋1 𝑖 + 𝐺)
1 − 𝐶1 0
ii)
1000 =
1
[150 − 0.5 ∗ 100 + 400 + 10,000𝑖 + 200]
1 − 0.5
Solve for i (interest rate)
I = 2%
iii)
Original equilibrium =
Y = 1,000
C = 150 + 0.5(1000-100) = 600
I = 400-10000(0.02) = 200
New equilibrium
Y = 900
C = 150 + 0.5 (900-200) = 500
I = 400 – 10000(0.02) = 200
(short cut)
(Change in Y = (-C1/1-C1) * change in T
= -0.5/1-0.5) * 100 = -100
iv)
𝜋 − 𝜋 𝑒 = 0.0001 ∗ (𝑌 − 𝑌𝑛 )
𝜋 − 𝜋 𝑒 = 0.0001 ∗ (900 − 1000)
𝜋 − 𝜋 𝑒 = 0.0001 ∗ (𝑌 − 𝑌𝑛 )
𝜋 − 𝜋 𝑒 = −0.01
𝑖 = 0.02 + 0.5(𝜋 − 𝜋̅)
𝑖 = 0.02 + 0.5(−0.01)
𝑖 = 0.015
𝑌=
1
[150 − 0.5 ∗ 100 + 400 + 10,000 ∗ 0.015 + 200]
1 − 0.5
𝑌 = 1000
C = 150 + 0.5(1000-200) = 550
I = 400 – 10,000(0.015) = 250
Question 4.
i)
Yes it does exhibit CTRS.
𝑌 = √𝐾√𝐴𝑁
ii)
𝑌 = √𝐴√𝐾√𝑁
Divide both sides by N
𝑌 √𝐴√𝐾√𝑁 √𝑁
=
∗
𝑁
𝑁
√𝑁
𝑌
𝐾
= √𝐴√
𝑁
𝑁