Consider a simple Keynesian economy described by the following equations:

𝐶
=
1800
+
0.6
(
𝑌
−
𝑇
)

𝐼
=
900

𝑇
=
100

𝐺
=
100

𝑋
=
50

What is the equilibrium level of output in this economy?

Question

Consider a simple Keynesian economy described by the following equations:

𝐶
=
1800
+
0.6
(
𝑌
−
𝑇
)

𝐼
=
900

𝑇
=
100

𝐺
=
100

𝑋
=
50

What is the equilibrium level of output in this economy?

BlackTom AI · Accepted Answer

We start by identifying the components of aggregate demand in this simple Keynesian model. The consumption function is C = 1800 + 0.6(Y − T). With T = 100, this becomes C = 1800 + 0.6(Y − 100) = 1800 + 0.6Y − 60 = 1740 + 0.6Y.

Investment I is given as 900, government spending G as 100, and exports X as 50.

The equilibrium condition in a small open economy with these components is:
Y = C + I + G + X.
Substitute C, I, G, X:
Y = (1740 + 0.6Y) + 900 + 100 + 50.
Compute the constant terms: 1740 + 900 + 100 + 50 = 2790. So the equation is:
Y = 2790 + 0.6Y.
Solve for Y by bringing terms together: Y − 0.6Y = 0.4Y = 2790, hence Y = 2790 / 0.4 = 6975.

Now, evaluate how each option fits the equilibrium condition:
- Option 2950: If Y = 2950, the left-hand side is 2950, while the right-hand side would be 2790 + 0.6×2950 = 2790 + 1770 = 4560. These do not match; the model would require Y to satisfy Y = 2790 + 0.6Y, which 2950 does not.
- Option 4975: Plugging Y = 4975 gives right-hand side 2790 + 0.6×4975 = 2790 + 2985 = 5775, not equal to 4975. So this fails the equilibrium condition.
- Option 5975: Right-hand side is 2790 + 0.6×5975 = 2790 + 3585 = 6375, not equal to 5975. Again, not an equilibrium.
- Option 6975: Right-hand side is 2790 + 0.6×6975 = 2790 + 4185 = 6975, which matches the left-hand side exactly. This option satisfies the equilibrium condition, while the others do not.

ECON10003_2025_SM1 Pre-Tutorial Quiz 3

Consider a simple Keynesian economy described by the following equations: 𝐶 = 1800 + 0.6 ( 𝑌 − 𝑇 ) 𝐼 = 900 𝑇 = 100 𝐺 = 100 𝑋 = 50 What is the equilibrium level of output in this economy?

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